^773 A?? /?J0 Cornell University Law Library. THE GIFT OF ^:.e-c-cy ZtYo-,^^ Q,t^JL^ Date / ?^ r / Z-? 3 . Cornell University Library HG 8773.M99 1920 Educational leaflets 3 1924 024 852 679 //^^ \\ \^'^^, ^/ , -^ 'Hv V'- : The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924024852679 Educational Leaflets Bevised November, 19S0 TheI Mutual Life INSURANCE Company of New York /3> /^^/s-q" copyright 1915 and i92o, by The Mutual Life Insurance Company OF New York INTRODUCTION THE Educational Leaflets of The Mutual Life Insur- ance Company of New York were first issued serially, in the year 1903, and afterwards bound in a single volume. This revision of the work is published primarily for the instruction of agents of the Company just entering upon their career as solicitors. The aim has been to adapt the language used to the comprehen- sion of the beginner ; but the decidedly primary character of the matter treated of in the first few pages will grad- ually give place to more technical discussions. Every new term will be printed in italics when it first appears and will be defined at once, although fuller explanations may come later. Several institutions have been recently established in this country for the purpose of teaching insurance by correspondence, and three or four universities have al- ready included in their curricula a course in life insur- ance, while others provide frequent lectures on the sub- ject. Those just entering upon the work of life insur- ance salesmanship have here the opportunity to secure, without expense, a thorough course of instruction in the principles of the business, while at the same time ac- quiring a practical knowledge of the work and making their own living by soliciting insurance imder the direc- tion of the Manager. George T. Dexter, Second Vice President. TABLE OF CONTENTS CHAPTER PAGE I. Origin of Life Insurance, Its Character AND Object 5 II. The Computation of the Premium 12 III. The Life Annuity 20 IV. The Different Kinds of Policies 30 V. Proving the Adequacy of the Net Premium 110 VI. Observations on the Reserve 52 VII. The Amount at Risk 66 VIII. The Loading 76 IX. Gains or Savings in Life Insurance .... 95 IX. 'Natural Premium Insurance 116 XL Sundry Topics 129 XII. Disability and Double Indemnity 137 CHAPTER I ORIGIN OF LIFE INSURANCE, ITS CHARACTER AND OBJECT DERVADING all nature we find the fundamental ■■■ principle of life insurance, help for the helpless. The birds of the air provide food and shelter for their nestlings. The beasts of the field minister to the wants of their helpless ofi^spring. Both savage and civilized man yield to the promptings of this universal instinct in caring diligently for their little ones and for their dependents. To supply the immediate needs of these is easy enough for the young and the strong, but the true man would provide also for their future necessities, when, by reason of ill health or old age, he is no longer able to care for them through his personal efforts. This, too, is a simple problem for the industrious and the thrifty. One has only to lay aside regularly and to invest safely a portion of his income to have in a few years, or at most in old age, a sufficient dependence for his family. But suppose death were to intervene before this end has been attained. To provide for this contingency modern Life Insurance has been devised. In its sim- plest form, a number of persons combine to create a common fund to be drawn upon in providing for the families of deceased members of the organization. Every member of the organization has a voice in its management, and each has a personal interest in the accumulated funds of the society in proportion to the amount he has contributed thereto. Mutual Companies Such an organization is appropriately termed a Mutual Life Insurance Company. The contract which is made by the company with the member^ fixing the amount to be paid in the event of his death, is called a Life Insurance Policy, and the person to whom the amount is payable is termed the Beneficiary. The contract or policy also stipulates the amount which the member is to contribute to the common fund, and defines his rights and privileges in other respects. The person holding such a contract is termed the Policy-holder. The contribution to be made by him to the common fund as stipulated in the policy, is termed the Premium, and this is usually payable yearly, or in half-yearly or quarterly instalments. The Mutual -Life Insurance Company of New York is precisely such an organization as that described above. It is purely mutual, owned and controlled by the policy-holders, and is directly managed by a board of trustees who are chosen by the policy-holders. Every member of The Mutual Life, who has held a policy for one year or more, is entitled to one vote which may be forwarded by mail or cast in person or by proxy. At a recent election, when matters of special importance were under consideration, more than .300,000 policy- holders expressed their choice for trustees at the polls, nearly, ninety per cent, of whom cast their votes directly by ballot, in most cases forwarded by mail. Stock Companies There is another class of companies known as Stock Companies, which are owned and controlled by 6 a limited number of individuals termed Stockholders, whose respective shares or interests are represented and defined by a written instrument termed a Certificate of Stock. These shares or certificates of stock may be sold or transferred at the will of the holder, and the control of the company will be changed accordingly. The stockholders of such an organization receive a portion or all of the savings or so-caUed "profits" of the business, and the officers who manage its affairs are chosen from their number. When the policy-holders of such a com- pany share with the stockholders in the gains, or savings, the organization is termed a Mixed Company. In The Mutual Life Insurance Company of New York there are no stockholders, and no officer or trustee has any proprietary interest in the organization or receives any perquisites or profits by reason of his position, other than a reasonable compensation for services rendered. His interest in the accumulated funds of the Company is no more and no less than that of any other policy-holder, in proportion to the insur- ance carried by him. In the; control of the Company he has but a single vote, the same as any other policy- holder, irrespective of the number of policies or the amount of insurance carried by him. The Mutual Life of New York is the oldest active company in America, having commenced business in February, 1843. It is also one of the strongest financial institutions in the world. As before stated, its assets are the property of the policy-holders, the interest of each being proportionate to the amount contributed by him thereto. Elementary Principles Let us now consider some of the underlying principles of scientific life insurance. It is perhaps not essential to the solicitor's success that he be proficient in all the technicalities of the science, but there are some things which he must knowj and he wiU the more readily comprehend and acquire these if he under- stands at least the elementary principles upon which the business rests. To illustrate the subject we shall treat first of the life insurance contract in its commonest form, the Ordinary Life .Policy. In the case of this contract the premium is to be paid every year during the life of the insured, the insurance amount being payable at death. Before entering into a contract of this kind it becomes necessary to fix the amount of the premium, which should be large enough to enable the company to meet the necessary expense of conducting the business and to accumulate a fund sufficient to pay the amount of the policy when the same matures by the death of the insured. Making the Premium If it were known to a certainty just how long the policy-holder would live, say, for example, twenty years, anyone could compute the amount of the necessary premium. Let us suppose, for illustration, that the face of the policy is $1,000, that the policy- holder will live just twenty years, and, to simplify the problem, that there will be no expenses connected with the business and no interest earned. In that event, a payment of $50 a year for twenty years would 8 amount to just $1,000, and would be therefore the yearly premium required. Let us assume, however, that while the business is still conducted without expense, the premiums are all to be invested at interest from date of payment. We do not know to a certainty what rate of interest can be earned during the whole period, and we shall therefore assume a rate that we can safely depend upon, say three per cent. Any schoolboy will solve the problem now, and tell us that a yearly payment of $86.13 invested at three per cent, compound interest will amount to $1,000 in twenty years, and that this is therefore the yearly premium required. Observe now, that if it were certain that the policy-holder would live just twenty years, and that his premiums would earn just three per cent, interest and that the business could be conducted without expense, the necessary premium would be $36.13. But there ivill be expenses, and there are certain other contin- gencies that should be provided for, such, for example, as a loss of invested funds, or a failure to earn the full amount of three per cent, interest. To meet these expenses and contingencies some- thing should be added to the premium. Let us estimate as sufficient for this purpose the sum of $7. This will make our gross yearly premium $43.13, the original payment ($36.13) being the Net Premium, while the amount added thereto for expenses, etc., ($7), is termed the Loading. The Net Premium is the amount which is mathe- matically necessary for the creation of a fund sufficient to enable the Company to pay the policy in full at maturity. The Loading is the amount added to the net premium to provide for expenses and contingencies. The net premium and loading combined make up the Gross Premium, or the total sum to be paid yearly by the insured. The Mortality Table If it were known to a certainty how long any man would live, the business of life insurance would be reduced to a very simple basis — would in fact become merely a commercial transaction of saving and lending. Although it is impossible to predict in advance the length of any individual life, as in the illustration given above, there is a law governing the mortality of the race by which we may calculate the average lifetime of a large number of persons of a given age. We cannot predict in what year the particular individual will die, but we may determine with approximate accuracy how many out of a large number will die at any specified age. By means of this law it becomes possible to com- pute the premium necessary to be charged at any given age with almost as much exactness as in the example given, in which the length of life remaining to the individual was assumed to be just twenty years. If you will study the mortuary records of any community and note the various ages at which the several deaths have occurred, you wiU find the yearly mortality governed by a law which is practically invariable. Let us suppose for example that your observations cover a period of time suflficient to include the history of 100,000 lives. Of these you will find a 10 certain number dying at age thirty, a higher death rate at age forty, and so on at the various ages, the extreme limit of life reached by anyone being in the neighbor- hood of one hundred years. The mortuary records of other communities, where conditions were practically the same, would give approximately the same results — ^the same number of deaths at each age in 100,000 born. The variation would not be great, and the larger the number of lives under observation the nearer the number of deaths at the several ages by the several records would approach to uniformity. In this manner Mortality Tables have been con- structed which show how many in any large number of persons born, or starting at a certain age, will live to age thirty, how many to age forty, how many to any other age, and likewise the number that will die at each age, with the average lifetime remaining to those still alive. The American Experience Table of Mortality was constructed about the year 1861 by Sheppard Homans, the then Actuary of The Mutual Life Insurance Com- pany of New York, and was based mainly upon the history of lives insured in that company. The table be- gins with 100,000 persons at age ten and fixes the Limit of Life at ninety-six years — ^the attained age at which the last three of the original 100,000 are assumed to die. The premium rates of practically all American companies are based upon this table. Fuller information regarding this and other mortality tables will be given in a later chapter. In the next chapter we shall show how the neces- sary premium in practical life insurance is determined with the aid of the mortality table. u CHAPTER II THE COMPUTATION OF THE PREMIUM WE propose now to explain the computation of the life insurance premium. This is information which, in one sense, is not essential to the success of the solici- tor, since he finds his premiums ready-made in his rate book; but a knowledge of the principle involved in the computation is essential to a perfect comprehension of other matters which he must know. We present for reference on page 13 the Ameri- can Experience Table of Mortality defined in the pre- vious chapter (page 11). As heretofore explained, the table begins with 100,000 lives, starting with the age of ten years. Of these, 81,822 will stiU be living at the age of thirty-five of whom 732 will die during the year. This will leave 81,090 still living at the beginning of the next year at age thirty-six, while 737 of this number wiU die in the ensuing twelve months. At age fifty-six there will be living 63,364 of the original number of these, 1,260 will die during the year. In the same way the table shows how many of the original 100,000 are living at each age from ten years on, and how many will die in each year thereafter until the last three, who have lived to attain the age of ninety-five, are assiuned to pass away during or at the end of that year, none living beyond the attained age of ninety-six. A Hypothetical Company Let us suppose, now, that we have crganized a life insurance company composed of 63,364 persons, each American Experience Table of Mortality Number Deatlis Dentli- Expecta- ffninber Ocatbs DeatU- Expecta- Age Uviiig; Kich rate tion of Age Each rate tion of Tear Per 1,000 life living Tear Per 1,000 life 10 100,000 749 7.49 48.72 B3 66,797 1,091 16.33 18.79 11 99,251 746 7.52 48.08 B4 65,706 1,143 17.40 18.09 13 98,505 743 7.54 47.45 SB 64,663 1,199 18.67 17.40 IS 97.762 740 7.57 46.80 B6 63.364 1.260 19.88 16.72 14 97,022 787 7.60 46.16 B7 62,104 1,325 21.33 16.05 IS 96,285 785 7.63 45.50 B8 60,779 1,394 22.94 15.39 le 95,550 732 7.66 44.85 S9 59,385 1,468 24.72 14.74 17 94,818 729 7.69 44.19 60 57,917 1,546 26.69 14.10 18 94,089 727 7.73 43.53 61 66,871 1,628 28.88 13.47 19 93,362 725 7.76 42.87 63 54,743 1,713 31.29 12.86 30 92,637 723 7.80 42.20 63 63,030 1,800 33.94 12.26 31 91,914 722 7.85 41.63 64 61,230 1,889 36.87 11.67 33 91,192 721 7.91 40.85 6B 49,341 1,980 40.13 11.10 3S 90,471 720 7.96 40.17 66 47,861 2,070 43.71 10.54 34 89,751 719 8.01 39.49 67 45,291 2,158 47.66 10.00 3B 89,032 718 8.06 38.81 68 43,133 2,243 62.00 9.47 36 88,314 718 8.13 38.12 69 40,890 2,321 66.76 8.97 37 87,596 718 8.20 37.43 70 38,569 2,396 61.99 8.48 38 86,878 718 8.26 86.78 71 36,178 2,448 67.66 8.00 39 86,160 719 8.34 86.03 73 33,730 2,487 73.73 7.65 SO 85,441 720 8.43 35.33 73 31,243 2,506 80.18 7.11 31 84,721 721 8.61 34.63 74 28,738 2,601 87.03 6.68 S3 84,000 723 8 61 33.92 7B 26,237 2,476 94.37 6.27 S3 83,277 726 8.72 33.21 76 23,761 2,431 102.31 5.88 34 82,551 729 8.83 32.60 77 21,330 2,369 111.06 5.49 SB 81,822 732 8.96 31.78 78 18,961 2,291 120.83 5.11 36 81,090 737 9.09 31.07 79 16,670 2,196 131.73 4.74 37 80,363 742 9.23 30.35 80 14,474 2,091 144.47 5.39 38 79,611 749 9.41 29.62 81 12,383 1,964 158.60 4.06 39 78,862 766 9.59 28.90 83 10,419 1,816 174.30 3.71 40 78,106 765 9.79 28.18 83 8,603 1,648 191.66 8.39 41 77,341 774 10.01 27.45 84 6,956 1,470 ■211.36 3.08 4» 76,567 786 10.25 26.72 SB 5,485 1,292 235.55 2.77 43 75,782 797 10.62 26.00 86 4,193 1,114 265.68 2.47 44 74,985 812 10.83 25.27 87 3,079 933 303.02 2.18 4B 74,173 828 11.16 24.54 88 2,146 744 346.69 1.91 46 73,345 848 11.56 23.81 89 1,402 666 396.86 1.66 47 72,497 870 12.00 23.08 90 847 385 454.54 1.42 48 71,627 896 12.51 22.36 91 462 246 532.47 1.19 49 70,731 927 13.11 21.63 93 216 137 634.26 .98 BO 69,804 962 18.78 20.91 93 79 68 734.18 .80 Bl 68,842 1,001 14.54 20.20 94 21 18 857.14 .64 B3 67,841 1,044 16.39 19.49 9B 3 3 1000.00 .50 fifty-six years of age, and each insured for $1,000 pay- able at death. We take the figures 63,364 as our total membership merely for convenience sake, that being the number of persons still living at age fifty-six as given in 13 the mortality table. If we can show what premium it would be necessary to collect at age fifty-six, we can by the same process determine the required premium for any other age. It is also for convenience sake — ^to make the problem as simple as possible — ^that we assume that each member of our hypothetical company wiU maintain his membership during his entire lifetime, and that no new members wiU be added after the date of organization. Withdrawals and additions have no effect upon the amount of premium which it is necessary to collect to en- able the company to fulfill its contracts, all of which wiU be more fully explained hereafter. In the same way, al- though members may die at any time during the year, and the practice is to pay losses as soon as possible after death, yet, theoretically, these losses are payable at the end of the year, and our computations are made on that basis. The practice of paying claims before the end of the year merely involves the loss of a little interest which the companies more than make Up from other sources. We have then 63,364 persons insured, each of whom is to receive at death $1,000. This will make a total ultimately to be paid of $63,364,000. This enormous sum is to come entirely from the premiums that are to be paid by the original 63,364 members and the interest which those premiums will earn. The prob- lem now is to determine how large a premium each mem- ber must pay in order to create a fund which, with the interest to be earned, will be suflScient for this purpose. The First Step If we could start out on the day of organization with this fund complete — ^money enough in hand to pay every one of these policies in fuU as it matures by the 14 death of the member, the business would be greatly simplified. We should then have no occasion to worry regarding future withdrawals and collections, nor con- cerning the ability of the company to pay the last man in full, even without the influx of "new blood" — the addition of new members. This is in fact the essential principle involved in so-called "old line" life insurance — the collection of a premium large enough to maintain a fund sufficient for the ultimate payment of all existing policies without the necessity of adding new members. The first step to be taken then, is to ascertain how large a total fund we ought to have on hand at once for the accomplishment of this end. Turn now to the figures of the mortality table given above. We have 6S,S64 members, all of whom, according to the table, will die within the next forty years. We do not know when any particular one will die, nor how long any individual member will live. The amount that each member should pay, therefore, cannot be determined by means of a computation based upon a single life, as in the example heretofore given on page 8. But if we do not know how long any one individual will live, the mortality table tells us how long certain groups of members wiU live. For example, we see by the table that, of the members of our company living at age fifty- six, 1,260 wiU live not more than one year; that 1,980 will die in the tenth year; 1,292 in the thirtieth year, etc. ; and that the last three will live not to exceed forty years, to age ninety-six. We must base our computations then, upon the aggregate number of lives — the length of time the members will live as a body, as shown in the case of these several groups. 15 Referring to the table, for example, we see that 1,980 members will die during or at the end of the tenth year, at the attained age of sixty-six. We know there- fore that we shall need $1,980,000 at the end of the tenth year in order to pay $1,000 for each death. We do not need that amount on hand to-day, for our funds will earn some interest during the next ten years. We require therefore, at this time, only a sum suflScient to amount to $1,980,000 in ten years, at such rate of inter- est as can be earned. The Interest Rate in Life Insurance Here again we do not know what amount of interest will be earned. A rate of five or six per cent., or a little more, may be had in some cases, but as a rule the rate will be less and we shall also have a small amount of idle funds on hand at times. Above aU, a safe investment is to be preferred to large earnings, and it is a rule of finance that, the higher the ratio of profit the poorer the security. It follows that in our haste to gain large earn- ings, the principal itself might be lost, thus defeating the purpose of our organization. That must not be. In life insurance, first of all, the funds must be safe. It would be no misfortune to have an accumulation larger than needed, but an insufjicieni fund would mean that widows and orphans must suffer. We must therefore assume a rate of interest such as the safest possible class of securi- ties may be depended upon to earn, not now merely but for many years to come. On that basis The Mutual Life Insurance Company of New York assumes that its in- vested funds wiU earn on the average not less than three 16 per cent. That they will earn a higher rate than that for many years may be conceded as certain. If it were not certain, less might be earned, for the exact rate cannot be determined in advance. The present worth' of $1,980,000 due in ten years is $1,473,305.94, that being the sum which at three per cent, interest will amount to $1,980,000 in ten years. If we have that amount on hand to-day and can safely in- vest it at three per cent, interest, it is mathematically certain that we shall be able to pay the death claims of the tenth year. Turning again to the mortality table, we see that in the twenty-fifth year, at age eighty, there will be 2,091 deaths calling for the payment at the end of that year of $2,091,000. The present worth of that sum at three per cent, is $998,673.25. If then we have that much on hand to-day for use in the twenty-fifth year and it can be safely invested at three per cent, interest, it is mathematically certain that we shall be able again to pay the death claims of that year. Or take the 1,260 deaths of the first year. These claims, payable at the end of the year, call for the sum of $1,260,000 and the present worth of that amount due in one year is $1,223,300.98. Is it not clear that we can in like manner deter- mine from the mortality table what our losses will be for each year, even to the last or fortieth year, when the death claims will amount to $3,000? And can we not thus find the present worth of the amounts which will be needed in each and every year to pay all the claims of such years until the last three members pass away in the fortieth year of their membership, at the attained age 17 of ninety-six? Nine hundred and nineteen dollars and sixty-seven cents on hand to-day will amount in forty years, at three per cent, interest, to $3,000, or sufficient to pay in full the policies of the last three members of our company. The Total Insurance Fund In the following table, we have arranged in columns the death claims of the first, tenth, twenty-fifth, and fortieth years as given above: Age Attained Begin- Year Age Death Present Wortli ning of End of of Claims Year Year 56 First year 57 $1,260,000 $1,223,300.98 * * * -x- * 65 Tenth year 66 1,980,000 1,473,305.94 * * * * * 80 Twenty-fifth year 81 2,091,000 998,673.25 * * * * * 95 Fortieth year 96 3,000 919.67 Totals $63,364,000 $39,360,583.39 The stars take the place of the other years as given in the complete mortality table for the several ages from fifty-six on, the figures for which may be determined in the same manner. You may work it out for yourself. Note the number of deaths in each year according to the mor- tality table until the last three members die. Find the present worth of the amount required in each year for 18 payment of claims, and place in the column headed present worth. Find the total of these present worths, and you wiU get the sum of $39,860,583.39. With this amount on hand to-day, on the assump- tion that the same will earn three per cent, interest, we shall have funds sufficient for the payment of every death claim that can possibly occur, according to the mortality table, in any year until the last three members die, in the ninety-sixth year of their age. That sum divided by 63,364, the number originally insured in our hypothetical company, gives $621.182113. In other words, if each member of our company will pay in cash the sum of $621.18. ., we shall have at date of organization a total of $39,360,583.39, or sufficient to pay every existing policy in full as the several deaths occur. This $621.18 is termed the Net Single Premium, and is the net amount, without provision for expenses, which a man at age fifty-six should pay for a full paid policy of $1,000. The net single premium having been deposited, no further payments would ever be required, but most men would find it inconvenient to pay for their life insur- ance in a single sum. By means, however, of an equally simple mathematical process we may apportion that net single premium into equivalent yearly payments to be made by the insured during life. Before entering into an explanation of that process, it becomes necessary to explain the meaning of several new terms which will be taken up in the next chapter. 19 CHAPTER III THE LIFE ANNUITY IT is our purpose to show now how the net single premium may be apportioned into small yearly pay- ments, to be made during life, which shall be the exact mathematical equivalent of the former. To understand the process, one must know something of annuities. An Annuity is a specific sum of money to be paid yearly to some designated person. The one to whom the money is to be paid is termed the Annuitant. If the payment is to be made every year until the annuitant dies, it is termed a Life Annuity. For example, a life insurance company or other financial institution, in con- sideration of the payment to it of a specified amount, say $1,000, will enter into a contract to pay a desig- nated annuitant a stated sum, say $100, on a specified day in every year so long as the annuitant continues to live. The latter may live to draw his annuity for many years, until he has received in the aggregate several times the original amount paid by him, or he may die after having collected but a single payment, or even earlier. In either case the contract expires and the annuity terminates with the death of the annuitant. The amount of yearly income or annuity which can be purchased with $1,000 will depend of course upon the age of the annuitant. That sum will buy a larger income for a man of seventy than for one of rifty- six, for the reason that the former has, on the average, a much shorter time yet to live. The net cost of an 20 annuity, that is, the net amount to be paid therefor in one sum, and which is termed the Value of the Annuity, is not a matter of estimate but, like the life insurance premium, is determined by mathematical computation, based upon the mortality table. The process is quite as simple as the computation of the single premium, and exactly similar. Computing the Value or the Annuity Let us undertake, for example, to determine the net amount which a company should charge in a single sum for a life annuity of $1 to be paid to every one of 63,364 persons, all of the age of fifty-six years, the first payment to be made immediately on the execution of the contract. The figures named will be recognized as the number of persons still living at age fifty-six out of 100,000 starting at age ten, as given in the American Experience Table of Mortality, page 13, and already adopted in our hypothetical life insurance com- pany. As each person is to receive $1 immediately, it is obvious that the company will require a sum in hand of $63,364 in order to pay the annuities due at the beginning of the first year, on the execution of the contract. It will also be seen by the table that 1,260 annui- tants will die during the first year after having received but one payment. Nothing more is to be paid on their account. This leaves 62,104 persons still living on the 21 first day of the second year, each of whom is to receive a payment of $1 on that day. The company -will require therefore to have on hand at the beginning of the second year a total of $62,104 to pay the annui- ties then due. The present worth of that sum at three per cent, is $60,295.15, which represents, therefore, the amount that it should have in its possession to-day to enable it to pay the annuities due one year hence. Turning to the table again we find 49,341 per- sons still living at the beginning of the tenth year at age sixty-five and each of these is to receive $1, re- quiring a total payment on that day of $49,341. The present worth of that sum at three per cent, interest due in nine years is $37,815.77, which represents the amount the company must have on hand to-day to enable it to pay the annuities due at the beginning of the tenth year. There will be three persons living on the first day of the fortieth year at age ninety-five, requiring the payment on that day of $3, the present worth of which sum payable thirty-nine years hence is $0,947, or ninety-five cents. It is not necessary to illustrate further the pro- cess by which we determine the present worth of the several amounts to be paid out in annuities to those living at the beginning of each year until the last three of the original 63,364 pass away in the fortieth year. As in the computation of the single premium, we have arranged in columns in the following table the several amounts to be paid out in annuities at the beginning of the first, the second, the tenth, and the fortieth years, and the present worth of those sums as given above. 22 Age Begin- ning of Year Year Number Wving Annuities to be paid Present Worth of Annuities 56 First year 63,364 $63,364 $63,364.00 57 Second year 62,104 62,104 60,295.15 * * * * * 65 Tenth year 49,341 49,341 37,815.77 * * * * * 95 Fortieth year 3 Totals 3 0.95 .$1,091,123 $824,117.31 The stars represent the figures for the ages omitted. If these omissions be correctly supplied, the total of all the present worths will be as given, $824,117.31. But $824,117.31 divided by 63,364 gives just $13.006082, or thirteen dollars and one cent. If, therefore, each one of our original 63,364 persons at age fifty-six will contribute the sum of $13,006. .toward the creation of an annuity fund, we shall have a total of $824,117.31, or just enough to pay each man an annuity of one dollar at the beginning of each year so long as he lives, provided that the deaths occur as indicated by the mortality table, and that our funds earn three per cent, interest. To Find the Net Annual Premium The value, or cost, of a life annuity of $1 at age fifty-six by the American Experience Table and three per cent, interest, is thus found to be $13,006. In other words, $13,006 paid down in one sum is the exact mathematical equivalent at age fifty-six of the 23 payment of $1 at the beginning of each year during life. We have seen that the net single premium for $1,000 life insurance at age fifty-six is $621.18. If $13,006 is the mathematical equivalent of $1 to be paid annually during life, $621.18 must be the mathe- matical equivalent of as many dollars to be paid yearly during life, as $13,006 is contained times in $621.18. Performing the division we get $47.76. In other words, $47.76 paid at the beginning of each year during life is the exact equivalent of the net single premium of $621.18, and is therefore the net annual premium of an ordinary life policy of $1,000 at age fifty-six, accord- ing to the American Experience Table and three per cent, interest. General Observations We have seen that at age fifty-six the sum of $13,006 will purchase a life annuity of $1; in other words, $13,006 paid in one sum is the mathematical equivalent of $1 to be paid at the beginning of every year during life. We have also seen that $621.18 paid in one sum is the mathematical equivalent of $47.76 paid yearly during life. These equivalents may be expressed in the fol- lowing proportion: $13,006 : $1.00 :: $621.18 : $47.76 That is, the value of a life annuity of $1, is to $1, as the net single premium at the same age is to the equivalent net annual premium. 24 Observe that the value of a life annuity of $47.76 at age 56 would be $621.18; that is to say the net single premium of a life policy will purchase a life annuity equal in amount to the net annual premium of the same policy. In all these observations we speak of net pre- miums only, the matter of loading for expenses remain- ing to be adjusted. Sufficiency of the Premium If you have read the preceding pages with care you have now some comprehension of the scientific basis of life insurance. You now know for yourself that it is possible to determine in advance the cost of insuring a given number of lives. You know for yourself that the premium, mathematically computed in the manner set forth, is sufficient for the payment of all claims that can ever occur until the last policy has matured by the death of the insured. There can be no uncertainty as to the adequacy of the premium so computed. There may, indeed, be uncertainty as to the rate of interest to be received, but only in respect of what the excess may be. We may easily earn more than the rate assumed, but that rate is so low that it is morally certain that, through a series of years, we shall not average less. It is therefore certain that, while the premium may be larger than necessary by reason of the increased interest earnings, it cannot be smaller than is requisite. The mortality, likewise, may prove to be less than indicated by the talble, but the universal experience of well-managed companies has 25 demonstrated that, through a series of years, it will not average more than the tabular rate. This again means that, by reason of a low mortality, our premium may prove larger than necessary, but it will not be smaller than required. It is better that the premium should be too large than too small. To have on hand more funds than may, perchance, be needed for the payment of death claims is not a serious misfortune; since the excess can be returnd to the policy-holders subsequently. To have less than sufficient for the payment of claims would mean insol- vency and dissolution. Effect of Withdrawals In our h3'pothetical company it was assumed that all members would continue to pay their premiums until death. In practice it is well known that many with- draw after having made one or more payments. The member who drops out, thereby forfeiting the payments he has already made, is said to Lapse. The question arises, what allowance should be made in the computa- tion of the premium for the gains that may accrue from lapses } We shall answer this question only briefly and partially now, but more fully in a later chapter. That there will be lapses is certain, but it does not follow that there will be a real gain from that source. Experience has shown that it is the sound life as a rule that withdraws. After a company has been in existence for some years many of the members are in impaired health. These are not likely to lapse. The man who is 26 about to die will cling to his insurance. The man who is in robust health is the one to withdraw. It is con- ceivable that lapses might multiply until presently we should have merely a company of invalids with a mor- tality in excess of any known table. In other words, the apparent gain from lapses is apt to be offset by an increased mortality. It is impossible to determine in advance what the lapse rate of any company will be, or what will be the relative proportions of invalids and sound lives among the withdrawing members. It is impossible, therefore, to determine beforehand what allowance, if any, should be made on account of the possible profits accruing from that source. Accordingly, it is assumed in the compu- tation of the premium that there will be no lapses and hence no gains therefrom. If, as a matter of subse- quent experience, there prove to be such gains, then, as in the case of excess interest and savings in mortality, the surplus thus accruing wiU be apportioned equitably among the members, after it is known that there has been a gain from that source. Notwithstanding the fact that the impaired risk is not apt to lapse his policy, there are indications that the mortality among withdrawals in after-life is as great as among the body of persistent members, for the reason that many of those that withdraw under normal condi- tions are of the shiftless, vacillating class, who are less likely to live to old age than the thrifty, determined class. However this may be, nothing is more clearly demon- strated than that when lapses are excessive, as when the policy-holders have lost confidence in the company or its management, the sound lives who can secure insur- 27 ance elsewhere withdraw in much larger proportion than under ordinary conditions. This is clearly shown by the excessive mortality in companies which have suffered from heavy withdrawals due to lack of confidence in the management or in the plan of insurance, as shown by the abnormal mortality in decadent assessment com- panies. Effect of New Members Another question naturally arising is, would not the addition of new members reduce the cost of insur- ance and render it practicable to charge a small net premium? As in the case of the preceding topic, we have space to answer only briefly now, but will explain more fully in a later chapter. We assumed that there would be no new members, chiefly to simplify the matter of computation, but it is also true that each age must bear its own natural cost, that the addition of new members is not essential to the successful career of a well-established company, and that such additions cannot effect the amount of premium mathematically necessary. Turn again to the mortality table. Notice that at age fifty there are 69,804 of the original 100,000 persons stiU living. Assume, now, the organization of another company of 69,804 members all fifty years of age, and by the method of computation heretofore illus- trated you will find the net annual premium at that age to be $36.36. This is the net amount mathemati- cally necessary for each member entering such a com- pany at age 50 to pay yearly during life to enable the company to pay all policies as they mature by death. 28 Can the net annual premium of $47.76 charged by our hypothetical company for members fifty-six years of age be reduced by the addition of "new blood" — ^the influx of younger men^ say, for example, the addition to our original company of 69,804 new members, all fifty years of age? We have seen that the net annual pre- mium mathematically necessary at age fifty is $36.36. If the payments of these younger men are to be applied in part to reducing the cost of the insurance to the older members, there wiU certainly be a deficit in their own funds unless their own premium of $36.36 is correspond- ingly increased. But to make such an increase would not be equity. To charge one set of members more than mathematical cost in order to furnish another class with insurance at less than cost would be monstrous. All schemes of life insurance based upon that idea — ^the as- sessment plan — ^have ended or must inevitably end in failure. 29 CHAPTER IV THE DIFFERENT KINDS OF POLICIES Ordinary Life and Limited Payment Life Contracts So far we have treated only of the Ordinary Life policy, a contract payable at death, with equal annual premiums to be paid during the lifetime of the insured. It is, however, often desirable to complete the payment of all premiums within a limited period, say within ten or fifteen or twenty years. A policy payable only at death but which is fully paid for in a limited number of premiums is termed a Limited-Payment Life Policy. Thus, when but ten premiums are to be paid, we have a Ten-Payment Life. If twenty premiums are called for, the contract is a Twenty-Payment Life, etc. If the reader has not thoroughly mastered Chapters II and III, he wiU do well to study them again with care before going further. The net single premium of a life policy issued at age fifty-six has been shown in Chapter II to be $621.18. Dividing this amount by the value of a life annuity of $1 issued at the same age, we obtain the net yearly premium payable during life. To apportion the net single premium into a limited number of equivalent payments, as for example, ten, or twenty is an equally simple process, the divisor in the case being the value of a temporary annuity running for a like period of 10 or 20 years instead of by the value of a life annuity. 30 Determining the Limited Payment Premium A Temporary Annuity is one which, like a life annuity, terminates on the death of the annuitant, but which, unlike the latter, must terminate also when a specified number of payments have been received, as ten or twenty, even though the annuitant be stiU living. To determine the net yearly premium of a Ten-Payment Life, divide the net single premium of a Life policy by the value of a temporary annuity of $1 terminating in ten years. The net yearly premium of a Twenty- Payment Life is likewise found by dividing the net single premium of a Life policy by the value of a twenty year temporary annuity. Computation of Temporary Annuity The value of a temporary annuity is computed by a process similar to that followed in the case of a life annuity. Assume, for example, that every member of our hypothetical company (page 12), is to receive a tem- porary annuity of $1 at the beginning of every year for ten years. Turn now to the illustration on page 23. The present worth of the amount required to make an immediate payment of $1 to each of 63,364 persons would be $63,364. The present worth of the amount required to pay the annuities of the second year at age fifty-seven would be $60,295.15. The present worth of the amount required for the tenth year at age sixty-five would be $37,815.77. The student will readily calculate the present worth of the amounts required to pay the annuities of each of the intervening years. The sum of 31 all these present worths from the first year to the tenth inelusivcj wiU be the total present fund required to enable the company to pay the annuities of the entire ten years. Dividing this sum by the original number of annuitants, to wit: 63,364, will give us the value of a temporary annuity of $1, granted at age fifty-six, and terminating with the tenth payment. The value of a twenty-year temporary annuity of $1 may be ascertained in the same manner. Term Insurance Men sometimes desire temporary life insurance for the sake of protection during a specified period pend- ing the development of a business enterprise, the matur- ity of a debt, the dependence of minor children, etc. Sup- pose, for example, that the insurance is taken for ten years instead of for the whole of life. If the insured dies within the period named his policy wUl be paid. If he lives longer than ten years, the insurance terminates — the contract is of no further validity. This is called Term Insurance. A Term Policy is one which is payable only at death and then only on condition that death occurs within a stated period — the term for which the contract is written. A contract cover- ing a period of ten years is a Ten-Year Term Policy. In the same way we have a One-Year Term, a Twenty-Year Term, a Thirty-Year Term, etc. Such a policy is sometimes renewable for one or more periods at a correspondingly higher rate, but without regard to the physical condition of the insured. 32 This is Renewable Term Insurance, and we have accord- ingly a Yearly Renewable Term, a Ten-Year Renewable Term, etc. A renewable term policy mayj nevertheless, by stipulation in the contract finally terminate at a fixed date. For example, we may have a ten-year renewable term "terminating at age seventy." Term insurance in The Mutual Life is not renewable save in the case of the "yearly renewable term," which expires at age 65 but may then be changed to Ordinary Life with premium corresponding to attained age. The discontinuance of a Term policy at the com- pletion of the period for which it was written is called a Termination by Expiry. Determining the Premium of a Term Policy The process of computing the premium of a term policy will be readily understood. Let us assume, for example, that the members of our hypothetical company (page 12), are all insured for a term of only ten years instead of for the whole of life. With 63,S64 persons insured at age fifty-six, we shall have the death claims of the first ten years only to pay. The 47,361 persons living beyond that period, although they have paid premiums for ten years, wiU receive nothing. Turning to page 1 8, we note that the present worth of the amount required to pay the losses of the first year is $1,223,- 300.98. In like manner the present worth of the amount required for the tenth year is $1,473,305.94. From ex- planations heretofore given, the reader will be able to compute the present worth of the several amounts re- 33 quired for the intervening years. The sum of the present worths of the first ten years will be the total insurance fund necessary to have on hand at the beginning to enable the company to pay all the losses of ten years, and this amount divided by ,the whole number of insured lives, to wit: 63,364, will give us the net single premium of a ten-year term policy at age fifty-six by the American Experience Table and three per cent, interest. Dividing the net single premium by the value of a ten-year tem- porary annuity of $1 (see page 31), will give us the net annual premium required. So-called "Profits" in Life Insurance The holder of a Term policy who lives beyond the end of the period for which the contract was written, has paid simply for protection during that period. There is nothing more coming to him for the premiums he has expended, yet he is neither gainer nor loser by the trans- action. He has received the protection for which he paid, and has had it at exact cost. The company which pays a loss of $1,000 in the first year, having received from the deceased but one yearly premium of possibly $39.26, is neither gainer nor loser by the transaction. It insures 63,364 persons for a period of ten years, and during those ten years it collects from the insured members the exact amount of money necessary for the payment of all losses, according to its computation based upon the mortality table and the as- sumed rate of interest, plus the necessary loading for 34 expenses. It is immaterial to the company whether this member or that member lives or dies; the total death claims cannot exceed a certain amount^ and for the pay- ment of those claims the company has collected the exact mathematical cost. All this is equally true of the Ordinary Life policy, the Limited Payment policy, and of every other form of contract written, all alike being based upon exact mathematical cost. In life insurance there can be neither gain nor loss, to company or policy-holder, so long as the mortality corresponds with that of the table, the interest received with the assumed rate, and the expense of management and outlay for contingencies with the provi- sion made therefor in the loading. In practice, however, there are gains in the case of every well-managed company. If, by reason of a careful selection of insured lives, the mortality is less than that indicated by the table upon which the pre- miums were based, the difference will be so much gain. Our hypothetical company anticipated 16,003 deaths in the course of its first ten years, as indicated by the mortality table, and accordingly made provision in its premium charge for the payment of $16,003,000 in claims during that time. Had its actual mortality proved to be but seventy-five per cent, of that amount there would have been a considerable gain in the saving thus effected. Such gains are not uncommon in practice. Most companies have an average mortality of not more than eighty or ninety per cent, of that shown by the table. A well-managed company will likewise make gains from interest received in excess of the assumed rate, and from the saving effected by incurring smaller expenses than 35 the amount collected for that purpose — all of which will be treated of in a later chapter. To Whom the Profits Go Bear in mind that in the case of a stock life insurance company (see page 6) the gains and savings thus effected all belong to the stockholders. In the case of a mixed company — ^that is, a stock company doing business on the mutual plan (page 7), a part of the savings go to the stockholders and the balance to the policy-holders. In a purely mutual organization, such as The Mutual Life Insurance Company of New York in which there are no stockholders, every dollar gained from first to last belongs to the policy-holders and will be returned to them when the apportionment of surplus is made in accordance with their several contracts. This subject will be more thoroughly discussed in a later article under the head of Surplus. Endowment Policies A man may wish to make some provision for his own future in addition to providing for his dependents. To this end Endowment Insurance has been devised. The Endowment Policy is one which is payable to the insured himself if he lives through a specified number of years or to a stated age, but payable to his legal repre- sentatives or beneficiary in the event of his prior death. Thus a polic}' payable to the insured himself if living at the end of twenty years, but to his beneficiary in case of 36 his prior death, is a Twenty-Year Endowment. In like manner we have a Fifteen-Year Endowment, a Thirty- Year Endowment, etc. Such a policy is a combination of term insurance and what is known as Pure Endowment. The latter form of policy is payable only to those who live to com- plete the endowment period. Those who die prior to that date receive nothing. This is purely "investment insurance." Assume, for example, the issue of a ten-year Pure Endowment for $1,000 to each of the 63,364 members of our hypothetical company at age fifty-six. During the next ten years 16,003 members will die. These receive nothing. There will be 47,361 survivors who are to receive $1,000 each, requiring a total pay- ment of $47,361,000. The present worth of that sum at three per cent., to wit: $35,241,031.67, represents the total insurance fund required at the beginning. This amount divided by the total number insured, 63,864, gives $556.17, the net single premium of a ten-year pure endowment at age fifty-six by the American Experience Table and three per cent, interest. That is to say, if 63,364 persons at age fifty-six contribute each the sum of $556.17, the fund will be just sufficient, with the aid of three per cent, interest, to pay $1,000 to each of the 47,361 members who survive the period. The Endowment Premium Keep in mind the fact that the holder of a pure endowment policy, who dies before completion of the endowment period, receives nothing. If, however, each 37 of our 6Sj364 members carries also term insurance covering the same period, then each one of the 16,003 who die will likewise receive his $1,000. Thus by combining the premium of a term policy with that of a pure endowment, we obtain the premium of the regular endowment which provides for both those who die and those who live. This may be illustrated as follows: The net single premium for a ten-year term policy of $1,000 at age fifty-six is $212.80, while the corresponding net single premium for a pure endowment, as already shown, is $556.17. The former provides for all who die within the ten years ; the latter for all who are still living at the end of that time. Combining the two we get $768.97, which is the net single premium of a regular Ten- Year Endowment. Reverting again to the pure endowment, written as a separate contract: observe that the net single pre- mium of $556.17 at three per cent, compound interest, will amount in ten years to only $747.44 instead of to $1,000. The difference is made up by the premiums forfeited by the 16,003 members who die during the term and receive nothing. Effect of Mortality in Endowment Insurance The pure endowment net single premium of $556.17 is based upon the expectation that the mortality will be the same as that indicated by the table. If there were no deaths at all during the ten years, en- titling every one of our 63,364 members to an endow- ment of $1,000 at the end of the period, the net single 3S premium for each one to pay would be $744.09, that being the sum which at three per cent, compound in- terest would amount to $1,000 in that time. That is, if there were no deaths at all during the ten years, a net single premium of only $556.17 would leave a large deficit. Likewise, it is obvious that if there were fewer deaths than indicated by the table, there would be more endowments to pay than were counted upon, and again there would be a deficit. On the other hand, if the deaths were to exceed the mortality table, there would be fewer endowments to pay than were anticipated, and this would result in a corresponding gain. In other words, in pure endowment insurance, the higher the mortality rate, the larger the gains to the company, while a mortality less than that of the table must result in actual loss. The reverse of this is found in term insurance, where the lower the mortality, the better for the company. By combining the two forms, the favor- able effect of a low mortality in term insurance more than counteracts the adverse effect of the same condition in pure endowment. 39 CHAPTER V PROVING THE ADEQUACY OF THE NET PREMIUM IF the reader has studied Chapters II and III with care, he is convinced of the correctness of the process by which the net yearly premium at age fifty-six is com- puted, and wiU readily comprehend that by a like process the necessary net premium at any other age may be ascertained. At the same time, a mathematical verifica- tion of the work may serve to fix the principle involved more firmly in his mind, and to emphasize more forcibly the certainty of the life insurance proposition. For example, by mathematical computation we have found the net annual premium of an Ordinary Life policy of $1,000 at age fifty-six, American Experience Table and three per cent, interest, to be $47-76. Ee- f erring again to our hypothetical company, page 12, we may prove the exact sufficiency of that premium by "working it out," computing the amount of premiums received the first year, adding interest assumed, deduct- ing claims paid, adding balance to premium income of the second year, improving the sum at interest, deducting claims, etc., until the premiums of the last three mem- bers have been collected in the fortieth year, and their policies paid. It should be explained here that inasmuch as computations in life insurance, as in other sciences, in- volve the use of decimals, exact results are not attainable. For example, we have had occasion on page 17 to find the present worth of $1,980,000, due in ten years, at 40 three per cent, interest. Now the present worth of $1 on the terms named would be $0.74, or, carrying it to three decimal places, $0,744; that is, seventy-four cents and four mills. Carried to five decimals we should have $0.74409; six places, $0.744094. If we regard the present worth of $1 as $0.74, then the present worth of $10 would be $7.40; but if we use three decimals ($0,744), we get $7.44 as the present worth of $10 instead of $7.40. Again if the present worth of $1 is $0,744 the present worth of $1,000 would be $744; but if we use five decimals in the present value of $1 (to wit $0.74409) we shall have $744.09 as the present worth of $1,000 instead of $744. It will be readily seen that the assumed present worth of a large sum like $1,980,000 will vary materially according to the number of decimal places employed in the computation. Three decimals in the present worth of $1 (to wit $0,744) would give us $1,473,120 as the present worth of $1,980,000, while six decimals ($0.744094) would give us $1,473,306.12, and the stiU larger number of decimals employed in our computation gave us $1,473,305.94 as a more nearly accurate result. It will be seen that in computations involving vast amounts, the greater the number of decimal places used the nearer will be the approach to actual accuracy. In compiling the Verifica- tion Table appearing in this chapter more decimal places were employed than is usual in ordinary work because of the great number of dependent computations involved. This explanation is made for the benefit of anyone who may find difficulty in verifying exactly the figures given herein. 41 The Exact Net Premium The net premium of $47.76 given above is the amount actually collected in practice, though a more nearly correct premium, carried to six decimal places, would be a fraction of a cent more than that, to wit: $47.760895. The proposition now is to prove that this net premium of $47.760895 is a sufficient charge for an Ordi- nary Life policy of $1,000 at age fifty-six. If this can be shown it will be conceded that by the same process the adequacy of the net premium charge at other ages can be proved. In practice it is not possible to collect the fractional part of the cent ($.000895), less than one- tenth, as we have assumed to do in the Verification Table, but the slight deficit resulting therefrom in large trans- actions is easily adjusted with gains from other sources. It might be well to repeat here that the gross premium in life insurance is composed of two parts, the net premium and the loading. The net premium, with which alone we have to do at present, is devoted solely to the payment of policy claims. No part of it can be used for any other purpose. The loading is an amount arbitrarily added to the net premium for payment of expenses not otherwise provided for, and for other con- tingencies, and does not aiFect the question of the mathematical sufficiency of the net premium. We have already stated, page 14, that, while in practice death claims may be paid at any time, yet, theoretically, they are all payable at the end of the year. It is upon this basis that the net premium is computed, and to prove the correctness of the computation, there - 42 fore, the same hypothesis must be adopted, — that all death claims are payable at the end of the year. Our hypothetical company has 63,364 members as stated. Collecting from each of these the sum of $47.760895, gives us a net premium income for the first year of $3,026,321.35. To this we add twelve months' interest at three per cent. ($90,789.64), which makes our total income $3,117,110.99. By turning to the mortality table (page 13), we note that at age fifty- six we shall have 1,260 deaths during the year, calling for the payment of claims to the amount of $1,260,000. Deducting these death claims from the total income, we get a balance of $1,857,110.99. The operations of the year may be tabulated in the following manner: Net premium income beginning of the year $3,026,321.35 Add one year's interest (three per cent.) 90,789.64 Total income first year $3,117,110.99 Deduct death claims 1,260,000.00 Balance end of first policy year $1,857,110.99 The Reserve Study the above figures. Note that the net pre- mium income, increased by one year's interest thereon at the assumed rate (three per cent.), constitutes our total insurance fund. This might be termed the Mortal- ity Fund, but the expression has not obtained in regular life insurance, the term Reserve being in universal use. The Reserve includes all funds in life insurance devoted 43 to the payment of policy claims — that is, the net premium receipts and the interest earned on those receipts to the extent of the assumed rate (three per cent.). The balance of the insurance fund on hand at the end of the policy year, after deducting policy claims, is, for the sake of distinction, called the Terminal Reserve; while the fund on hand at the beginning of the year (consist- ing in the first year of the net premium income only), is termed the Initial Reserve. If the terminal reserve in the above case ($1,857,110.99) be divided by 62,104, the number of members still living (see page 60), we shall obtain $29.90, which is the terminal reserve pertaining to each policy still in force at the end of the first year. At the commencement of the second policy year we have 62,104 persons living at the attained age of fifty-seven years. Each of these pays the same net premium as before, making our total premium income at the beginning of the second year, $2,966,142.62. Adding to this the amount reserved from the preceding year ($1,857,110.99, see table of operations first year, page 43), we now have an insurance fund of $4,823,253.61, which is the initial reserve of the second year. Again we add to this sum one year's interest at three per cent., to wit: $144,697-61, and we get a total fund for the second year of $4,967,951.22. Deducting from this the death claims of the year according to the mortality table, to wit: $1,325,000, we have a balance of $3,642,951.22, which is the terminal reserve at the end of the second policy year. If this amount be divided by 60,779, the number of members still living, we shall get $59.94, which is the terminal reserve pertaining to each policy at the end of the second year. The operations of the year may be tabulated in the following manner : Net premium income second year $2,966,142.62 Add terminal reserve of pre- ceding year 1,857,110-99 Total beginning second year (initial reserve) $4,823,253.61 Add one year's interest (three per cent.) 144,697.61 Total end of second year.... $4,967,951.22 Deduct death claims 1,325,000.00 Balance end of second year, (terminal reserve) $3,642,951.22 A Verification Table The complete solution of the problem — the proof of the sufficiency of the net yearly premium is illustrated in the annexed figures which, for convenience of refer- ence, we have termed a Verification Table. Column four gives the net premium income for each year. Column five shows the initial reserve, consisting (after the first year) of the net premium income plus the terminal reserve of the preceding year. To the sum of these is to be added one year's interest, which is set out in column six. From this amount (not entered in the table for lack of room) will be deducted the death claims of the year as indicated by the mortality table and shown in column seven. The balance (column eight) will be the terminal reserve for the year. This divided by the number of members still living (see column two, next higher age) will give the terminal reserve pertaining to each policy, as shown in column nine. 45 VERIFICATION Ordinary Life, $1,000 Age 56 Net Yearly 1 2 3 4 S Age Members Living Deaths Net Premium Income Initial Reserve 66 S7 B8 S9 60 63,3«4 62,104 60,779 59,385 57,917 1,260 1,325 1,394 1,468 1,546 $3,026,321 35 2,966,142 62 2,902,859 44 2,836,280 75 2,766,167 76 $3,026,321 35 4,823,253 61 6,545,810 66 8,184,465 73 9,728,167 46 61 63 63 64, 65 56,371 54,743 53,030 51,230 49,341 1,628 1,713 1,800 1,889 1,980 2,692,329 41 2,614,574 67 2,532,780 26 2,446,790 65 2,356,570 32 11,166,341 89 12,487,906 82 13,682,304 28 14,739,564 06 15.649,321 30 66 67 6S 69 70 47,361 45,291 43,133 40,890 38,569 2,070 2,158 2,243 2,321 2,391 2,262,003 75 2,163,138 70 2,060,070 68 1,952,943 00 1,842,089 96 16,400,804 69 16,985,967 53 17,397,617 24 17,629,488 76 17,679,463 38 71 73 73 74, 7S 36,178 33,730 31,243 28,738 26,237 2,448 2,487 2,505 2,501 2,476 1,727,894 16 1,610,975 50 1,492,194 14 1,372,553 11 1,253,103 10 17,546,741 44 17,236,119 18 16,758,396 90 16,128,701 92 15,364,666 08 76 77 78 79 80 23,761 21,330 18,961 16,670 14,474 2,431 2,369 2,291 2,196 2,091 1,134,847 14 1,018,740 39 905,595 84 796,174 87 691,291 19 14,484,453 20 13,506,727 19 12,448,524 85 11,327,155 47 10,162,261 32 81 82 83 84 85 12,383 10,419 8,603 6,955 5,485 1,964 1,816 1,648 1,470 1,292 591,423 16 497,620 77 410,886 98 332,177 02 261,968 51 8,967,552 32 7,770,199 66 6,598,192 63 5,480,315 43 4,436,693 40 86 87 88 89 90 4,193 3,079 2,146 1,402 847 1,114 933 744 555 385 200,261 43 147,055 80 102,494 88 66,960 77 40,453 48 3,478,055 63 2,615,453 10 1,863,411 57 1,242,274 69 764,996 41 91 92 93 94 95 462 216 79 21 3 246 137 58 18 3 22,065 53 10,316 35 3,773 11 1,002 98 143 28 425,011 83 202,078 54 74,914 01 20,164 41 2,912 62 46 TABLE Premium $47.760895 American Experience 3 Per Cent 6 7 8 9 10 Add One Year's Interest Deduct Death Claims Balance, Terminal Reserve Reserve on each Policy End of $90,789 64 144,697 61 196,374 32 245,533 97 291,845 02 $1,260,000 1,325,000 1,394,000 1,468,000 1,546,000 $1,857,110 99 3,642,951 22 5,348,184 98 6,961,999 70 8,474,012 48 $29 90 59 94 90 06 120 21 150 33 I Yr. 4 " 5 " 334,990 26 374,637 20 410,469 13 442,186 92 469,479 64 1,628,000 1,713,000 1,800,000 1,889,000 1,980,000 9,873,332 15 11,149,544 02 12,292,773 41- 13,292,750 98 14,138,800 94 180 36 21025 239 95 269 41 298 53 " 7 " « " 9 " 10 " 492,024 14 509,579 03 521,928 52 528,884 66 530,383 90 2,070,000 2,158,000 2,243,000 2,321,000 2,391,000 14,822,828 83 15,337,546 56 15,676,545 76 15,837,373 42 15,818,847 28 327 28 355 59 383 38 410 62 437 25 11 " 19 " IS " 14, " IS " 526,402 24 517,083 58 502,751 91 483,861 06 460,939 98 2,448,000 2,487,000 2,505,000 2,501,000 2,476,000 15,625,143 68 15,266,202 76 14,756,148 81 14,111,562 98 13,349,606 06 463 24 488 63 51347 537 85 561 83 16 " 17 " 18 " 19 " 30 " 434,533 60 405,201 82 373,455 75 339,814 66 304,867 84 2,431,000 2,369,000 2,291,000 2,196,000 2,091,000 12,487,986 80 11,542,929 01 10,530,980 60 9,470,970 13 8,376,129 16 585 47 608 77 631 73 654 34 676 42 gl " gS " 93 " 94 " 95 " 269,026 57 233,105 99 197,945 78 164,409 46 133,100 80 1,964,000 1,816,000 1,648,000 1,470,000 1,292,000 7,272,578 89 6,187,305 65 5,148,138 41 4,174,724 89 3,277,794 20 698 01 71920 740 21 761 12 781 73 96 " 97 " 98 " 99 " 30 " 104,341 67 78,463 59 55,902 35 37,268 24 22,949 89 1,114,000 933,000 744,000 555,000 385,000 2,468,397 30 1,760,916 69 1,175,313 92 724,542 93 402,946 30 801 69 820 56 838 31 855 42 872 18 31 " 39 " S3 " 34 •■ SB " * 12,750 36 6,062 36 2,247 42 604 93 87 38 246,000 137,000 58,000 18,000 3,000 191,762 19 71,140 90 19,161 43 2,769 34 887 79 900 52 912 45 923 11 36 " 37 " 38 " 39 " 40 " 47 By means of the table one can quickly follow the process through and see for himself that the net premium is precisely adequate. The figures assume the collection of that amount in each year from each living member. Interest at three per cent, is included from the first on all funds on hand- Every death claim is paid in full as it matures, according to the mortality table. At ninety-five there are but three members yet living. These pay their last premiums on that day, making the total net premium income of that year $143.28. To this is added the terminal reserve of the preceding year, to wit: $2,769.34, making an initial reserve for the fortieth year of $2,912.62. Adding to this one year's interest, to wit: $87.38, we get $3,000, or just sufficient to pay the three remaining policies in full. The Limit of Life It is assumed in the mortality table that the last three members remaining at age ninety-five, will not live beyond the end of that year. The premium having been computed on that basis, the total insurance fund, that is, the reserve, must necessarily equal the face of the policy at that time, the end of the fortieth year, when the insured has reached the age of ninety-six. In other words, the reserve is equal to the face of the policy at the limit of life which, by the American Experience Table, is the attained age of ninety-six years — the age when the last man is presumed to die. The fact that in actual experience men do some- times live beyond the age of ninety-six, is not against but in favor of the sufiiciency of our premium. If, for 48 example, the ultimate limit of life were in fact three- score and ten, or four-score years, none ever living beyond that period, our premium, computed on the basis of some attaining the age of ninety-six, would be insuffi- cient. It will be seen by the Verification Table (pages 46 and 4)7) that the reserve on each policy at the end of twenty-five years amounts to only $676.42. In other words, if the 12,383 members then remaining were all to die at that time, at the attained age of eighty-one years, the total funds on hand would suffice to pay only $676.42 on each $1,000 policy. If on the other hand, the three members remaining at age ninety-five shall continue to live beyond the attained age of ninety-six, — say to one hundred or longer, the fact will not affect the result. The reserve on hand is equal to the face of the policy — ^there can be no failure to pay the death claim when it occurs. Examples of Remarkable Longevity The American Experience Table indicates that out of 81,822 persons living at age 35, only 3 will still be living at age 95, and that none of these will live beyond the attained age of 96. The experience of The Mutual Life has been much better than that. It is commonly assumed that the average age at date of insur- ing is 35. Of the 470 persons insured in the first year of The Mutual Life, 2 lived beyond the age of 96. In that proportion (if each of the 470 persons had been 35 years of age at date of insuring), the American Experience Table would show 348 out of 81,822 living to age 96, instead of 3. These data, however, are too 49 meager to enable us to form an accurate conclusion. Taking larger figures, in the first four years the Com- pany insured 3,126 persons. These have aU passed away, 5 of them living beyond age 96. Proportion- ately, the American Experience Table, in the case of 81,822 persons at age 35, would show 131 attaining the age of 96 instead of 3. The Company has already had 23 policyholders to live beyond the age of 96 out of 247,608 insured in the first 40 years. As many of those insured in that time are still living, some of whom may live beyond 96, we cannot give comparative results in figures, but it is evi- dent that the mortality in The Mutual Life has been far more favorable than that indicated by the table. In this connection it must not be overlooked that many of the 247,608 policies issued in the first forty years termi- nated by lapse or surrender, many Term policies ended by expiry, and many Endowment policies matured before the death of the insured. We have no record of the after-lifetime of these policyholders, some of whom probably lived, or will yet live, to age 96. The following table is a record of the Company's experience up to September 21, 1920. The names in the list marked with an asterisk are those of policy- holders who, upon attaining the age of 96, or later at their option, surrendered their insurance, receiving the original face amount of the policy and accrued additions in cash. This is a privilege always accorded by The Mutual Life to policyholders who have lived to the age named, for the reserve is then equal to the face amount of the insurance at 96. 50 List of Policyholders Who Lived and Maintained Their Insurance in Force Until Attaining the Age of 96 Years or Longer. WAMW Date of Date of Date of Age at ^'Iff " :*;f J,?' NAMB gjj.jjj J jj j^ I ent Death Age Yrs. Mos. Chas.H. Booth Sept. 30, 1803 Feb. 7, 1843 May 29, 1904 39 100 8 Geo. L. Newman . . . July 15, 1816 Jan. 24, 1844 Oct. 11, 1913 28 97 3 Robert Street June 12, 1806 June 27, 1845 Feb. 1,1903 39 96 8 Jesse W. Hatch May 20, 1812 June 30, 1845 Jan. 24, 1910 33 97 8 Charles Rhind Feb. 10, 1810 Feb. 27, 1846 April 23, 1908 36 98 2 Thos. J. West* April 19, 1822 Nov.30, 1848 27 Homer Blanchard... April 1, 1806 Mch. 13, 1850 Nov. 27, 1902 44 96 7 Charles A. Maison.. May 7,1824 Sept. 26, 1853 29 96 JohnP. Daniels*.... April28, 1815 Nov.25, 1854 Nov. 11, 1912 40 97 6 John P. Mesick June 17, 1813 May 13, 1856 June 30, 1915 43 102 Aaron E. Ballard*. . . Dec. 27, 1820 Jan. 14, 1857 36 PeterVanPelt Sept. 29, 1817 June 3, 1863 June 11, 1916 46 98 9 Gilbert FoUansbee* . Jan. 5, 1821 Jan. 5, 1864 43 James M. Woltz .... Dec. 14, 1818 May 25, 1864 Nov. 3, 1915 46 96 11 Jesse C.Green Dec. 13, 1817 Sept. 7, 1865 July 26, 1920 48 102 7 Abner Lincoln* .... May 12, 1819 Apr. 27, 1866 47 Nahum Morrill*.... Oct. 3,1819 Apr. 12, 1868 Mar. 3,1917 49 97 5 E. C. Stephenson. . . . Jan. 19, 1821 Oct. 3, 1871 51 100 Elias Greenbaum*. . . June 24, 1822 Dec. 23, 1871 50 William A. Miller*. . Mar. 5, 1824 Mar. 30, 1872 48 Barr Spangler Jan. 21, 1822 Mar. 28, 1881 59 99 James Kittler* July 23, 1820 Dec. 23, 1875 55 Wm. P. Dickinson. . Oct. 17, 1820 Dec. 18, 1883 June 18, 1918 63 97 8 CHAPTER VI OBSERVATIONS ON THE RESERVE "New Blood" not Essential to Permanence IN the Verification Table, pages 46 and 47, we have the mathematical proof that a regular life insurance com- pany — the assumptions as to miortality and interest be- ing realized — ^might cease writing new business alto- gether, and by continuing to collect from each member the requisite mathematical premium, would be able to pay all policies in full including that of the last man, — the balance on hand when the last policy matures at the attained age of ninety-six being just sufficient for that purpose. Reserve all for Mortality Purposes The Verification Table illustrates, theoretically, the actual progress of a life insurance company from the beginning of its career to the fulfillment of its last contract. It illustrates also the fact that the so-called Reserve in life insurance is simply the insurance fund or mortality fund of the company, from which all policy claims are paid. Observe that at the beginning of the very first year the initial reserve, which the company under the law must hold on the day when it commences business, comprises the entire net premium income. Observe that thereafter the entire net premium receipts, plus 3 per cent, interest thereon at the assumed rate, con- stitute the actual insurance fund of the company, always 52 designated as the reserve. Note that the reserve is con- stantly applied to the payment of policy claims, until the last claim is met at age ninety-six, to which the last dol- lar of the net premium receipts and interest is devoted. In other words, the net premium is all for mortality pur- poses, or the payment of policy claims, and for nothing else. Some Popular Errors Several primary text books, in attempting to explain in a simple manner the scientific features of life insurance, unwisely state that the gross premium is com- . posed of three parts, to wit: the Reserve Element, the Mortality Element, and the Expense Element. The statement is technically incorrect and has led to much confusion. The explanation is made that the reserve and mortality elements combined constitute the net premium, while by the term "expense element" is meant the loading, the three parts making up the gross premium. Some of these elementary writers have published tabular exhibits purporting to show the division of the gross premium at the several ages into mortality, reserve, and expense elements. These apparently authoritative statements seem to indicate, and have been interpreted by the uninformed to mean, that the so-called "mortality element" is the estimated necessary provision for pay- ment of probable death claims, while the "reserve ele- ment" is supposed to be purely an accumulation for possible emergencies, such as extraordinary claims result- ing from epidemics, etc. S3 Moreover, the division indicated is commonly understood to be fixed — the inference being that the amounts apportioned for mortality, reserve, and expense elements remain the same in the case of all future premiums. Most promoters of assessment schemes have so understood these figures, and many of these, by adopting as a net rate the so-called "mortality element," plus an addition of perhaps twenty per cent, for possible excess mortality, have loudly proclaimed their conserva- tism and foresight in making a "larger provision for mor- tality" than is made by the so-called "old line" compa- nies. The "old line" reserve they vaguely designate as the "investment element," which is alleged to have no place in legitimate life insurance. In fact, the assertion is made by the promoters of such organizations that the reserve is never drawn upon for the payment of death claims. Even fairly well-informed persons have con- ceived the erroneous notion that the reserve is merely a special fund pertaining to each policy, formed by the accumulation of the "reserve element" of the premiums paid on that policy at a given rate of interest, and that such individual fund is never drawn upon, save as part payment of that particular policy when the same becomes a claim. Composition of the Premium This aggregation of errors results largely from the confusion caused by the hypothetical division of the net premium into reserve and mortality elements. There is in reality no such division save as a bookkeeping ex- pedient, designed to facilitate computations in connection 54 ■with the apportionment of surplus or the solution of similar problems. It is based upon the fact that only a part of the net premium income of the earlier years is required for the payment of current death claims, the balance being reserved to meet future claims ; wherefore, in an individual statement of account, it has been found convenient to charge to mortality such proportion of the net premium as constitutes its pro rata contribution to the death claims of the year, while the balance thereof is carried to reserve account. Thus, for convenience sake merely, we may designate one portion of the year's net premimn as the "mortality element" and the balance as the "reserve element," but it is nevertheless apparent that the division as made is in no way fixed. The so- called elements necessarily vary in their relative propor- tions from year to year, just as the mortality of the company steadily increases with the age of the members, while the contribution from interest also increases yearly as the reserve grows larger. We have referred to these errors at length be- cause they are still widely prevalent and constitute the basis of most assessment fallacies, making it quite essen- tial that the solicitor in the beginning of his career should know how to meet and refute them. Let us state then, as emphatically as possible, that the gross premium is not composed of three ele- ments, "mortality, reserve, and expense," but consists of two parts only, the net premium and the loading, and that the net premium is all for mortality purposes. As already stated, you have seen in your study of the Veri- fication Table, pages 46 and 47, that there is but one "in- surance fund" from which all death claims are paid. This 55 fund consists of the entire net premium receipts plus in- terest thereon at the assumed rate; and the Reserve is simply the balance of the fund on hand at any given time. That indeed is the literal meaning of the term. That portion of the insurance fund which has been expended has not been reserved. That which remains is reserved for the payment of the claims of succeeding years ; hence its designation as "The Reserve." This balance is increased yearly by the addition of the current net premium income and interest at the assumed rate. It is likewise constantly drawn upon for the payment of claims. The balance on hand is always the reserve. (Verification Table, columns 5 and 8.) In short, there is absolutely no distinction between mortality element and reserve element, or between mortality fund and reserve fund, save the distinction between money which is ex- pended now and money which is held for future dis- bursement. Cash Values and Endowments: Their Relation to The Reserve If a policy-holder surrenders his contract and withdraws from the company, the latter is relieved of further liability on account of that policy. It will never mature as a death claim. It is no longer necessary, therefore, to hold a reserve for that policy and accord- ingly the member may be permitted to withdraw as a Cash Surrender Value a sum not exceeding his propor- tionate share of the whole reserve. If less than the full 56 proportion of the reserve pertaining to the cancelled pol- icy is allowed as a surrender value, the remainder no longer constitutes a part of the fund, but becomes sur- plus, available for subsequent apportionment among the remaining members as hereafter explained. The fucd will then stand the same as if the withdrawing policy- holder had never been a member of the company. The Verification Table demonstrates the suffi- ciency of the Ordinary Life net premium. Had every member of our hypothetical company carried an Endow- ment policy instead of an Ordinary Life, a similar com- putation would have proved likewise the sufficiency of the endoment net premium. Indeed, the Ordinary Life pol- icy at age fifty-six as illustrated by the Table might be regarded as a Forty-Year Endowment, since the reserve becomes equal to the face of the policy at the end of forty years, at the attained age of ninety-six. In reality, every life policy is the mathematical equivalent of an Endow- ment policy in some form. This may be illustrated by the interesting case of Charles H. Booth, the first policy- holder to attain the age of 96. Mr. Booth's policy was an Ordinary Life, issued at age thirty-nine Fifty-Seven years later, therefore, he reached the assumed limit of life, ninety-six years. The reserve then became equal to the face of the policy, the premium having been computed upon the assumption that he would not live beyond that age and that the face amount would then become payable. Had he applied for a Fifty-Seven Year Endowment at age thirty-nine, the face of his policy would likewise have become payable at age ninety-six. In either case the net premium would have been precisely the same and the reserve on the two policies would have been identical in 57 amount at every stage during the fifty-seven years. In other words, an Ordinary Life policy and a Fifty-Seven Year Endowment, issued at age thirty-nine, are mathe- matically identical. Likewise an Ordinary Life policy at fifty-six is, mathematically, a Forty- Year Endowment is- sued at the same age. Every Life policy is, mathe- matically, an Endowment policy payable at age ninety- six. There is this difference, however, to be noted. While the reserve of a Life policy is equal to the face amount at age ninety-six, so that the policy may properly be paid in cash at that time, it is not, by its terms, pay- able until death, which may be several years later. On the other hand, a Forty- Year Endowment issued at age fifty-six is by its terms absolutely payable at ninety-six. Single Premiums and Reserves You have seen on page 19 that if each of the 63,364) members of our hypothetical company were to pay for his insurance with a single premium ($621.18), we should have a total insurance fund of $39,360,583.39. No further payments on the part of any member would ever be necessary, since the stated fund, with the help of interest at three per cent., would be precisely sufBcient for the payment of all claims as they mature, including those of the last three members at age ninety-six. In other words, each member would hold from the start a fully paid life policy of $1,000. 58 The following table shows the net single premium required for a fully paid Whole Life policy at every age from twenty to ninety-five: Net Single Premiums, or Reserve Values on Paid-up Life Policies Per $1,000 Net Single Net Single Net Single Present Premium Present Premium Present Premium Age or Reserve Age or Reserve Age or Reserve 20 $330 94 46 $514 30 72 $796 67 21 336 68 47 524 23 73 806 28 22 340 57 48 534 37 74 815 70 23 345 62 49 544 70 75 824 93 24 350 82 50 555 22 76 834 01 25 356 18 51 565 89 77 842 97 26 361 72 52 576 71 78 851 80 27 367 43 53 587 67 79 860 49 28 373 82 54 698 74 80 869 06 29 879 39 55 609 92 81 877 42 30 385 64 56 621 18 82 885 60 31 392 09 57 632 51 83 893 63 32 398 73 58 643 89 84 901 59 33 405 68 59 666 30 85 909 51 34 412 63 60 666 72 86 917 32 35 419 88 61 678 13 87 924 88 36 427 36 62 689 51 88 932 02 37 435 04 63 700 83 89 938 75 38 442 95 64 712 08 90 945 23 39 451 07 65 723 24 91 951 58 40 459 42 66 734 27 92 957 49 41 468 00 67 745 16 93 962 31 42 476 80 68 756 89 94 966 84 43 485 83 69 766 42 95 970 87 44 495 10 70 776 73 45 504 59 71 786 82 If any large number of persons, say 100,000, all of the age of twenty years, were each to contribute toward a common insurance fund the net single premium of $330.94, the total resulting fund of $83,094,000 would be just sufficient with three per cent, interest for the payment of all outstanding policies as the same 59 mature according to the mortality table. Likewise at age fifty the net single premium required to accomplish this result would be $555.22. At ninety-five the net premium required is $970.87- If to that sum we add one year's interest at three per cent. ($29.18), we shall have at the end of the year $1,000, or just enough to pay the member in full at his then age of ninety-six. But the total insurance fund on hand is always the reserve, and, dividing that fund by the number of living members, we obtain the reserve pertaining to each policy. One thousand members at age fifty, contributing each a net single premium of $555.22, create a total insurance fund of $555,220; and dividing that fund again by the number of members, we obtain necessarily the sum of $555.22 as the reserve on each paid-up policy. In other words, the net single premium at a given age is always the reserve on a paid-up policy at that age. To illustrate: Turn to the schedule of reserve values in your Life Insurance Manual or Handy Guide. Take the case of a Fifteen-Payment Life policy issued at age twenty-five. It becomes paid-up at age forty. Note that the accumulated reserve then amounts to $459.42, corresponding to the net single premium at that age as given in the above table. Or take a Life policy issued at age thirty and paid for in ten equal annual premiums. This also becomes fully paid-up at age forty, and again you find the reserve at that age to be $459.42. In short, for "Net Single Premiums" in the foregoing table, you may read "Reserve Values of Paid-up Policies," for the two terms are precisely equivalent. 60 The Reserve Not the Property of the Individual Policy-Holder It is scarcely necessary to point out that while the reserve on a paid-up policy at the age fifty-six is $621.1 8j the reserve on the same policy one year later, at age fifty-seven, will be $632.51, and ten years later, at age sixty-six, will be $734.27, as shown in the fore- going table, page 59. This enables us to correct an- other very common misconception as to the nature of the reserve. The beginner often conceives the idea that the reserve is a distinct fund belonging to each policy — a fund which goes on accumulating at three per cent, interest until the death of the insured, when it is applied in part payment of his policy ; or, if he continues to live, accumulating until he reaches the age of ninety six years, when it amounts to the face of the policy. This view of the reserve is essentially erroneous. Take for instance the reserve of a paid-up policy at age fifty- six, to wit: $621.18. Add three per cent, interest ($18.64) and you obtain $639.82, while the actual reserve one year later as shown by the table (see age fifty-seven), is only $632.51. In like manner, com- pounding the interest for ten years on $621.18, the reserve at fifty-six, you will obtain a much larger sum than $734.27, the reserve at age sixty-six; while on the same basis the reserve of $621.18 at age fifty-six would amount to $1,000 long before reaching the age of ninety- six. The error consists in assuming that the reserve is a distinct fund specially belonging to each policy and 61 never drawn upon until applied as part payment of that policy at death. In life insurance the reserve is the common insurance fund belonging to the whole body of policy-holders, — not their property as individuals, but as a company. It does accumulate at three per cent, interest, but is constantly drawn upon, both principal and interest, for the payment of claims. For many purposes it may at any time become desirable to ascertain the pro rata portion of the reserve on hand pertaining to each policy in force, as we have done in this discussion, but this does not mean that the ascertained pro rata reserve is in any case a distinct fund actually belonging to that policy, or to the holder thereof as an individual. Neither can the terminal reserve, even in the case of a paid-up policy, be determined by adding three per cent, to the reserve of the preceding year, for the reason that the fund is constantly drawn upon to meet the demands of the current mortality. At age ninety-five, and at that age only, this process will give the correct result, because the limit of life is reached at ninety-six. Reserve Tables In the Verification Table (column 9) is shown the pro rata terminal reserve for each year in the case of an Ordinary Life policy issued at age fifty-six. Tables have been constructed showing the pro rata reserve at the middle and end of every policy year, corresponding to various forms of policies issued at any age. The initial reserve, which is the reserve at the beginning of a policy year, is found by adding the terminal reserve of the preceding year to the net premium. The balance on hand at the middle of the policy year is termed the 62 Mean Reserve. It is, of course, one-half of the sum of the initial and terminal reserves of that year. Rapid Accumulation of Reserves Referring again to the Verification Table, observe that, although no new insurance is written by our hy- pothetical company, the total reserve rapidly increases until the end of the fourteenth year, when it amounts to $15,837,373.42. From that time on the aggregate amount decreases yearly because of the greater drain resulting from an increasing death rate. Uninformed people are prone to conclude, on per- ceiving how greatly the premium receipts in the earlier years exceed the death claims, that we are collecting more money than necessary, and that the net premium is larger than need be. Advocates of assessmentism and of other unscientific forms of life insurance constantly urge this view; but to perceive the fallacy involved we have only to glance down the table to age sixty-eight, in the thirteenth year, to find the death claims already exceed- ing the premium receipts; while twelve years later, at age eighty, the yearly mortality is over three times the premium income. Uninformed persons also complain of the enor- mous reserves piled up by life insurance companies, not knowing that the accumulation is merely the result of a low mortality in the earlier years, thus leaving a large balance on hand at the end of each year, every dollar of which, however, will be needed to meet the much higher mortality of later years. If the death rate were uniform through life, the same number per thousand dying at age 63 twenty as at age eighty, the premium, which would be the same for all ages, would be precisely sufficient for the payment of current death claims, leaving no balance at the end of the year, and no large accumulation would be necessary. The reader will readily perceive that if new mem- bers in large numbers were added to our hypotlietical company each year, the aggregate reserve would increase still more rapidly, and if the yearly additions to the membership were steadily maintained at a uniform rate, it would necessarily be many years before the accumula- tion of funds would become stationary; yet every dollar of this reserve would be needed ultimately for mortality purposes, being merely the balance on hand of the insur- ance fund mathematically necessary for the final pay- ment of outstanding policies. The Meaning or Large Reserves As an illustration of the rapid accumulation of the reserve in actual practice, that of The Mutual Life Insurance Company of New York, which amounted to $366,620,552.73 on the 31st of December, 1904, had in- creased ten years later, on December 31, 1914, to the sum of $496,438,884, not including the Company's con- tingency reserve, reserve for supplementary contracts, and accumulations for deferred dividends of over seventy millions more. This increase has been merely com- mensurate with the rapid growth and increasing obli- gations of the Company, and the fund is no greater than it was ten years ago in proportion to the requirements of existing policy contracts. Likewise our "hypothet- ical company" (see Verification Table, pages 46 and 64 47) is no stronger at the end of eight years with a reserve of $12,292,773.41, or at the end of fourteen years with a reserve of $15,837,373.42, than at the end of its first year, with only $1,857,110.99; since in each case the balance on hand is merely the amount which is mathe- matically necessary, in connection with future premiums called for by existing policies, for the ultimate payment of those policies. For the same reason the company is no stronger at the end of thirty-five years, when the pro rata reserve pertaining to each policy is $872.18, than at the end of its first year when it is only $29.90. The amount of the reserve at any given time depends also upon the nature of the business written. Were the members of our hypothetical company each insured under a Thirty- Year Endowment contract, the necessary reserve or insurance fund at the end of the thirtieth year would be $4,193,000 instead of $3,277,- 749.20, since the policies of the 4,193 members still living would all be payable in full at that time. In endowment insurance the reserve necessarily equals the face of the policy at the end of the endowment period, and (if the endowment is payable before age 96) is correspondingly larger in each preceding year than the reserve of a Life policy. The reader will perceive the absurdity of exploiting the ratio of "Accumulated Re- serves to Mean Insurance in Force," sometimes re- sorted to in comparing one regular life insurance com- pany with another, the company with the larger reserves per $1,000 of outstanding insurance (both being on the same reserve basis) absurdly claiming to be the stronger institution. 65 CHAPTER VII THE AMOUNT AT RISK WHEN a life insurance policy matures as a death claim, the difference between the face of the policy and the terminal reserve may be regarded as the net loss to the company, for the reason that the pro rata reserve of the policy represents the amount of that policy's con- tribution to the insurance fund which still remains on hand. In other words, the pro rata reserve of the policy may be regarded as the amount which it contributes towards its own payment. The difference between the face amount of the policy and the reserve is therefore called the Amount at Risk, and the reserve itself has been termed Self Insurance. These are technical terms, useful in the statement of certain propositions, but not to be understood in their literal sense. Strictly speaking, the maturing of a policy by death can not be regarded as a loss to the company, either in whole or in part, provided the mortality of the company is not in excess of that indicated by the table upon which its rates are based. (See page 34). It is the business of a life insurance company to pay death claims, and the entire cost of the payment, whether the particular policy has been in existence for a day or a year or for many years, has been provided for in the premium rates. The pajrment of a death claim is no more a loss to the company than is the payment of its ordinary expenses, full provision for the one item hav- ing been made in the reserve or insurance fund, for the other in the loading. 66 An Endowment policy maturing by completion of the endowment period is technically and literally a Claim, not a Loss. On the other hand, a policy maturing by the death of the insured may be technically termed a Loss, but is literally a Death Claim. It is a claim for its face amount, and the face of the policy is literally, though not technically, the amount at risk. The latter term is in general use, and its technical signification is fully established and must be kept in mind. The use of the term wiU be clearly illustrated by the following table, based on the figures of our hypothetical company, (See Verification Table, pages 46 and 47.) No. of Face of Terminal Amount No. of n-ad Age Members Policy Reserve At Risk Deaths Year 56 63,364 $1,000 00 $29 90 $970 10 1,260 1 60 67,917 1,000 00 150 33 849 67 1,646 5 70 88,569 1,000 00 437 25 662 75 2,391 15 80 14,474 1,000 00 676 42 323 58 2,091 25 85 5,485 1,000 00 78173 218 27 1,292 30 90 847 1,000 00 872 18 127 82 385 35 95 3 1,000 00 1,000 00 000 3 40 Cost of Insurance Taking the amount at risk in its technical sense as the actual loss in the case of a death claim, we determine the mortality cost, or Cost of Insurance, for the year as follows. At age fifty-six the amount at risk on an ordi- nary life policy in the first year is $970.10. Of the 63,364 members comprising our hypothetical company, 1,260 will die during the year, making the net loss $970.10 multiplied by 1,260 or $1,222,326, which is the total cost of insurance for the year. Dividing tliis amount by 63,364, the number living at the beginning of the year, we obtain $19.29, which is the pro rata cost of 67 insurance per $1,000 for the first year. In the fifth year the amount at risk is $849.67, and multiplying this by 1,546, the tabular number of deaths, we get $1,813,- 589.82 as the total cost of insurance for the year. Di- viding by 57,917, the number living at the beginning of the year, we obtain $22.68 as the cost of insurance per $1,000 in the fifth year. At ninety the amount at risk is $127.82 and the total cost of insurance is that sum multi- plied by 385, or $49,210.70. Dividing by 847, the number living at the beginning of the year, we obtain $58.10 as the cost of insurance per $1,000 in the thirty-fifth year. Mortality The death rate per 1,000 lives as indicated by the mortality table is termed the Tabular Mortality. If the lives insured have been well selected, the Actual Mortality will probably be less than the tabular, or that which was expected according to the table. If in the fifth year of our hypothetical coHipany, for instance, the number of deaths should be only 1,500 instead of 1,546, the actual cost of mortality would be the amount at risk, $849.67, multiplied by 1,500, the actual number of deaths, or $1,274,505. In that case we should have: Total cost of Insurance, or Expected Mortality - $1,318,589.82 Actual Mortality 1,274,505.00 Saving in Mortality $39,084.82 In legitimate life insurance the ratio or per- centage of "Death Claims Incurred to Mean Amount of Insurance in Force," so often exploited in competitive literature, is of no significance whatever since it ignores 68 two essential factors — the ages of the insured and the amount of reserves accumulated. Likewise the ratio of the "Face Amount of Death Claims Incurred to the Face Amount of Expected Death Claims" is misleading, for the reason that again the accumulated reserves are ig- nored. Only by comparing the total amount at risk on accruing claims (actual mortality) with the total amount at risk on expected claims as indicated by the mortality table ("cost of insurance" or expected mortality), can we determine whether or not there has been a Saving in Mortality. To illustrate: Our hypothetical company has at the beginning 63,364 members at age fifty-six, with $63,364,000 insurance in force. (See Verification Table, pages 46 and 47, also Amount at Risk, page 66). Twelve hundred and sixty members, according to the table, are dead at the end of the year, making total death claims $1,260,000. Dividing we obtain the ratio of "Death Claims to Insurance in Force," to wit: $19.88 per $1,000, or practically twenty deaths per thousand members. ($1,260,000 :63,364=$19.88.) In the same way the "insurance in force" during the fifteenth year, when our members have attained the age of seventy years, is $38,569,000, the death claims $2,391,000, and the mortality per $1,000 is $61.99, or nearly sixty-two deaths per thousand members. In this instance the apparent mortality, or the ratio of death claims to insur- ance in force, is over three times that at age fifty-six j and yet in either case we have only the normal mortality, or precisely what we counted on and provided for in the computation of the premium. 69 The apparently high death rate at seventy does not affect the financial condition of our hypothetical company, conducted as it is on a plan which is mathe- matically correct. In fact, without increasing premium rates in the least, it is precisely as easy, because of the accumulated reserves, to meet the mortality of $61.99 per $1,000 at age seventy as that of $19.88 at age fifty- six. Indeed, notwithstanding the death claims at seventy are largely in excess of the premium income — ^in excess, in fact, of total income — the reserve pertaining to each policy in force at the end of the year has grown to $437.25, an increase of $26.63 over that of the previous year (see Verification Table, pages 46 and 47). In the same way at age eighty-five, with $235.55 of death claims per $1,000 of insurance in force, and with total death claims amounting to nearly five times the premium income and to over three times the total income, the mortality is promptly met, while the individual reserve increases as before from $761.12 to $781.73. That is to say, in legiti- mate life insurance, so long as the actual mortality does not exceed the expected, it is immaterial whether the ratio of death claims to mean insurance in force is $19.88, or $61.99, or $235.55 per $1,000; i. e., whether the death rate is 20, or 62, or 236 per 1,000 members. The mortality is precisely what was expected and what has been provided for, and is as easily met in the one case as in the other. On the other hand, in assessment life insurance a death rate in excess of ten per 1,000, or a mortality of more than ten dollars per $1,000 insurance in force, is significant; for it means increasing assessments and cost, with the inevitable result of a decreasing member- 70 ship and ultimate dissolution. The relatively small emergency funds of the assessment society are insufficient to meet the increasing death claims pertaining to the increasing ages of the several members. In legitimate life insurance the reserve pertaining to each policy increases proportionately with the advancing age of the policy-holder, and the ratio of Actual to Expected Mortality, which takes into account these accumulating reserves, is alone of any significance. The Average Age In 100,000 persons all of the age of thirty-five years, the tabular or expected deaths according to the American Experience Table (see page 13) will be 89.'5, a mortality rate of 8.95 per thousand. In the same number of persons of various ages but with an average age of thirty-five, the tabular or expected mortality may or may not be 8.95 per thousand. It depends upon the relative proportions of young and aged members, not upon the average age. For example: In 50,000 persons all of the age of twenty years, the tabular number of deaths will be 390. In the same number of lives at age fifty the tabular deaths will be 689. The average age of the 100,000 persons will be thirty-five, but the total deaths according to the mortality table will be 1,079, (390-(-689), a death rate of 10.79 per thousand. Thus it is apparent that the average age of a body of men is of little significance. The normal or tabular death rate at age thirty-five is 8.95, but in a body of men whose average age is thirty-five, an actual mortality 71 of 10.79 or more may or may not be excessive. All depends upon the several ages of the individual members. Nothing can be predicated upon the average age. Probability of Dying At age fifty-six, of 63,364 persons, 1,260 will be dead at the end of one year according to the American Experience Table of Mortality. The Probability of Dy- ing within the year, therefore, will be represented by the fraction ^l^s^s^o^ . This fraction is equivalent to the deci- mal .019885, which means a death rate of 19.88 per 1,000. Of the same body of men there will be 62,104 still living at the end of the year, so that the Probability of Living through the year will be |.|.'i^^, equivalent to the decimal .980115. Observe that the smii of the two decimals is unity, the probability of living being the com- plement of the probability of dying. Again, of 63,364 persons living at age fifty-six, 2,585 will be dead at the end of two years, the proba- bility of dying within that period being -^^^^^, or .040796, while the probability of living beyond that period is ||;-m , or .959204. The Expectation of Life The Expectation of Life is the average length of time that a number of persons of a given age will live according to the specified table of mortality. Thus, taking the case of our hypothetical company, it is as- sumed by the American Experience Table (page 13), that of the 63,364 persons living at age fifty-six, three will live thirty-nine complete years, to age 95— the last 72 one of the three not heyond age 96, — eighteen will live thirty-eight full years, 2,091, twenty-four fuU years, 1,980, nine full years, 1,260, less than one fuU year, etc., and that the whole body will live for an average time of 16.72 years, which is accordingly the expectation of life at age fifty-six. A better term than "expectation of life" is that of Average Future Lifetime, or Average After-Lifetime. The expectation of life at a given age does not mean that one-half of all persons living at that age will die in that time. For example: At forty-three, the expectation of life is twenty-six years, but it does not follow that half the persons now living at age forty-three will die within the next twenty-six years. On the con- trary, by reference to the mortality table (page 13) it will be seen that of 75,782 persons living at forty-three, 40,890, or considerably more than half, will stiU be living twenty-six years later at age sixty-nine. One half of the original nmnber, 37,891, according to the Table, wiU die within twenty-seven years, three months, and twelve days. This period — the length of time during which one- half of the persons of a given age will continue to live — is technically termed the Probable Life — ^the French term, Vie Probable, being commonly used. The term is not a satisfactory one, since there is in every case a defi- nite probability, according to the Table, of living to any age up to ninety-six, the degee of probability varying ac- cording to the length of the period under consideration. Inasmuch as 40,890 of 75,782 persons living at age forty-three will still be living at age sixty-nine according to the table, the probability at the former age of living to sixty-nine will be expressed by the fraction tf.'ttIi 73 while the probability of living fifty years, or to age ninety-three, will be expressed by i^j^j-g-^ > or .001042, since out of 75,782 persons at forty-three, seventy-nine will still be living at ninety-three. The foregoing observations sufficiently illustrate the fallacy involved in the notion entertained by the advocates of assessment insurance that the expectation of life has any relation to the cost of life insurance. It is an error to suppose that a man who bids fair to live through his expectation of life is for that reason a good risk, or that the man who has paid his premiums for that length of time has paid the full cost of his insurance. If every member of our hypothetical company still living at the end of seventeen years — his expectation of life — were then to be relieved of paying further premiums, the total receipts from that source would be reduced by several millions (see Verification Table, pages 46 and 47), and the net premium of $47-76 would have to be materially increased. The distinction should be made between the probability of dying within a certain number of years, and the probability of dying in a particular year. At forty-three, the chances of dying within twenty-seven years, three months, and twelve days, or of living beyond that period, are even; but, while a man of forty-three is more likely to live to sixty-nine than to seventy-five, he is at the same tim.e more likely to die at seventy-five than at the particular age of sixty-nine, since out of 75,782 living at forty-three, 2,476 will die at seventy- five, against 2,321 at sixty-nine. Again at age thirty-five the expectation of life is 31.78 years, but the probability of dying in the thirty-second year thereafter, at age 74 sixty-six, is not so great as that of dying in the thirty- third, or in the fortieth, or even in the forty-fifth year. Expectation op Life not Used in Computing Cost OP Life Insurance The expectation of life cannot be used in com- puting the premium for the reason that the computation of compound interest as involved in the cost of life insur- ance is impossible on the basis of the average after-life- time. Compound interest is an essential factor in the computation of the premium, but, for the reason stated, the calculation must be made from year to year instead of upon the basis of the average time involved. The theory that the expectation of life may be used as a basis for computing the probable cost of life insurance, is one of the widespread errors of assessmentism, which the intelligent life agent should be prepared to refute. 75 CHAPTER VIII THE LOADING UP to this point we have dealt with the net premium only, the whole of which is calculated for mortality purposes. As a provision for expenses and other con- tingencies, a specified sum called the Loading is added to the net premium, the two combined making up the gross premium as given in the rate book. The Loading is sometimes a percentage of the net premium; in other cases it is composed of two parts — a constant sum (as $2 per $1,000 of insurance, the same at all ages), and a percentage of the net premium; while various other methods are employed, the plan vary- ing with different companies, and often with different forms of policies in the same company. On the theory that it cost no more to care for a policy issued to a member sixty years of age, than for one issued at age forty or twenty, the claim is sometimes made by the advocates of assessmentism, that the loading should be a constant sum at all ages, instead of being, in whole or in part, a percentage of the net premium. This position rests upon a false premise — ^that the loading is for expenses only. The theory is also untenable on other grounds. The loading is not for expenses only, but is in- tended to provide for all other possible contingencies, such, for instance, as a mortality in excess of the tabular rate, interest earned less than the assumed rate, deprecia- tion in the values of securities, loss of invested funds, etc. While the assumptions as to interest, mortality, etc., in 76 While the assumptions as to interest, mortality, etc., in the computation of the premium, have been on the most conservative basis, nevertheless, so long as human judg- ment is fallible, the possibility of error must be conceded. The foundation principle of life insurance is safety, and if mistakes are to be made at all, they must be made on the side of safety. It is better to collect too much money than too little; hence the importance of making provision for unforeseen contingencies. But mortality, interest, investments, etc., all affect the cost of life insur- ance; wherefore, that part of the loading which is de- signed to cover possible excessive mortality, deficit in interest earnings, etc., has a direct relation to the cost of the insurance, and, like the net premium, must vary with the age of the insured. This is accomplished by making it a percentage of the net premium. Neither is it true that the expense incident to a policy issued at sixty is no more than that pertaining to a policy issued at forty or twenty. The chief item of expense with any company is that of commissions, and this is almost universally a percentage of the premium; wherefore the "loading" to provide for that expense must be greater at sixty than than at forty or twenty. Taxes levied by the various states are an important part of a company's expenses, and these also are almost always a percentage of the premium income. It is the common practice of assessment people to refer to the loading as exclusively an appropriation for expenses, charging directly that it is all appplied to that end. In refutation of this charge the agent will explain the true office of the loading as set out above, and will also point out the fact, that so much thereof as may not 77 be required for the purpose designated is subsequently returned to the policy-holder when a division of savings, is made. For example: Of the loadings coUected by The Mutual Life Insurance Company in 1919, there remained at the end of the year an unexpended balance of no less than $2,678,210.86 available for return to policy-holders. To Ascertain the Loading The amount of the loading can be ascertained by taking the difference between the net and gross pre- miums. Tables of net premiums and reserves for various forms of policies at the several ages and on diiFerent reserve bases are published in convenient form for refer- ence. For example: The net premium of an Ordinary Life policy of $1,000, issued at age thirty-five, American Experience Table and three per cent, interest, is $21.08. If the gross premium for such a policy is $28.11, the difference, $7-03, will be the loading. The net premium of a particular policy, however, cannot always be ascertained from the published tables, since the amount depends upon the guarantees contained in the contract. To illustrate: On an Ordinary Life policy of the usual form but on a three and a half per cent, reserve basis, the net annual premium at age thirty- five is $19.91, and the regular reserve at the end of twenty years will be $810.75. On such a policy, how- ever, as issued in the past by The Mutual Life, with a twenty-year distribution period and a gross premium of $27.88, the company guarantees a cash surrender value 78 at the end of twenty years of $S89, which necessarily requires a larger net annual premium than $19.91. The Cash Value, or Cash Surrender Value, of a policy is the amount which the company will pay to the withdrawing policy-holder in cash for the surrender and cancellation of his contract. It is usually a large fraction of the reserve pertaining to the policy, rarely the full reserve until after some years. Inasmuch as, the- oretically, only the good risk will' surrender his policy for cash, the invalid preferring to maintain his insurance in force, it is customary for a company to retain a part of the reserve pertaining to withdrawing policies, as a Surrender Charge to compensate for the anticipated se- lection against the company. (See page 56.) In view of the guaranteed cash surrender value of $389 on the policy ahove described, persons not versed in the scientific principles of life insurance sometimes assert that The Mutual Life is offering a cash value of $78.25 in excess of the accumulated reserve, a practice which they characterize as unwise if not dangerous. The answer is simply that the cash value named is not in excess of the reserve actually held by the company against that policy. If, for example, the contract, instead of being an Ordinary Life of $1,000, were a twenty-year pure endowment of $389, with term insurance of $1,000, everyone would readily understand that the com- pany would necessarily hold a reserve of $389 at the end of twenty years, since the reserve must equal the face of the endowment at the end of the endowment period. Now, although The Mutual Life contract re- ferred to is in form an Ordinary Life with a gross pre- mium of only $27.88, inasmuch as the company guaran- 79 tees to pay $389 cash at the end of twenty years^ the policy becomes virtually a twenty-year pure endow- ment for that amount (besides the $1,000 term insur- ance), and under the law the company is required to accumulate against it a reserve to the full amount of that endowment, to wit: $389. In other words, every com- pany is obliged to maintain a reserve sufficient to make good every guarantee contained in its contract. To accumulate a reserve of $389.00 in twenty years necessarily requires a larger net premium than to accumulate one of $310.75. It follows that the net pre- mium of The Mutual Life policy described is consider- ably more than $19.91, and the loading correspondingly less than $7-97. To accumulate a reserve of $389 in twenty distribution policies, issued since 1898 with a dividend period of fifteen or twenty years, which includes most of the business written between 1898 and 1907, are larger than those guaranteed by most other companies, even though the latter may be on a higher reserve basis and collect a larger gross premium. This simply means that the loading in the case of the Mutual Life policy under discussion is less, and that the company sets aside a somewhat larger part of the gross premium for reserve, and a somewhat smaller amount for expenses and con- tingencies. A Misleading Ratio The foregoing observations illustrate the unfair and misleading character of such a ratio as that of "Expenses Incurred to Loading Earned." It is very 80 often the case that the company which shows the smaller ratio of expenses to loading is able to do so by virtue of the fact that it has a much larger loading to start with than its competitor. With the same gross premium, the former may have a loading of $7-97, while the latter has but $5 or $6. The former may have a saving from loading, simply because it has a large loading to begin with. The latter may have no saving from this source and yet be the more economically managed of the two ; or, it may have a very large saving from loading, as The Mutual Life has, but in either case the ratio would fail to give it proper credit. Net Valuation The insurance laws of the several states require every regular life insurance company to have on hand at all times cash or approved securities not less in amount than the Net Value of its oustanding policies, ac- cording to the Minimum Legal Standard of Valuation. By Net Value is meant the amount of the reserve pertaining to the policy at any stated time. It is always the difference between the present worth of the net premiums to be paid on the policy, and the present worth of the benefits guaranteed thereunder — such as amounts payable at death, at maturity, on surrender, etc. Net Valuation is the process of determining the legal net value or reserve of a company's outstanding policies, the net premium only — ^not the gross premium — ^being considered. To understand what is meant by the term Minimum Legal Standard of Valuation, ob- serve that in the computation of the premium it is SI assumed that the reserve will earn a specified rate of interest. In the case of our hypothetical company the rate assumed is three per cent. On this basis, the required net annual premium of an Ordinary Life policy issued at age fifty-six was found to be $47-76. The reserve or in- surance fundj consisting of the net premium receipts plus the interest earned thereon at the assumed rate, suffices for the payment of all existing policies at maturity. It is obvious that, in order to accumulate a spe- cific sum of money, as the reserve of a life policy, within a stated time by means of small yearly deposits or pre- miums, the deposits must be larger, and the fund on hand at any time prior to age 96 must be greater, if the inter- est to be added to the fund is at the rate of only three per cent, than if three and a half or four per cent, inter- est is to be received. It is, therefore, equally clear that, if the net premium receipts of a life insurance company were certain to earn three and a half or four per cent, interest, the premium rates necessary to provide funds sufHcient for the payment of all policies at maturity would be smaller than when it is assumed that only three per cent, interest will be realized. In other words, when the reserve is to be accumulated at three per cent inter- est, larger net premiums are necessary than when a higher interest rate is assumed. In all cases, whatever the rate of interest as- sumed, the reserve at the attained age of ninety-six is equal to the face amount of the policy. Observe that in our Verification Table the reserve at the end of the thirty-ninth year at the attained age of ninety-five is $923.11. That sum plus the next year's net premium, $47-76, plus three per cent, interest, amounts to $1,000 82 at the end of the year at the attained age of ninety-six. Had it been assumed in the computation that the funds would earn four per cent., the required net premium would have been only $45 instead of I47.76, and the reserve at the attained age of ninety-five would have been $916.54 instead of $923.11. Observe that $916.54, plus the next year's net premium of $45, plus four per cent, interest, likewise amounts to $1,000 at the end of the year at the attained age of ninety-six. Thus, as stated before, the higher the rate of interest assumed, the smaller will be the reserve pertaining to any policy. A three and one-half per cent, reserve is larger than one computed on a four per cent, basis and smaller than a three per cent, reserve. The laws of the several states prescribe the maximum rate of interest that may be assumed, and the mortality table that shall be used, in computing the reserve or net value of a company's policies. This re- quirement is termed the Legal Standard of Valuation. The net value computed by the legal standard is termed the Legal Net Value or Legal Reserve. In several states the rate of interest fixed by the Minimum Legal Standard, or the lowest standard prescribed by law, is four and one-half per cent. — in others four per cent. In New York, Massachusetts, and one or two other states, the minimum legal standard calls for three and one-half per cent, interest, so that a company whose premiums are computed on a four per cent, reserve basis must, in order to do business in those states, submit to a valuation by the higher standard of three and one-half per cent. Many companies, such as The Mutual Life, hav^ adjusted their premiums for new business 83 to a 3 per cent, basis, and are accumulating 3 per cent. reserves accordingly, notwithstanding the lower mini- mum standard authorized by law. Determining the Net Value Knowing the ages of the several policy-holders, we may determine how many of these, according to the mortality table, will die in each year thereafter, and how many will be living at the end of each year, and hence may compute the amount of claims to be expected in each year until all existing policies have matured, either by the death of the policy-holder or the expiration of the term for which the contract was written. Having these data we may compute the present worth or present value of all outstanding policies — that is, the sum which ac- cumulated at a given rate of interest, say three per cent., will make an amount sufficient to pay every policy in full as the policies mature. (See Computation of Premium, page 12.) In like manner, knowing how many policy-holders will be living according to the table at the beginning of each subsequent year, to pay the premiums called for by the several policies, we may determine the net premium income of each year until the last existing policy has matured. Hence we may compute the present worth of all future net premiums to be collected on outstanding policies. Let us now take for illustration the case of a com- pany which has just issued 100,000 policies, aggregating 84 a total of $100,000,000 insurance. Assume that the pres- ent worth of those policies — ^that is, the present worth of the benefits to accrue under their terms, is found to be $37,055,000. This sum then constitutes the present value of the policy obligations which the company has assumed. To pay these policies as they mature, the company has no other certain resource than the net premiums stipulated to be paid thereon plus the interest which those premiums will earn at the assumed rate, say three per cent. If now the present worth of these premiums is likewise found to be $37,055,000, it is obvious that the company is solvent and will — if three per cent, interest is earned and the mortality does not exceed that indicated by the table — be able to meet its obligations at maturity. A statement of its assumed condition would be as follows: Credit Side Present worth of net premiums to be col- lected on existing contracts $37,055,000 Debit Side Present worth of benefits under outstanding policies $37,055,000 Such would be the exact status of a legally sol- vent mutual company the day it begins business, after a number of policies have been written but before any premiums have been collected. Let us, however, take the same company after several years' premiums have been collected and a num- ber of policies paid, a reasonable amount of new business having been written in the meantime. As some of the net premiums called for by existing contracts have been 85 received and disbursed, the present worth of the pre- miums remaining to be collected will no longer equal the present worth of benefits under policies now outstanding. Assume, for example, the present worth of those benefits to be now $38,000,000, and the present worth of future net premiums, $34,000,000. The present worth of bene- fits promised, or obligations assumed, will be larger than at first, because every existing policy is nearer matur- ity, while the present worth of net premiums to be col- lected in the future will be less than before, because some part of the premiums originally called for by every existing policy have already been collected. Our debits then in this case woidd exceed our credits by $4,000,000, and the statement would now be as follows: Credit Side Present worth of net premiums to be collect- ed on existing policies $34,000,000 Deficit 4,000,000 $38,000,000 Debit Side Present worth of benefits under outstand- ing policies $38,000,000 The company is now clearly insolvent under the law, for the present worth of net premiums to be received — its only apparent resources — is $4,000,000 less than the present worth of the benefits to be paid. This deficit represents the Legal Reserve Liability of the company — that is, the Net Value of its outstanding policies ac- cording to the legal standard of valuation, being the dif- ference between the present worth of the benefits for which the company is liable under its policies, and the 86 present worth of all the net premiums to be received. If the company, however, after providing for the tabular mortality and matured endowments, has reserved from year to year the balance of its net premium and interest income, the funds so reserved will now aggregate exactly the amount of the computed reserve liability. In other words, it will have on hand the reserve required by law to maintain solvency, and the statement of its condition will now assiune the following form: Credit Side Present worth of net premiums remaining to be collected on existing policies . . . $34,000,000 Reserve (cash and invested funds) 4,000,000 $38,000,000 Debit Side Present worth of benefits contracted for in outstanding policies $38,000,000 This suggests the definition of the legal reserve given above, to wit: "A fund equal in amount to the excess of the present value of benefits under outstanding policies over the present value of net premiums to be paid on those policies." On the basis of the statement as last rendered, the company is technically solvent, since the credits and debits are equal. The form of the statement may be simplified by eliminating the two items, "Present worth of net premiums" and "Present worth of policies," and simply carrying to the debit side of the account the difference between the present worth of policy obliga- tions and the present worth of premiums to be collected, 87 ■which is the company's legal reserve liability, or the net value of the benefits guaranteed under its outstanding policies. As the company holds cash and invested funds to the amount of this liability, the statement will assume the following form: Crbdit Side Cash, invested funds, and credits (Assets). .$4,000,000 Debit Side Net value of all outstanding policies (Lia- bility) $4,000,000 The Test or Solvency The comparison of a company's Admitted Assets — money, invested funds, and valid credits, approved by the insurance authorities — with its total liabilities consti- tutes the legal test of its solvency. By the financial statement last above set out, the company in question is legally solvent — its assets being exactly equal to its lia- bilities; nevertheless, a company in just that condition would in fact be upon the verge of bankruptcy, for the loss of a small amount by depreciation of values, extra mortality, or other cause, would render it insolvent un- der the law. Such being the case, it is of the first im- portance for every company to maintain as a margin of safety an additional fund in excess of all legal liabilities, variously termed "surplus," "indivisible surplus," "un- assigned funds," etc. Under the New York law this ex- tra fund or margin of safety is called the Contingency Reserve. Assuming that the company in question has such additional funds to the amount of $1,000,000, a statement of its financial condition would then read: Admitted Assets Cashj invested funds, and credits $5,000,000 Liabilities Net value of all outstanding policies $4,000,000 Contingency reserve (surplus) . . 1,000,000 $5,000,000 A Misleading Ratio In the above case, a loss of assets in excess of $1,000,000 would sweep away the contingency reserve and render the company insolvent. The smaller the amount of such additional fund, the more imminent the danger. It is obvious, therefore, that the measure of a company's strength is to be gauged rather by the amount of extra or surplus funds which it holds in addition to the legal reserve or net value of its outstanding policies, than by the percentage which such extra funds are of the total liabilities, i. e., the company's "Ratio of Assets to Liabilities." For example : According to the statistics for a recent year, a certain company of well-known excellence had surplus funds at the end of that year of more than $3,600,000, and a ratio of admitted assets to liabilities of 106.6; that is, its assets exceeded its liabili- ties by only 6J4 per cent. On the other hand, the assets of a smaller com- pany of considerable prominence exceeded its liabilities by twenty-nine per cent., yet its total surplus funds were less than $130,000. Assuming that the assets in each case were of the highest class, there can be no doubt as to the 89 relative strength of the two organizations — the fact being the reverse of what might be inferred if only the ratios cited were to be considered. A surplus of only $1 30,000 might readily be wasted or lost in a single transaction- far more readily, it will be conceded, than a surplus of more than $4,000,000. A stiU more striking illustration of the misleading character of this ratio is afforded by the figures of a still smaller company with a ratio of assets to liabilities of 592 and a total surplus of less than $21,000. Eeserve Basis Must Be Considered There is another test, however, that is too often overlooked by the ordinary insurance man as well as by the insuring public, and that is the question of reserves. Let us compare two companies, A and B, assuming that each has $100,000,000 of insurance in force, all issued 10 years ago, at age 40, on the Ordinary Life plan. Let us also assume that each company, by the valuation of the insurance department, shows a surplus of $1,000,000. The natural assumption would be that the two companies are of equal strength, but this does not necessarily fol- low. Neither company knows in advance what rate of interest will be earned during the entire existence of its outstanding policies. In order to be on the safe side, Company A assumes that it will earn as little as SJ4 per cent, and, accordingly, it must create and maintain a reserve or insurance fund which, with future net premi- ums received and interest added thereto yearly at 3J^ per cent., will suffice for the payment of all accruing claims each year until the total of $100,000,000 has been 90 paid. Company B, still more conservative, bases its calculations upon earning only 3 per cent. Accordingly, it must create and maintain a reserve which, with future net premiums received and only 3 per cent, interest add- ed thereto yearly, shall likewise be sufficient for the pay- ment of all accruing claims, until the total of $100,- 000,000 has been paid. As both companies are to pay the same amount ultimately, it is obvious that Company B, which adds only 3 per cent, to its reserve each year, must at all times maintain a larger fund than Company A, which adds 3J4 per cent, yearly. This illustrates the fact that a 3 per cent, reserve, at any and every date until the last policy matures, must be larger than a reserve based on 3J^ per cent. Tabulated Illustration Each company has $100,000,000 of outstanding policies all written 10 years ago at age 40. Turning to your reserve tables you will find that the reserve of an Ordinary Life policy issued ten years ago at age 40 on a 334 per cent, basis would amount now to $166.89 per $1,000, and on 100,000 policies of $1,000 each, the total reserve would be $16,689,000. The reserve tables also show that the 3 per cent, reserve of an Ordinary Life policy issued ten years ago at age 40 would now be $177.20 per $1,000, while the total reserve on 100,000 policies of $1,000 each would be $17,720,000, the amount held by Company B. As each company has $1,000,000 of surplus, the financial statement in each case would be as follows: 91 Company A Reserve, 3^^ per cent $16,689,000 Surplus 1,000,000 Total Assets $17,689,000 Company B Reserve, 3 per cent $17,720,000 Surplus 1,000,000 Total Assets $18,720,000 Company B's reserve exceeds that of Company A by $1,031,000; but, if a 3J^ per cent, reserve is large enough for Company A, it should be large enough for Company B. If, therefore, we value the latter com- pany's business on a basis of 33^ per cent., the excess in the reserve of Company B will be transferred to surplus, and the two financial statements will stand as follows : Company A Reserve, 3}4 per cent $16,689,000 Surplus 1,000,000 Total Assets $17,689,000 Company B Reserve, syi per cent $16,689,000 Surplus 2,031,000 Total Assets $18,720,000 It now appears that our 3 per cent, company, valued on a 3J4 per cent basis, the same as Company A, 92 has a surplus more than double that of the latter com- pany. It is obviouSj therefore^ that, in quoting surplus as a test of strength, the reserve basis must be considered. With equal surpluses, the S per cent, company wiU be stronger than one on a syi per cent, basis; and the former may even have the smaller surplus and yet be the stronger company. In the foregoing examples, Com- pany B valued on a 3 per cent, basis, might show a sur- plus of less than half a million — indeed, it might show no surplus at all — and yet be stronger than Company A ; for, in the latter case, on a 3J4 per cent, valuation, it would still have a surplus of $1,031,000 against a surplus of $1,000,000 for Company A. Another extremely important point as between dif- ferent reserve bases is this : A 3 per cent, company will make surplus more rapidly than a 3^ or 4 per cent, com- pany. For example : suppose companies A and B both to be earning a net rate of 4J/2 per cent, interest. All inter- est earned by Company A in excess oi syi per cent. — that is, one per cent. — ^becomes surplus, while Company B has the excess over 3 per cent. — ^that is, one and one- half per cent. — or one-half more than Company A. It is obvious that Company B will the more quickly recover from unexpected losses, will the more quickly restore a depleted surplus, and the more readily withstand any unusual strain. Several modifications of the system of net valua- tion described in the foregoing pages have been estab- lished by recent legislation and will be explained in a later chapter. (Page 119 et seq.) 93 The Annual Statement The laws of the several states require every regu- lar life insurance company to file with the insurance department in every year as of the date of December 31, a sworn statement of its assets and liabilities, including the legal net value or reserve of all outstanding policies as determined by the minimum standard of valuation. As every such company is required under the law to maintain at all times a reserve not less in amount than the net value of all policies in force, such organizations are called "Legal Reserve" companies. They are also sometimes termed "Old Line" to distinguish them from Co-operative, Stipulated Premium, Fraternal, and other assessment organizations whose premium rates or assess- ments are not iixed, but are subject to increase as experience may demand. These assessment societies are not required by law to maintain an adequate reserve, nor are they subjected to any standard system of valuation to determine their solvency or the sufficiency of their rates, save that in certain states fraternal societies must submit to valuation, although not yet required to maintain mathematical solvency. So long as the funds on hand are sufficient to meet accrued death claims, little or noth- ing more is required of them. Future deficits are to be met by an increase of rates or a scaling down of death benefits, but the members of such assessment societies are prone to regard the probability of such a contingency as quite remote. CHAPTER IX GAINS OR SAVINGS IN LIFE INSURANCE IN the computation of the premium it was assumed that the mortality of our hypothetical company would correspond with the American Experience Table and that our funds would earn just three per cent, interest. Upon this hypothesis the net premium is precisely sufficient for the payment of all claims that may accrue. It follows that if the mortality of the company should exceed that of the table, and the rate of interest earned should be less than that assumed, our premium would be inadequate and our reserve would fall short of the requirements. It would be impossible, however, to construct an infallible table — - one that would indicate with absolute accuracy the mortality to be experienced. Inasmuch then as our actual death rate wiU certainly differ somewhat from the tabular, it is of the first importance that the variation be on the side of safety — a lower rather than a higher mortality. Accordingly, in the construction of the table all doubts have been resolved in favor of this position, with the result that in practice the mortality experience of every well-managed company is less than that indicated by the table upon which its premium rates are based. In like manner, as heretofore explained, it is morally certain that the actual interest earnings will be in excess of the rate assumed, so that in practice there will be a gain from both sources named, and our receipts will be in excess of the amount required to meet our obligations. 95 Sources of Gain To the end that the comments following may be readily comprehended, it is suggested that the reader keep the Veriiication Table (pages 46 and 47) before him for constant reference. Saving in Mortality In our hypothetical company of 63,364 members, all of the age of fifty-six, we have made provision for 1,260 deaths the first year, that being the tabular mor- tality. As each member is insured for $1,000, the expected death claims will amount of $1,260,000. Let us assume now that the actual deaths number only 1,160, making actual death claims $1,160,000, or $100,000 less than was counted upon and provided for in the premiums collected. The actual saving in mortality, however, is not $100,000; for at the end of the year, at the attained age of fifty-seven, we shall have 62,204 members living instead of 62,104. The 100 additional lives must be paid for ultimately, and in the valuation of its assets and liabilities, the company wiU be charged with a terminal reserve of $29.90 for each of these lives, making an additional reserve liability of $2,990. This sum being deducted from the $100,000 of death claims saved, makes the actual saving in mortality $97,010. In other words, the saving in mortality consists, not of the face amount of death claims saved, but of the amount at risk pertaining to those claims. In the case of our hypothetical company the amount of risk on each life during the first policy year is $970.10. (See page 67.) With one hundred 96 fewer deaths than were expected, the saving in mortality will be $970.10 X 100 = $97,010. The Actual Saving The beginner is sometimes puzzled at this stage by a problem which suggests itself in the following form: Kef erring to the saving in mortality of $97,010 in our first year, has this amoimt really been saved, or has its payment simply been deferred? After all, the one hun- dred lives are still with the company and will pass away within the limit of life, some very shortly, others after many years; and the policies represented by them must ultimately be paid. Instead of an actual saving of $97,010 then, do we not in reality save merely the interest on the $100,000 of death claims whose payment has been deferred? You have seen by the Verification Table that for each of the 62,104 members living at the end of the first year at the attained age of fifty-seven, we hold a terminal reserve of $29.90, and that these accumulated reserves plus the future net premiums to be received, will provide funds exactly sufficient for the payment of all existing policies as they mature. If this is true of 62,104! mem- bers, it will likewise be true of 62,204, or of 100,000, or of any other large number. We have therefore had an actual saving in mortality of $97,010, and have accumu- lated an actual profit or gain of that amount, since for each of the 62,204 members of the age of fifty-seven now belonging to the company, we hold a reserve of $29.90, and are to collect from each a net premium of $47.760895 every year hereafter, even as in the case of the original number of 62,104. 97 To illustrate further: let us take the case of the twenty-one members living at the age of ninety-four. Assume that there will be seventeen deaths instead of eighteen^ a saving of one. As the terminal reserve on one life is $923.11, the amount at risk will be $76.89, which will accordingly be the saving in mortality. The four lives now remaining will begin the next year at the attained age of 95, and, according to the table, none of these will live beyond the end of that year, or beyond the attained age of 96. The payment of the claim on the fourth life, therefore, is simply deferred for one year. Does it not seem, then, that the saving in mortality will be merely the interest on $1,000 for one year, to wit: $30, instead of the amount at risk, $76.89? Let us see how it works out. Taking age ninety- four, we have now four members living at the end of the year, at the attained age of ninety-five, instead of three, and we shall accordingly have a total reserve of $3,692.45 (making due allowance for decimal correction), instead of $2,769.34. ($2,769.34 + $923.11 = $3,692.45). Modifying the Verification Table accordingly, the opera- tions of the last year may be tabulated as follows : Net Premium Income at age 95 ($47.760895x4) $191.04 Add Terminal Reserve of preceding year. . . . 3,692.45 Initial Reserve, age 95 $3,883.49 Add one year's interest at three per cent 116.51 Terminal Reserve, attained age of 96 $4,000.00 The result proves that the saving in mortality is measured by the amount at risk, and not by the interest earned on the face of deferred death claims. 98 When Saving in Mortality is Greatest Experience has shown that the saving in mortality ■will be greatest in the case of business most^ recently ■written, owing to the culling out of impaired lives by medical examination. For instance, the mortality in the first year of insurance is rarely so much as fifty per cent, of the tabular rate, and is much less than the normal for several years longer. The benefit derived from medical selection, however, is commonly assumed to be lost within about five years, and much the greater part of it undoubtedly does accrue within that period. This does not mean that a thousand lives, five years after medical examination, would average no better physically than a like number of new risks, accepted without any examination at all. Any company which might adop't the latter course would be quickly overwhelmed with impaired lives that would not ordinarily apply for insur- ance because conscious of their inability to pass an examination. A Misleading Ratio The low death rate in the years immediately suc- ceeding medical examination is instrumental in effecting a large saving in mortality in the case of new companies, and of old companies writing a large new business. While this saving in mortality is largely offset by the increase in the expense account, owing to the relatively large cost of new business, it is also true that the new company, or the company writing a large new business will necessarily show a comparatively high expense ratio, owing to the 99 large outlay for commissions and other items of initial costj but this increased expense may be more than offset by the increased saving in mortality. The facts cited simply indicate the inevitably misleading character of an expense ratio which fails to take into account com- pensating conditions. Inasmuch as a low mortality is incidental to all new business and therefore to all new companies, whether assessment or "old line," the absurdity of citing it as something phenomenal, and as evidence of extraordinary care in selection of risks, is apparent. It is undoubtedly true that careful selection will go far toward increasing the saving in mortality; but it is likewise true that the low death rate of the new company is mainly attributable to the fact that it is new, its members, or a large pro- portion of them, being fresh from the medical examiner's hands. In addition to saving in mortality and excess of interest earned, there may be gains from other sources, though in a less degree. The loading for expenses and contingencies may be in excess of the requirements, or there may be an apparent saving by reason of reserves released on lapsed and surrendered policies. The word "apparent" is used because such savings are, under modern conditions, rarely more than enough, even if enough, to defray the expense of replacing the risks with new lives. Lapses Not a Desirable Source of Profit If all Life or Endowment policies written were to lapse at the end of two years, the forfeited reserves might constitute an important source of profit; or if all 100 policies were certain to lapse at the end of three or four years and not sooner, there would dou%tless be a profit from that source, notwithstanding a surrender value is allowed at the end of the third year. The amount that may be withdrawn at the earlier years is usually less than the full reserve, a part of the latter being retained by the company as a Surrender Charge. Although so much of the reserve as may be forfeited in the case of a lapsed or surrendered policy is technically termed a "gain" and necessarily appears as such in the company's annual statement, this supposed gain is largely or wholely offset by the fact that it is ordinarily the sound lives that lapse or withdraw. The man about to die, or whose health has become impaired, clings to his insurance. Thus lapses naturally tend to increase the normal proportion of in- valids and impaired lives in a company, resulting in an increased mortality. This is certain to be the case when the number of withdrawals is excessive through loss of confidence in the company or dissatisfaction with the management. This tendency of sound lives to withdraw and of impaired lives to maintain their insurance in force, or to seek new or more insurance, merely because they are in impaired health, is termed Selection Against the Company, or Adverse Selection. On the other hand, some extended observations would indicate that when lapsing is normal — not unduly stimulated by special causes — the withdrawals as a class may be little or not at all better than the risks remaining. Neverthe- less, the generally accepted theory is, that lapses tend to a deterioration of the business, and it is always a question of grave concern to the company whether the surrender charge exacted is sufficient to compensate for the adverse selection. 101 Lapses and Termination by Expiry It should be noted here that some companies give an extended insurance surrender value at the end of the first year^ or even at the end of the first quarter. If the premium is not paid and the policy is not surrendered for cash or paid-up value, the insurance is not entered on the books as lapsed, but becomes automatically a paid-up term policy good for a brief period, at the end of which, if not reinstated, it terminates by expiry. In some cases a small cash value is offered, even after the payment of but one quarterly premium. By this means the apparent number of lapses or withdrawals, most of which occur during or at the end of the first year, is very greatly diminished. The reader will per- ceive the absurdity of comparing the figures of official reports as to "lapsed and surrendered" policies, unless this class of terminations be included. Slight Gains from Saving in Mortality at the Older Ages Recent observations tend to show that improved sanitary conditions and the great advances made in modem medical science and surgery, have increased somewhat the average length of human life. The prob- able effect has been to prolong the lives of many who, under former conditions, would have succumbed in child- hood or youth to the effects of disease or injury. In the case of insured lives doubtful risks are eliminated, but as the accepted lives grow older the benefits of medical selection gradually disappear, and we find the actual mortality approaching more nearly to the tabular. For in2 this reason it may be anticipated that the saving in mor- tality will be slight in the case of insurance that has been long in force. As a matter of fact and for another reason, the saving in mortality does steadily decrease with the age of the policies, even though the actual death rate of the company continues to be much below the normal. This is because the saving is measured by the amount at risk, and not by the face of the claim. To illustrate: referring to the table on page 67, showing the amount at risk in the case of an Ordinary Life policy issued at age fifty-six, assume the actual mortality for a series of years to be $1,000 less than the tabular. The saving in mortality then will be $970.10 in the first year at age fifty-six, $562.75 at age seventy, $323.58 at age eighty, and $127.82 at age ninety. Savings Vary According to Reserve Basis The savings or gains will vary accoMing to the reserve basis, the gain from interest being greater in case of a three than of a three and a half or four per cent, reserve. To illustrate, for example, the gain from interest earned in excess of the assumed rate, suppose the rate actually earned to be 5 per cent. The gain in the case of a three per cent, reserve will, then, be two per cent., against one per cent, on a four per cent, basis. In the former case there is not only a larger percentage of gain, but it is a percentage of a larger sum, since a three per cent, reserve is larger than a four per cent, reserve. On the other hand, inasmuch as the amount at risk is less in the case of a three per cent, reserve, the saving in mortality will likewise be less than on a four 103 per cent, basis. For example: at age fifty-six the three per cent, reserve at the end of the first year is $29.90 and the amount at risk (saving in mortality in case of one death less than expected) $970.10, while the four per cent, reserve is $27.46, making the saving in mortality $972.54. The diifference, however, will not be great in comparison with gain from interest, for the variation in amount at risk will be but slight in the earlier years, when the accumulated reserves are small; while at the older ages, when the actual death rate approaches more nearly the tabular, and the saving in mortality is, for that reason, little or nothing, the reserves are large and the gain from interest more pronounced. To illustrate this subject more fully, consider the case of one thousand persons all of the age fifty-six insured for $1,000 each on the Ordinary Life plan. The three per cent, reserve at the end of the first year would be $29.90 on each policy, and the amount at risk $970.10. The expected number of deaths in these one thousand lives according to the table would be 19.88, and the total expected death claims $19,880. (See "Death Rate per 1,000," mortality table, page 13). Assuming the actual death rate in the first year to be fifty per cent, of the tabular, the actual number of deaths would be 9.94 and the actual mortality $9,940. That is, the num- ber of deaths would be 9.94 less than expected, and as the amount at risk (saving in mortality) in each case is $970.10, the total saving in mortality would be $970.10 multiplied by 9.94, or $9,642.79. On a four per cent, basis in the same company the reserve on a single policy would be $27.46 and the amount at risk $972.54. The total saving in mortality, 104 thereforCj would be $972.54 multiplied by 9.94, or $9j667.05. That is, in the case of these one thousand policies the total saving in mortality on a four per cent, basis would be just $24.26 more than in the case of a three per cent, reserve. Let us now consider the gain from interest in the same case. The three per cent, initial reserve on a single policy in its first year being $47.76 (net premiiun), the total reserve on one thousand policies at the beginning of the first year would be $47,760. Assuming that the actual interest earned is five per cent., the total gain from interest during the year would be two per cent, computed on a total initial reserve of $47,760, or $955.20. The total four per cent, initial reserve would be $45,000, and the gain from interest would be one per cent, of that amount, or $450, being $505.20 less than in the case of the three per cent, reserve. Let us see now how it would be at the end of the year in which the insured reaches the age of seventy years. Of 1,000 persons living at fifty-six, 609 would still be living at seventy according to the table, and of these the expected number of deaths within a year would be 37.76. On policies more than five years old, it is generally assumed that the actual death rate will be approximately the same as the tabular. ■ In that case there would be virtually no saving in mortality at all; but let us assume, for the sake of illustration, that the actual number of deaths in this case will be two less than the tabular. As the three per cent, terminal reserve on such a policy for the fifteenth year would be $437.25, the amount at risk would be $562.75. The saving in mor- tality, therefore, would be just $562.75 for each of the 105 two risks saved, or a total of $1,125.50. On the other hand, the four per cent, terminal reserve would be $416.39, the amount at risk $583.61, and the saving in mortality also $583.61 for each life saved, a total of $1,167.22, or $41.72 more than on a three per cent, basis. Again, the three per cent, initial reserve in this case being the terminal reserve of the previous year ($410.62, Verification Table, pages 46 and 47), plus the net premium ($47.76), or a total of .$458.38 on a single policy, the total reserve on 609 policies would be $279,- 153.42, and a gain from interest of two per cent, would be $5,583.07. On the other hand, the four per cent, initial reserve being $435.17 on a single policy, the total reserve on 609 policies would be $265,018.53, and a gain from interest of one per cent, would be $2,650.19. The saving in mortality in the case of the 4 per cent, policy is the greater by $41.72, but the gain from interest in the case of the 3 per cent, policy is the greater by $2,932.88. Methods of Distribution The so-called "profits" in life insurance — saving in loading, gain from interest, etc., — are in reality savings, not profits. Having assumed that our funds would earn a certain rate of interest and that our mortality would follow the table, the net premium was fixed accordingly. Subsequent experience having de- veloped a lower mortality rate and a higher rate of inter- est than were assumed, the actual or net cost of the insur- ance was foimd to be less than had been anticipated. The diflFerence represents an overcharge, which, being re- turned to the policy-holder, is so much saved in the cost of his policy instead of a profit earned on his investment. Such savings are usually referred to as Surplus, being funds received by the company in excess of what is nec- essary to enable it to fulfill its contracts. In a stock company, where such savings go to the stockholders instead of to the policy-holders, they are, as to the former, genuine profits. In a mutual company, such as The Mutual Life, the surplus or savings are all returned to the policy- holder, the amount apportioned to each policy being termed, somewhat ineptly, a Dividend. Dividends may be apportioned to policy-holders yearly or at the end of a stated period of years, as five, ten, fifteen, twenty, etc. The former plan is known as the Yearly Dividend or Annual Dividend system, while by the latter plan the apportionment is made after diiFerent methods variously designated as Tontine, Semi-Tontine, Deferred Distribu- tion, etc. In most companies the policy-holder himself elects, at the time of making application, by what system his share of the gains or savings shall be apportioned, whether yearly or at the end of a stipulated period. Since December 31, 1906, all surplus in the case of new issues has been distributed by The Mutual Life yearly. Semi-Tontine Plan Under the Semi-Tontine method of distribution the policy-holders are divided into classes, commonly according to date of entry and length of distribution period selected. For example: the members joining in a 107 specified year, say 1 900, and selecting a particular distri- bution period, say fifteen years, constitute a class to themselves. All gains and savings accruing to the policies of this class during the fifteen years are set aside and accumulated to their credit. The beneficiaries of the members who die during the period receive payment of the face value of their policies, and lapsing or withdraw- ing members receive such surrender values as may have been stipulated in the contract or required by law ; but in either case, the interest of such members in the gains or savings that may have accrued up to the date of death or withdrawal, is forfeited to the remaining members of the class, among whom they are accordingly distributed at the end of the stipulated period. Observe that Semi- Tontine distribution implies the accumulation of gains or savings for the benefit of a particular class, and involves the forfeiture of the gains of those members of the class who die or withdraw during the period, for the benefit of those who live or persist to the end. The Tontine Method Tontine distribution differs from semi-tontine in that not only the gains of the lapsing members are for- feited, but their reserves as well. The beneficiaries of those who die receive payment of the face value of their policies, but those who lapse or withdraw before the end of the tontine period receive nothing, no surrender values being allowed. This form of insurance is no longer written in this country, and would in fact be illegal in most states under the non-forfeiture laws. 108 The Mutual Life Method The method which is followed by The Mutual Life in determining the dividends upon its policies issued in former years and having a distribution period longer than one year, differs essentially from the methods just mentioned. The Mutual Life's method is to base these long term distribution dividends upon the annual divi- dends which have been declared each year during the distribution period in the case of otherwise similar poli- cies, which were entitled by contract to receive dividends annually. The method of calculation is as follows : (1) The annual dividends which the policy would have received had it been entitled by contract to receive dividends annually are taken: (2) these annual dividends are accumulated at compound interest to the end of the distribution period: (3) the amount of these accumulated annual dividends is increased by a percent- age as compensation for the risk run of losing surplus by death, discontinuance or otherwise. In the case of fifteen- and twenty-year distribution policies issued on the 1899 form, which guarantee surrender values at the end of the distribution periods greater than the reserves on similar annual dividend policies, the difference between such surrender values and such reserves is deducted from the accumulated amount above described. As is evident, this method places the holders of annual dividend policies, and the holders of deferred distribution policies having different distribution periods, on a perfectly equitable basis as compared with one an- other, as well as with those having policies with the same distribution period. 109 The Contribution Plan The Contribution Plan for the apportionment of gains or savings in life insurance was introduced in 1863 by The Mutual Life Insurance Company of New York, having been devised by its then Actuary, Mr. Sheppard Homans, and his assistant, Mr. David Parks Fackler. It has since been adopted by American companies in original or modified form with practical unanimity, and by some companies abroad. For annual dividends this method in its original form consists in crediting the individual policy with the reserve pertaining thereto at the end of the previous year, and with the annual premium paid at the beginning of the current year, less an expense charge, adding interest at such rate as the circumstances permit. Against the sum so found are charged the cost of insur- ance (which may or may not be assessed according to the standard mortality table), and the reserve required at the end of the current year, the balance being that policy's "contribution to surplus," or its annual dividend. Prior to the introduction of the contribution plan by The Mutual Life, dividends were apportioned in most companies by the Percentage Method, the same percent- age of the premium being returned yearly or at the end of five-year periods on all policies alike, regardless of age or form of contract and often without reference to the length of time the latter had been in force. Methods more or less similar to that outlined were employed by other companies. Non-Participating Insurance Gains and savings in life insurance are not always apportioned to the policies from whose premiums they 110 were derived. In some cases, in consideration of the payment of a smaller gross premium, it is agreed that the policy-holder shall receive no part of the accruing surplus — that is, he is to receive no dividends at any time. The policy in such case is said to be Non-Participating, since it is not entitled to participate in distributions of surplus. On the other hand, policies which are entitled to divi- dends are termed Participating contracts. The term Stock Rate is sometimes used as synonymous with non- participating. Under the New York law, no home company can write both participating and non-participating contracts. If a mutual company, it can obviously write only the former. If a stock or mixed company, it must choose which form of policy it will write, and can then issue no other, either at home or abroad. Outside companies may write only one form within the state, but may issue either form elsewhere. Similar participating and non-participating policies having the same reserve basis, whether issued by the same or by different companies, necessarily have the same net premium and the same reserve values. The difference in gross rates is due merely to a difference in loading. The latter is rarely, if ever, sufficient in the case of a non-participating policy to provide for neces- sary expenses, the purpose being to make up the deficit from the surplus accruing from other sources — saving in mortality, gain from interest, etc. This form of insur- ance is supposed to be issued at as nearly net cost as practicable, after providing for dividends to stockholders. Ill Life Insurance at Actual Cost If it were certain that the future death rate would correspond precisely with the mortality table, and if the rate of interest to be earned in the future could be determined in advance with absolute accuracy, it would then be possible to determine with certainty the exact net premium which it would be necessary to charge in order to furnish life insurance at actual cost. Such certainty, however, is impossible. Omniscience alone can say in advance what the actual cost of life insurance in the future will be. If the actuary were to undertake to name a figure that would precisely meet the case, he would inevitably name a sum either too large or too small. The latter alternative is not to be contemplated for a moment. To be on the safe side, therefore, it is essential to fix the premium at a figure which, we are morally certain, will prove to be larger than actual cost, and the margin over cost must, beyond a peradventure, be a sufficient margin. If that margin be too small, un- foreseen contingencies may wipe it out and involve the company in insolvency and ruin. A slight margin may be safe enough if, by good fortune, all goes well. A driver may urge his team within an inch of the precipice and not go over the brink, but the prudent driver will keep further back. In other words, the life insurance premium, even the non-participating premium, Tnust be larger than actual cost. That is a condition which is universally conceded to be essential. In fact, every advocate of non-participating insurance wiU stoutly maintain that there is an ample margin or overcharge in non-participat- 112 ing rates. To admit the contrary would be to concede that those rates^ under adverse conditions, might prove too low and thus involve the company in ruin. What Becomes of the Overcharge? Although the actual cost of life insurance cannot be determined in advance, it can be computed at the end of each year when the books are balanced. The mutual company — that is, a company writing participat- ing insurance — will then return the overcharge to the policy-holder in the form of a so-called dividend. Thus from year to year the insured does, hy the participating plan, obtain his insurance at actual cost. In the case of the stock company which writes only non-participating policies, the overcharge, or margin over actual cost, goes to the stockholders. Nothing is returned to the policy- holder in any event. The cost to him is absolutely fixed. He knows in advance "just what he is to pay," and he knows, too, that he will get nothing back. Let us not complicate this question by discussing the merits of different companies, or the varying condi- tions under which they operate. To decide whether the participating or non-participating system is correct, we must assume in advance that the two companies are man- aged with equal honesty and efficiency, and that attendant conditions are substantially the same. It then follows, as certainly as two and two are four, that only in partici- pating insurance is protection at actual cost a possibility. The advocate of the non-participating plan will claim that, while his premium does include an overcharge 113 as a provision for stockholders' profits and as a margin of safety, the participating premium carries a larger margin than is necessary. This may sometimes be true, but inasmuch as that difficulty is adjusted at the end of each year, when the books are balanced and the over- charge returned, the policy-holder will be content to have it so, since the larger margin affords greater assurance of safety. No one can tell what the exigencies of the future may develop. Adverse legislation, excessive taxation, other unforeseen contingencies, such as would wipe out the margin in the non-participating premium and en- danger the solvency of the company, would result only in a diminution of dividends in case of a mutual company with its larger participating premiums. Safety is of more importance in life insurance than all else. It is better to keep away from the brink of the precipice, even at some temporary inconvenience. Within the last fifteen years, many new companies have been organized. A number of these institutions have very limited resources — are in fact still in the ex- perimental stage — and some are directed by men who, however successful they may have been as insurance agents, have had little or no experience in company management. A large number of these organizations write participating insurance with a sufficient margin in their premiums to enable them to survive the mistakes commonly incidental to the inexperience and over-confi- dence of youth. Others propose to write non-participat- ing insurance exclusively, thereby taldng chances that companies long established and of great strength might well hesitate to assume. The company that essays to write this class of business, not having the reserve strength aiForded by the redundant premiums of participating insurance, should at least possess large capital as a guaranty against possible disaster from the use of rates that may, under adverse conditions, prove insufficient. lis CHAPTER X NATURAL PREMIUM INSURANCE WE have seen that the net annual premium of an Ordinary Life policy at age fifty-six based on the American Experience Table of Mortality and three per cent, interest, is $47.76, or more accurately, $47.760895. This is the net amount mathematically necessary to be paid yearly during life by each of the 63,364 members of our hypothetical company, to make possible the payment of $1,000 for each death until the last three members pass away at age ninety-six. By reference to the Verifi- cation Table, pages 46 and 47, it wiU be seen that this amount paid by each of the 63,364 members, yields in the first year the sum of $3,026,321.35, while the death claims to be met in that year are only $1,260,000. We hare therefore collected much more than was necessary for the payment of current claims, but it has been proved in the ^'^erification Table that the excess collected in the earlier years will all be needed at a later period, when the members are older and the death rate higher. It is obvious, therefore, that if we were to collect only enough in any year to pay the death claims of that year, we should have to charge a continually increasing premium in subsequent years. To illustrate: Of the 63,364 persons at age fifty-six comprising our hypothetical company, 1 ,260, according to the Mortality Table, will be dead at the end of the year, requiring a payment at that time of $1,260,000. To provide for this amount we shall have to colect from the members at the beginning of the year a premium sufficient to amount in the aggregate to the pres- ent worth of that sum ; that is, a fund which at three per cent, interest will amount of $1,260,000 at the end of the year. The present worth of $1 due in one year is $0.97087379. Hence the present worth of $1,260,000 is $1,223,300.98. ($0.97087379 x 1,260,000 = $1,223,- 300.98). Dividing this amount by 63,364, the number of members living at the beginning of the year, we get $19.31. That is to say, if each member at the beginning of the year will pay a net premium of $19.31, or, more accurately, $19.3059305, we shall have a total insurance fund of $1,223,300.98, which at three per cent, interest will amount of $1,260,000 at the end of the year, or just enough for the payment of the accrued claims. At the beginning of the second year we have 62,104 members still living, of whom 1,325 will be dead at the end of year, requiring the payment at that time of $1,325,000. The present worth of this sum due in one year is $1,286,407-77, which is therefore the amount to be collected at the beginning of the year. Dividing by 62,104 we get $20.71, which is the net premium to be paid by each member in the second year. By like process we find that the net premium for the third year at age fifty-eight is $22.27. The premium thus determined is called the Natural Premium as distinguished from the Level Premium, with which we have heretofore had to do, the latter being a fixed charge that can never be increased, and which is sufficient both for current and future cost. The Natural Premium represents the actual current cost and increases each year as the insured advances in age, and in proportion to the probability of his dying. This 117 form of insurance as in use with the fraternal orders is sometimes called the Step-Rate plan, and is the same as yearly renewable term insurance heretofore described. The natural premium does not increase rapidly at the younger ages, but advances at a vastly greater rate as the insured approaches the limit of life, as will be seen by the following table : Age Natural Prem. Age Natural Prem. 35 $8.69 60 $25.92 36 8.82 70 60.19 37 8.97 80 140.26 40 9.51 90 441.31 50 13.38 95 970.87 The Cost of New Business One of the principal items of expense with a life insurance company is the cost of new business. Ordi- narily, the agent who places a policy receives a Com- mission for his services, which may be a percentage of the first premium only, termed a Brokerage, or it may include a smaller percentage of a stated number of subsequent premiums, termed a Renewal Commission. Although the renewal commission is a percentage of subsequent prem- iums, a part of it, at least, should be included in the cost of new business. This is clear from the fact that the agent is induced to accept a smaller brokerage, or per- centage of the first premium, by the offer of a sub- stantial renewal. Moreover, it is often the case that the agent receiving the renewal commission has noth- ing whatever to do with the collection of subsequent premiums, the contract even providing in some cases for 118 the continuance of renewals after the death of the agent^ or after the termination of his connection with the company. There are other matters of expense pertaining partly to the cost of new insurance, partly to the care of old business, which it would be equally impracticable to apportion with entire accuracy between the two items. However, the New York law, for the purpose of placing a limit upon expenses, designates the items which shall be considered as constituting the cost of new business, but without assuming scientific accuracy. The Preliminary Term System The statement may be safely made that the ordi- nary loading of a life insurance premium is never suffi- cient in the first year to meet the expenses incident to securing the business. To illustrate: If the gross prem- ium of an Ordinary Life policy at age fifty-six, American Experience Table and three per cent, interest, is $63.68, we find, by deducting the net premium of $47.76, that the loading is $15.92. The principal items of expense the first year will be the agent's commission, say forty per cent., or $25.47, and the medical examiner's fee, $5, making for these two items alone $30.47, or nearly double the amount of the loading earned by the new policy. Inasmuch as the agent, when settling for prem- iums collected, usually retains his commission, remitting only the net amount, the erroneous impression has gained acceptance that the commission is paid from the first premium. As a matter of fact, the commission and other 119 costs of new business are paid from the entire loadings of the company, earned on all policies outstanding, or from other funds available for expenses. The com- mission could not be paid from the first premium, for the net premium, or reserve, must not be trenched upon, as would occur in that case. Neither is the re- quired amount "borrowed" from the "surplus belonging to old policy-holders," as so ofter stated. The loadings of all policies in force are for expenses, including the cost of new business. In the case of young companies, however, which have but little insurance in force and hence small receipts from loading, the policy sometimes provides that the con- tract shall be valued in the first year as term insurance, the regular life insurance policy beginning one year later. Thus the entire first premium, less only the charge for the actual mortality of the year, is available as a loading for meeting the cost of new business. This method is variously designated as the Preliminary Term, or First Year Term, system, and has been adopted by most com- panies organized in recent years. In the case of a pre- liminary term Ordinary Life policy at age fifty-six, the net premium in the first year would be merely the natural premium, or yearly term rate, that is, $19.31, as given above (page 117). The practice of preliminary term companies is, however, to charge the same gross premium in the first as in subsequent years. If the gross premium is $63.68, we shall have, after deducting the net premium of $19.31, a loading the first year of $44.37, or about seventy per cent. Deducting $5 for medical examina- tion, there remains a balance of $39.37, or nearly sixty two per cent., for commissions and other expenses. 120 In the valuation of such a contract the company is not, of course, charged with any reserve at the end of the first year, but during the second and subsequent years the net premium required will be that of an Ordinary Life corresponding to age fifty-seven, the attained age of the insured when the regular life policy begins. In this case, then, the net premium in the second and subsequent years would be $50.13 instead of $47.76 (the net premium at age 56), and if this amount be deducted from the gross premium of $63.68, the balance of $13.55 will be the permanent loading instead of $15.92. Thus it will be seen that by this system the loading is greatly in- creased in the first year, but is materially less than the regular loading in subsequent years. There will be no re- serve at the end of the first year, and the reserve of the second policy-year will be the same as the first year re- serve of a regular Ordinary Life policy issued at age fifty-seven. In fact, from the beginning of the second year the policy will be valued as an Ordinary Life issued at age fifty-seven, or one year later than its actual date, as stated above. It follows that the accumulated reserve of an Ordinary Life policy issued on the preliminary term plan will at all stages be less than it would have been had it been issued at the same age on the regular Ordinary Life plan, because always one year behind in the process of accumulation. This difference will con- tinue until age ninety-six, when the reserve in either case becomes equal to the face of the policy. It wiU be ap- preciated that smaller reserves mean smaller cash values, and also that smaller loadings mean smaller dividends. We have heretofore defined the terms "level premium" and "net valuation." Under the preliminary 121 term system the gross premium may be level from date of issue of policy, but the net premium is not so. For example, in the case just illustrated, the net premium in the first year is $19.31 and in subsequent years $50.13, although the gross premium is $63.68 for every year. On the other hand, we have seen that the net premium of the equivalent Ordinary Life policy on the regular legal reserve plan is $47.76, the same fixed amount for every year including the first. In that case we have a Level Net Premium as distinguished from the net premium of the preliminary term plan, which is not level. In the case of a "limited premium" policy the preliminary term plan varies somewhat from that illus- trated. Let us consider its application, for example, to a Fifteen-Payment Life. The net three per cent, premium of the regular policy at age fifty-six would be $60.17. If the gross premium is $78.16, the yearly loading will be $17.99. On a preliminary term basis, the equivalent contract would consist of a combined one year term policy and a Fourteen-Payment Life, the latter beginning at age fifty-seven. The net premium for one year's term insur- ance would be the same as before, $19.31. Deduct- ing this amount from the gross premium of $78.16, we obtain a first year loading of $58.85. The three per cent, net premium of the Fourteen-Payment Life at age fifty-seven would be $64.55, which leaves a yearly load- ing of $13.61, instead of $17-99, for the remaining four- teen years. As in the case of the preliminary term Ordinary Life, there will be no reserve at the end of the first year. At the end of the second policy year the reserve will be $46.14. This is larger than the first year reserve of the regular policy, but much smaller than the reserve of the latter at the end of the second policy year, it being then $86.72. The preliminary term reserve at the end of each subsequent policy year approaches more and more nearly to the corresponding reserve of the regular Fifteen-Payment Life until the end of the fifteenth year when, at the attained age of seventy-one, both reserves are necessarily the same, since both poli- cies are now fully paid up. In other words, on the regular Fifteen-Payment Life the reserve of a fully paid policy is accumulated in fifteen years, while on the pre- liminary term Fifteen-Payment Life the same reserve is accumulated during the last fourteen years. The preliminary term system, as applied to an Ordinary Life policy, is not an unreasonable method of providing for the cost of new business in the case of a young company, notwithstanding the apparent injustice of charging a premium of $63.68 for term insurance during a single year, the net natural cost of which is $19.31. Indeed, only by the use of some such expedient would it be possible for a new company to establish itself at all on the mutual plan, since, being in receipt of little or nothing from loadings on old business and having no accumulated surplus, it would be unable to meet the necessary cost of new insurance and provide at the same time for the required legal reserve of the first year. Only on the stock plan, with the stockholders personally advancing extra funds for the purchase of new business, could a new company comply with the requirement to put up the full level net premium reserves on its policies beginning with the year of issue. The adoption of the preliminary term plan by an old company, however, is commonly regarded as a confession of weakness or of an 123 extravagant management, since it is a virtual admission that the company is unable to keep its expenses within its aggregate receipts from loadings on all business, and that it dare not trench upon its limited surplus. If the application of the preliminary term plan to the Ordinary Life policy is defensible, it nevertheless becomes decidedly objectionable when applied without modification to limited payment and Endowment Poli- cies, as illustrated in the following table showing the loadings of the first year: Policy, Age 56 p^^^°?f„ Natufal'cost ^-^^^ing Ordinary Life $63.68 $19.31 $44.37 Fifteen Payment Life .. . 78.16 19.31 58.85 Ten Payment Life 99.33 19.31 80.02 Twenty Year Endowment 72.66 19.31 53.35 Ten Year Endowment. . . 121.06 19.31 101.75 The grotesque absurdity of such loadings suffi- ciently condemns the Full Preliminary Term system, by which is meant the application of preliminary term without modification to all forms of policies. Modified Preliminary Term In 1897 there was introduced a modification of the preliminary term plan, which consisted in limiting the loading of the first year on all limited payment and Endowment forms to the amount available, on a prelimi- :24 nary term basis, on the Ordinary Life policy. For ex- ample, referring to the table above, while the gross premiums would vary on the different forms as indicated, the loading could in no case exceed that of the Ordi- nary Life policy, to wit: $44.37. From the balance of the premium on limited payment and Endowment forms the company would put up a reserve in the first year, thus reducing the net premium and in- creasing the loadings of subsequent years. The tendency of this plan would be to encourage the sale of Ordinary Life policies rather than limited payment and Endowment contracts. Several modifications of "modified preliminary term" have been legalized in different states. Select and Ultimate Valuation This method of computing reserves was devised as a substitute for modified preliminary term. To a correct understanding of the system a knowledge of the several classes of mortality tables is necessary. Assume, for illustration, that we wish to ascertain how many of 100,000 persons, all thirty years of age, will die within one year. If to that end we note the history for twelve months of 100,000 persons of the age stated, who have just passed a rigid medical examination for life insurance, we shall find a much smaller number dying than in 100,000 of the same age who were exam- ined five years ago, at twenty-five. If we note the his- tory of both classes during the succeeding year, we shall find a larger percentage of deaths in each instance than in the first year, and, as before, a smaller percentage of 125 deaths in the first than in the second class, but the death rates of the two classes wiU now be nearer together than in the first year. In the third year, wliile the death rate of each class will again be higher than formerly, the difference between the two rates will again be less than in the second year. With each added year the differ- ence in death rates of the two classes will diminish, until ultimately, after the benefit of medical selection has worn off, the two death rates will be theoretically the same. It is commonly assumed that this stage will be reached in five years. Lives which have just been selected by a medical examination are called Select Lives, and a mortality table based on the subsequent history of such lives is called a Select Table. As it is assumed that the effects of medical selection ultimately disappear, say in about five years, a mortality table based on the history of lives insured five or more years before is called an Ultimate Table. A mortality table based on the history of lives insured, some within the year, others within two or three or ten years or more, is called a Mixed Table. The American Experience Table of Mortality, which is in general use in the United States, is an "ultimate table," its compilation having been based upon the subsequent history of lives insured for five years or more. The rate of mortality indicated by this table, therefore, is materially greater in the first five years, at least, than that pertaining to select lives at corresponding ages. As a basis for establishing a mini- mum standard of valuation and for fixing a limitation of expenses in securing new business, the New York Law 126 assumes that the mortality of select lives in the first policy-year immediately following medical examination will be fifty per cent, of the tabular mortality of the American Experience Table; in the second year, sixty- five per cent.; in the third year, seventy-five per cent.; in the fourth year, eighty-five per cent. ; in the fifth year, ninety five per cent.; and in the sixth and subsequent years, one hundred per cent. On this basis smaller ter- minal reserves will be required during the first four years than by the American Experience Table though they will be the same from the fifth year on, as illustrated in the following comparison of terminal reserves computed by the two methods on an Ordinary Life policy issued at age fifty-six. End of Year First Second Third Fourth Fifth Sixth Temiina; American Ex- perience Table I Reserves Select and Ultimate $29.90 $14.41 59.94 50.84 90.06 85.87 120.21 119.13 150.33 150.33 180.36. 180.36 This is the system of Select and Ultimate Valu- ation authorized by the laws of New York as a minimum standard. In this standard the new company, which might find it impracticable to put up the level net pre- mium reserves in the first and immediately succeeding years, has a substantial measure of relief. The company collects during the first four years, as well as thereafter, the full gross premium. The margin in the first year's 127 premium by reason of the smaller reserve required — the full reserve being made up in subsequent years by the saving in mortality — is available for other purposes and. may be anticipated and expended in securing new business. 128 CHAPTER XI SUNDRY TOPICS T N the foregoing pages we have discussed in their logi- •*■ cal order such technical subjects and defined such terms as seemed important for the life insurance agent to understand. The items treated of may well be supple- mented by a few others, heretofore omitted because not necessary to the proper comprehension of the current text. Insurable Interest The question of insurable interest is frequently an important one. Since, however, the law on this subject varies so much in the different states, it is impossible to make a satisfactory general statement of the law relating to it. In some of the states (for instance, New York) a very liberal view obtains, and it is held that where the person whose life is insured makes application for the insurance he can name any person as the beneficiary, and that in such a case it is not necessary to inquire whether the proposed beneficiary has an insurable interest in the life of the insured or not. In other states it is necessary in all cases to inquire whether the proposed beneficiary has such a pecuniary interest in the life of the insured as would permit him, the beneficiary, to apply for and obtain insurance upon the life of the insured. In the case of certain near relationships such as husband and wife, parent and child, an insurable interest is pre- sumed. In some states, however, an adult child is held 129 not to have an insurable interest in the life of his parent unless the child is actually dependent upon the parent for his support. It is quite generally held that a creditor has an insurable interest in the life of his debtor to the extent of his debt; also that one partner has an insurable in- terest in the life of another partner. The question of insurable interest also arises in connection with assignments of life insurance policies. Some states, including New York, take the liberal view that an assignee need have no insurable interest in the life of the insured unless it appears that the assignment is made for the express purpose of speculating on the life of the insured. In other states the assignee is required to have an actual pecuniary interest in the life of the insured; that is, the assignee must sustain such relation to the insured that the death of the latter would cause a pecimiary loss to the assignee. Standard Policies All policies issued in New York State by New companies must include the "standard provisions" pre- scribed by the New York Laws. New forms of policies may be issued when approved by the insurance depart- ment after a public hearing open to all persons interested. The approved forms then become "standard" and may be written by any company. Annuities In addition to the life annuity (page 20) and the temporary annuity (page 31), several other forms re- quire our attention. 130 A Survivorship Annuity is one which becomes payable to a designated person, beginning at the death of the insured. This contract, as written by The Mutual Life, enables the insured to provide a life income for a designated beneficiary, an aged parent for example, at a much smaller outlay than by any other form. A Deferred Annuity is one, the payments of which do not begin until a specified future date, or the occurrence of a designated future event. This contract enables the insured, who may have no one dependent upon him, to provide an income for his own old age at a smaller outlay than by any other method. When an annuity, is to be paid for a specified number of years, no more and no less, as ten or twenty, whether the annuitant continues to live or not, and re- gardless of any other contingencies, we have an Annuity Certain. If the proceeds of a policy, for instance, are to be paid in a fixed number of yearly instalments of a stated amount each, such instalments constitute an annuity certain. The present worth of such instalments, that is, the sum in hand which, at a given rate of interest, will produce instalments of the stated number and amount, is termed the Commuted Value thereof, and is, of course, also the value of the annuity in that case. A Perpetual Annuity is one wliich is to be paid continuously, without limit of duration. Such annuities are, perhaps, imknown in this country, but are common in England. Corporation shares or bonds which are never to be redeemed, but which bear a specified rate of interest in perpetuity, come within this designation, the interest payments constituting a perpetual annuity. The British consol is an example of a perpetual annuity. 131 Neither the annuity certain nor the perpetual annuity involves any question of Life Contingency; that is to say^ they are not based upon the probability of the continuance or termination of a designated life, and life insurance companies accordingly do not issue such contracts, save annuities certain as supplementary to in- surance policies. All New York standard policies of the Ordinary Life, Limited Payment Life, Term, or Endowment forms, may, at the election of the insured (or at the election of the beneficiary if the insured has not acted in his life- time), be made payable either in a specified number of equal yearly instalments, as an annuity certain, or in Continuous Instalments. The latter plan involves two forms of annuity, to wit: An annuity certain and a deferred annuity. To illustrate : Upon the death of the insured, an annuity contract will be issued providing, first: for the payment of annual instalments of an amount stated in the policy for twenty years certain, and second: for the continuation to the beneficiary of this annuity as long as she may live beyond the twenty years certain. When this form of settlement is applied to policies which by their terms are payable in a single sum, the amount of each instalment, or the annuity, depends upon the age of the beneficiary when the policy becomes payable. Any policy on the books of the Company, which is payable in a single sum of not less than $1,000, may be settled in this manner, no matter how long ago issued, unless there are difficulties in the way. The regular Continuous Instalment policy, in its original form, provides by its terms for payment to a designated beneficiary in yearly or monthly instalments. It diff^ers from the mode of settlement first described in that each instalment is for a specified sum fixed at time of issue, the unit being $50 yearly or $10 monthly. The amount of the premium in this form is determined according to the age of both the insured and the beneficiary at date of issue. The Continuous Instal- ment (also known as Life Income) contract is the ideal policy for the average family, providing, as it does, without danger of loss and without care of investment, an absolute income for a period of twenty years, whether the beneficiary lives so long or not, within which time the youngest child becomes self-sup- porting, and provides further for a continuance of the income during the lifetime of the beneficiary, if the latter survives the period named. The policy is now written by most companies under one name or another, but, in its original form, was devised in 1892 by Emory McClintock, then and for many years the renowned Actuary of The Mutual Life Insurance Company of New York, and was introduced by that Company in its semi-centennial year, 1893. Within the last few years numerous assess- ment companies have been organized to write a some- what similar contract, sometimes with the additional provision that the annuity in case of a widow shall termi- nate upon the remarriage of the latter. Their rates, not being scientifically computed, are absurdly inadequate; the annuity payments are in all cases for the same amount per $1,000 of insurance, regardless of the at- tained or previous age of the annuitant ; and the contract does not contemplate the accumulation of a mathematical reserve. Furthermore, the contingency of marriage, like that of lapse, cannot well be considered in the computa- 133 tion of the premium. The law of probabilities cannot be applied satisfactorily to an event which, like that of lapse or marriage, is largely or wholly within the control of the party most concerned. It is a diflFerent question from the application of the law to events which, like death, sickness, or accident, are wholly fortuitous. A Contingent Annuity is one which is to terminate on the happening of a stated future event, as the death of a designated person other than the annuitant, the marriage of the annuitant, the inheritance of an estate, etc. The specified event may be one which is bound to occur, as in the first-mentioned case, or one which may never take place, as in the last instance. It is possible, therefore, that a contingent annuity may prove to be perpetual, as it might, for instance, when payable during the life of the annuitant and thereafter to his next of kin. The extinction of his line would terminate the annuity, but this event may never occur. The contingent annuity is not written by The Mutual Life, nor, probably, by many American legal reserve companies, if any. A Joint Annuity is one in which two or more lives participate and which is to terminate upon the death of any one of the lives concerned. The Joint and Survivor Annuity, also called Annuity on the Last Survivor, is to be paid so long as any one of two or more designated persons continues to live. NON-FOHFEITURE A Non-Forfeitable policy is one which, by its terms, provides for a definite surrender value, accruing after a stated number of premiums have been paid. It has been the practice of most companies from an early 134 date to allow an equitable paid-up or cash surrender value after the expiration of a reasonable time, but a policy is not strictly non-forfeitable unless a provision for a definite and automatic paid-up, cash, or extended insur- ance surrender value is incorporated in the contract. Incontestability The policies of most companies provide that, dur- ing a stated period from date of issue, the insured shall not engage in certain extra-hazardous occupa- tions, the policy to be void in case of death resulting from a violation of these conditions, or in case of suicide within a stated period. The purpose of such restrictions is the prevention of fraud by repelling or excluding applicants who are seeking insurance for the very purpose of de- frauding the company through suicide, or for the very reason that they contemplate engaging in some extra- hazardous occupation, etc. After the expiration of the limit named, such restrictions become inoperative, the presumption then being that the policy was originally taken out in good faith. Thereafter the contract usually becomes by its terms incontestable for any cause, the premiums having been duly paid. The mere elimination of restrictions, however, does not render a policy incon- testable, an express provision to that effect being neces- sary. Some policies are wholly free from restrictions from date, yet not incontestable by their terms until after the experiation of a stated period. Others are incon- testable from date of issue, while still others are never incontestable, even after stated restrictions have become inoperative. The two forms of contract just mentioned are now very rare. 135 Effect of Fraud The question has been raised as to whether under the rule of law that "fraud vitiates any contract," an absolutely incontestable policy can be written. It has been held in Kentucky that a policy, by its terms "in- contestable from date," may be cancelled for fraud, while in Rhode Island a policy, purporting to be incon- testable after two years from date of issue, was held to be strictly so. The company having reserved a stated period within which the contract should be contestable, it would be presumed that the period was a reasonable one and, accordingly, the fraud must be discovered and acted upon within that time. 136 CHAPTER XII Total and Permanent Disability Benefits For a number of years straight life insurance companies have added a special clause to some of their contracts, providing for the payment of certain benefits in event of Total and Permanent Disability. It will be noted (see paragraph entitled "Double Indemnity Benefits") that accident companies have in their accident contracts agreed to the payment of certain benefits in event of non-fatal accidents. .The application of the "Total and Permanent Disability" clause in life con- tracts is similar in that it provides for the payment of benefits prior to the natural maturity of the policy, but • it contemplates a much more restricted use of the word "Disability." Disability may be Partial and Tempo- rary, as in the case of an injured but not an incurably injured hand, or it may be Total and Temporary, as in the case of any acute illness, not incurable, such as ty- phoid fever, or it may be Partial and Permanent, as in the case of the loss of a band, or it may be Total and Permanent, as in the case of incurable insanity. It is only to the last group of cases that the special "Dis- ability" clause of life contracts applies. A typical clause reads in part as follows : When Such Benefits Take Effect. — If the Insured, after payment of premiums for at least one full year, shall, before attaining the age of sixty years and provided all past due premiums have been duly paid and this Policy js in full force and effect, furnish due proof to the Company at its Home OfBce, either (a) that he has become totally and permanently disabled by bodily injury or disease, so that he is, and will be, 137 permanently, continuously, and wholly prevented thereby from performing any worli for compensation, gain, or profit, or from following any gainful occupation, or (b) that he has suffered any of the following "Special Disabilities" (which shall be considered total and permanent disabilities here- under), namely, the entire and irrecoverable loss of the sight of both eyes or the severance of both entire hands or of both entire feet or of one entire hand and one entire foot, the Com- pany, upon receipt and approval of such proof, will grant the following benefits: etc. The loss of both hands or both feet would in some cases not be evidence of total and permanent disability in case of non-manual workers, but these and certain other disabilities are included by special reference as is noted above. The same general principles are carried out in the determination of the rate as are applied to the deter- mination of the rate for an Ordinary Life policy. By observation, the rate of disability, that is the ratio of the number disabled to the number exposed to the risk of disablement at each age, is determined, and a further investigation is made to determine the rate of mortality among disabled lives. A Combined Mortality and Dis- ability Table is then constructed as follows, where the word "active" is applied to lives not Totally and Per- manently disabled: Age Number of "Active" Lives I^iving Number of "Active " I^ives Dying Within the Year Number of "Active " lyives Being Disabled Within the Year Number of Disabled Lives Living Number of Disabled Lives Dying 16 96,285 785 49 16 9S,601 720 49 49 12 17 94,782 708 48 86 21 There are thus two ways by which the number of "active" lives living is diminished, and this complex table 138 is the instrument by means of which the net premium for Total and Permanent Disability Benefits are de- termined, just as the net premiums for Ordinary Life insurance contracts are determined from the ordinary mortality table. The details are too involved to be of interest here. The earliest benefits of this type were limited to "Waiver of Premium": that is, upon proof of dis- ability, satisfactory to the company, the company would waive the requirement of payment of the annual premium and would cpntinue the policy as if the premium had been paid in full in cash. Later, some contracts pro- vided for the payment of the face of the policy in in- stalments as soon as disability had been proven, thus not only relieving the policyholder of payment of the premium, but also granting him an income so long as the instalments continued; in the event of death the balance of the face of the policy would be payable to the beneficiary. A variation of the latter contract was that upon occurrence of disability the insured should have the option of accepting the Waiver of Premium Benefit only and having the policy payable in full at his death, or having the policy payable in instalments certain, of say 10^^ of the face of the policy, each, for ten years whether he survived or not, premiums being waived as in the former case; obviously, if the insured considered his chances of longevity good, he would choose the latter, otherwise the former. At length it was observed that under such types of instalment settle- ment the insurance was in whole or in part exhausted during the insured's lifetime, and it was determined 139 to add to the waiver of premium benefit an income upon disability which did not reduce the policy in any way, the face of the policy being payable in full upon the insured's later death. Some variation exists in connec- tion with this contract as to the amount of income, i. e., its relation to the face of the policy (annual income usually 10% or 12% of face of policy), as to whether the income shall be payable monthly or annually and as to when, i. e., how soon after disability, it shall begin. It is, however, in general the most popular form in which the Disability clause is issued at present. Total and Permanent Disability is evidenced, as is seen by the extract from the clause, by inability to engage in any work for compensation or profit. It is therefore granted only to applicants who are within the active period of life, i. e., for example, under fifty-five years of age, and it is not granted to applicants who are habitually unemployed, such as women who are not self-supporting or who are not engaged in business. Furthermore, disability tp result in a valid claim against the insuring company must usually occur prior to attain- ment of a specified age, sixty or sixty-five, because after that time it is practically impossible to distinguish be- tween disablement within the terms of the policy and senility. A Modified Waiver benefit has been granted by some companies, providing for waiver of premiums in event of disability above the limiting age, this benefit providing for the deduction of the premiums so waived from the face of the policy, or what is the same thing, the carrying of the waived premiiuns as successive loans without interest. But this benefit is not of great value. 140 The chief causes of Total and Permanent Dis- ability are Tuberculosisj Insanity, and Paralysis, and risks for these benefits are selected with this fact in view. The mortality among disabled lives is very high, especially immediately after acceptance of proof of dis- ability, the average lifetime after disability being only two or three years, among those cases which have be- come claims in The Mutual Life Insurance Company of New York since the benefits were first granted a few years ago. Double Indemnity Benefits We have explained (see page 10) how the Mor- tality Table is formed, either from vital statistics relat- ing to the population or to some part of it, or from the records of a life insurance company, by observing the ratio of the number of deaths within a given period at each age to the number of lives exposed to risk of death at that age during the same period, and thence deter- mining the rates of mortality at successive ages. Similarly, we may observe the ratio of the num- ber dying in one year from a specific cause to the number exposed to risk of death in that year and thence deter- mining a rate of mortality for that particular cause of death. This is what is done by accident insurance com- panies who pay a claim under an accident policy if the insured meets his death "through external, violent, and accidental means." 141 Companies transacting an ordinary life insurance business have in recent years made such a special insur- ance clause a feature of some of their contracts, by pro- viding that if the insured dies in consequence of an acci- dent of a certain type, an amount equal to double the face of the policy wiU be payable as a death claim. Hence the name Double Indemnity. A typical clause providing for this benefit, if it is to become payable as the result of a fatal accident while the insured is travel- ing as u, passenger on a public conveyance, is as follows : If there further be received at said Home Of5ce due proof that such death before the end of the endowment period resulted directly from bodily injury effected solely through external, violent, and accidental means, and sustained by the Insured after the date of issue of this Policy while traveling as a passenger on a railway train, a, steamship licensed for regular transportation of passengers, a street car, or other public conveyance operated by a common carrier, except aeroplane, dirigible balloon, or submarine, and that such death occurred within sixty days after such accident, promises to pay to said beneficiary, instead of the face amount of this Policy, Dollars, provided, however, that this Double Indemnity shaU not be payable in the event of the Insured's death at any time by his own act, whether sane or insane. A typical clause providing for additional payment pro- vided the Insured's death results from an accident of any kind is as follows : If there further be received at said Home Office due proof that such death resulted directly from bodily injury, received after the date of issue of this Policy, Independently and ex- clusively of all other causes, and that such bodily injury was effected solely through external, violent, and accidental means, and that such death occurred within sixty days after the date of such bodily injury, promises to pay to said beneficiary, instead of the face amount of this policy, Dollars, provided, however, that this Double Indemnity shall 142 not be payable in the event of the Insured's death as a result of military or naval service in time of war, nor shall it be payable in the event of the Insured's death at any time by his own act, whether sane or Insane, nor if such death be caused directly or indirectly, wholly or partly, by riot, insurrection, or war or any act Incident thereto, nor if such death be a result of participation in aeronautics or submarine operations, nor if such death result from any violation of law by the Insured, or from police duty in any military, naval, or police organization, or directly or indirectly from bodily or mental infirmity or disease of any sort. The Company shall have the right and opportunity to examine the body and to make autopsy, unless prohibited by law. The rate charged has been based on an investiga- tion of the ratio of the loss at each age on account of such violent deaths as come within the meaning of the clause to the insurance exposed to risk of death at each respective age. There is a slight increase in the observed accident rate as the age advances, and some companies take account of this in fixing their premiums; other companies have assumed a constant accident rate at all ages with a provision that no entrants over a specified age shall be granted this benefit. Not too much reliance can be placed on the past experience of this Company, because such old business was not accepted with this benefit in mind ; and the same remark applies to the rate charged by accident companies; the latter comparison is further complicated by the fact that accident com- panies, so-called, grant certain benefits in case of non- fatal as well as in case of fatal accidents, which intro- duces some variation in their method of selecting risks from those applying for such policies. The rate charged by The Mutual Life is $1 per $1,000 at all ages in case of Ordinary Life policies, and in case of Endowment policies where the number 143 of premiums is the same as the number of years in the Endowment period, such as a Ten Year Endowment, or a Twenty Year Endowment. In other words, the annual flat rate of $1 applies to all policies with premiiuns pay- able throughout the entire period of risk. In the case of Limited Payment Life and Limited Payment Endow- ment contracts the premium covering the entire period of risk must be "commuted" into one payable for a limited period; that is, a rate is determined which is such that its present value, according to the basis of mortality and interest adopted in the calculation of the Company's rates, is the same as the present value on the same basis of the premium of $1 per $1,000 for the entire period of risk. INDEX A FAOB Accumulated Reserves to Mean Insurance in Force, Ratio of 65 Actual Cost, Life Insurance at 112 Actual Mortality 68 Actual Saving in Mortality 97 Actual to Expected Mortality, Ratio of 71 Adequacy of Net Premium, Proving the 40 Admitted Assets 88 Adverse Selection 101 Age, the Average 71 American Experience Table of Mortality 11, 13 Amount at Risk 66 Annual Dividend 107 Annual Statement 94 Annuitant 20 Annuities 1 30 Annuity 20 Annuity, Certain 131 Annuity, Computation of Temporary 81 Annuity, Computing the Value of 21 Annuity, Contingent 1 34 Annuity, Joint 184 Annuity, Joint and Survivor 1 84 Annuity, Life 20 Annuity on the Last Survivor 184 Annuity, Perpetual 131 Annuity, Survivorship 181 Annuity, The Deferred 131 Annuity, Temporary 29, 30 Annuity, Value of 21, 24 PAGE Assessment Insurance. 28, 54, 74, 75, 76, 77, 94, 100, 133 Assessment Plan 28 Assets, Admitted 88 Assets to Liabilities, Ratio of 89 Average After Lifetime 73 Average Age 71 Average Future Lifetime 73 B Beneficiary 6 Booth, Charles H 57 Brokerage 118 C Cash Surrender Value 56, 79 Cash Value 79 Cash Values and Endowments 56 Certificate of Stock 7 Charles H. Booth Policy 57 Claim 67 Conunission 118 Commission, Renewal 118 Commuted Values 131 Company, A Hypothetical 12 Company, Legal Reserve 89 Company, Mixed 7 Company, Mutual 6 Company, Old Line 94 Company, Stock 6 Composition of the Premium 54 Computation of Temporary Annuity 31 Computation of the Premium 12 Computing Limited Payment Premium 31 Computing the Value of the Annuity 21 Contingency, Life 132 Contingency Reserve 88 ii PAGE Contingent Annuities 134 Continuous Instalment Policy 132 Contribution Plan 110 Co-Operative Company 94 Cost of Insurance 67 Cost of New Business 118 D Death Claim 67 Death Claims Incurred to Mean Amount of Insurance in Force, The Ratio of 68 Deferred Annuity 131 Deferred Distribution 107 Deferred Dividend 107 Determining Premium of Term Policy 33 Determining the Limited Payment Premium 31 Determining the Net Value 84 Different Kinds of PoUcies 30 Disability Benefits 137 Distribution, Deferred 107 Distribution, Methods of 106 Distribution, Mutual Life Method 109 Distribution, Semi-Tontine 107 Distribution, The Contribution Plan 110 Distribution, The Percentage Method 110 Distribution, Tontine 108 Dividend 107 Dividend, Annual 107 Dividend, Deferred 107 Dividend, Yearly 107 Double Indemnity 141 Dying, Probability of ; 72 E Effect of Fraud 136 Effect of Mortality in Endowment Insurance 38 Effect of New Members 28 iii PA6K Effect of Withdrawals 26 Election 6 Elementary Principles 8 Endowment, Fifteen- Year 37 Endowment Insurance 36 Endowment Insurance, Effect of Mortality in. . . . 38 Endowment Policies 36 Endowment Premium 37 Endowment, Pure 37 Endowments, Cash Values and 36 Endowment, Thirty- Year 37 Endowment, Twenty- Year 37 Errors, Some Popular 53 Examples of Remarkable Longevity 49 Expectation of Life 72 Expectation of Life Not Used in Computing Cost of Life Insurance 75 Expected Mortality 68 Expense Element 53 Expenses Incurred to Loading Earned, Ratio of . . . 80 Expiry, Termination by 33, 102 F Face 67 Fifteen-Year Endowment. 37 First Step 14 First Year Term 120 Fraternal Insurance 94, 118 Fraud, Effect of 136 Full Preliminary Term 124 Fund, Mortality 43 Fund, Reserve 43 G Gain, Sources of 96 Gains or Savings in Life Insurance 95 General Observations 24 Gross Premium 10 iv PAGE H Hypothetical Company 12 I Incontestability 135 Initial Reserve 44 Insurable Interest 129 Insurance, Assessment 28, 54, 74, 75, 76, 77, 94, 100, 133 Insurance, Cost of 67 Insurance, Effect of Mortality in Endowment. ... 38 Insurance, Endowment 36 Insurance, Natural Premium 116 Insurance, Non-Participating 110 Insurance, Participating Ill Insurance, Renewable Term 33 Insurance, Stock Rate Ill Insurance, Ten- Year Reneweable Term 33 Insurance, Term 32 Insurance, Yearly Renewable Term 33 Interest Rate 16 Interest, The Insurable 129 Introduction 3 "Investment Element" 54 J Joint and Survivor Annuity 134 Joint Annuity 1 34 L Lapse 26 Lapses and Terminations by Expiry 102 Lapses Not Desirable Source of Profit 100 Legal Net Value 83 Legal Reserve 83 V PAGE Legal Reserve Company 94 Legal Reserve Liability 86 Legal Standard of Valuation 83 Level Premium 117 Level Net Premium _ 122 Liability^ The Legal Reserve 86 Life Annuity 20 Life Contingency 132 Life, Expectation of 72 Life Insurance at Actual Cost 112 Life Insurance, Origin of 5 Life Insurance Policy 6 Life Insurance, Profits in 34 Life, Limit of 11,48 Life, Probable 73 Life, Ten-Pa3Tnent 30 Life, Twenty-Payment SO Limit of Life 11, 48 Limited Payment Life Policy 30 Limited Payment Premium, Determining the 31 Living, Probability of 72 Loading 9, 10, 76 Loading, To Ascertain the 78 Loading, True OflSce of 77 Longevity, Examples of Remarkable 49 Loss _ 66, 67 ~ M Making the Premium 8 Meaning of Large Reserves 64 Mean Reserve 63 Methods of Distribution 106 Minimum Legal Standard 83 Minimum Legal Standard of Valuation 81 Mixed Company 7 Mixed Table 126 vi PAGE Modified Preliminary Term 124 Mortality 68 Mortality, Actual 68 Mortality, American Experience Table of 11, 13 Mortality Element 53 Mortality, Expected 68 Mortality Fund 43 Mortality in Endowment Insurance, Eifect of 38 Mortality, Saving in 68, 96 Mortality at Older Ages, Saving in 102 Mortality Saving, When Greatest 99 Mortality Table 10 Mortality Table, American Experience 11, 13 Mortality Table, The Mixed 126 Mortality Table, The Select 126 Mortality Table, The Ultimate 126 Mortality, Tabular 68 Mortality, The Actual Saving in 97 Mutual Companies 6 Mutual Life Insurance Company 6 Mutual Life Method of Distribution 109 Mutual Life of New York 7 N Natural Premium 117 Natural Premium Insurance 116 Net Annual Premium, to Find the 23 Net Premium 9, 10 Net Premium, The Exact 42 Net Premium, Proving the Adequacy of the 40 Net Single Premium 19, 59 Net Valuation 81 Net Value 81 Net Value, Determining the 84 Net Value, Legal 83 "New Blood" 29, 52 ■"New Blood" Not Essential to Permanence 52 vii PAGE New Members, Effect of 28 New Business, The Cost of 118 Non-Forfeiture 1 34 Non-Participating Insurance 110 O Observations on the Reserve 52 "Old Line" Company 94 Oldest Policyholder 51 One- Year Term Policy 32 Ordinary Life Policy 8 Origin of Life Insurance 5 Over-charge, What Becomes of the 113 P Participating Insurance Ill Percentage Method 110 Perpetual Annuity 131 Policies, Different Kinds of 30 Policies, Standard 130 Policy, Continuous Instalment 132 Policy, Determining Premium of Term 33 Policy, Endowment 36 Policyholder 6 Policyholder, The Oldest 51 Policy, Life Insurance 6 Policy, Limited Payment Life 30 Policy, One- Year Term 32 Policy, Ordinary Life 8 Policy, Ten- Year Term 32 Policy, Term 32 Policy, The Standard 130 Policy, Thirty- Year Term 32 Policy, Twenty- Year Term 32 Preliminary Term System 119 viii FAGB Preliminary Term, The Full 124 Preliminary Term, The Modified 124 Premium 6 Premium, Composition of the 54 Premium, Computation of 12 Premium, Determining Limited Payment 31 Premium, Endowment 37! Premium, Gross 10 Premium, Making the 8 Premium, Net 9 Premium, Net Single 19 Premium Not Composed of Three Elements 55 Premium, Proving Adequacy of the Net 40 Premium, Stipulated 94 Premium, Sufficiency of 25 Premium, The Exact Net 42 Premium, The Level 117 Premium, The Natural 117 Premium, The Level Net 122 Premium, To Find the Net Annual 23 Probability of Dying 72 Probability of Living 72 Probable Life 73 Profit, Lapses Not Desirable Source of "..... 100 Profits in Life Insurance 34 Profits, To Whom Go 36 Proving the Adequacy of Net Premium 40 Pure Endowment 37 R Rapid Accumulation of Reserves 63 Ratio, A Misleading 80, 99 Ratio of Accumulated Reserves to Mean Insurance in Force 65 Ratio of Assets to Liabilities 89 Ratio of Death Claims Incurred to Mean Amount of Insurance in Force 68 Ratio of Expenses Incurred to Loading Earned. ... 80 ix PAGE Remarkable Longevityj Examples of 49 Renewable Term Insurance 33 Renewal Commission 118 Reserve 43 Reserve Account 55 Reserve All for Mortality Purposes 52 Reserve Basis, How Savings Vary According to. . . 103 Reserve Basis Must Be Considered 90 Reserve Element 58 Reserve, Initial 44 Reserve, Legal 83 Reserve, Mean 63 Reserve Not the Property of Individual Policyholder 61 Reserve, Observations on the 52 Reserves, Rapid Accumulation of 63 Reserves, Single Premiums and 58 Reserves, The Meaning of Large 64 Reserve Tables 62 Reserve, Terminal 44 Reserve, The Contingency 88 Reserve Values on Paid-up Policies 59 Risk, Amount at 66 S Saving in Mortality 68, 96 Saving in Mortality at Older Ages 102 Saving in Mortality, When Greatest 99 Savings Vary According to Reserve Basis 103 Select and Ultimate Valuation 125 Selection Against the Company 101 Select Lives 126 Select Table 126 Self Insurance 66 Semi-Tontine Distribution 107 Semi-Tontine Plan 107 Single Premiums and Reserves 58 Slight Gains from Saving in Mortality at the Older Ages 102 J PAGE So-called "Profits" in Life Insurance 34 Some Popular Errors 53 Sources of Gain 96 Standard Policies 130 Statement, The Annual 94 Step-Rate Plan 118 Stipulated Premium 94 Stock, Certificate of 7 Stock Companies 6 Stockholder 7 Stock Rate Insurance Ill Sufiiciency of the Premium 25 Sundry Topics 129 Surrender Charge 79, 101 Surrender Value, Cash 56, 79 Surplus 107 Survivorship Annuity 131 Survivor, Annuity on the Last 1 34 T Table, Verification 41, 45, 46, 47 Tabular Mortality 68 Tabulated Illustration 91 Temporary Annuity 31 Temporary Annuity, Computation of 31 Ten-Payment Life 30 Ten- Year Renewable Term 33 Ten- Year Term Policy 32 Term, First Year 120 Terminal Reserve 44 Termination by Expiry 83, 102 Term Insurance 32 Term Insurance, Renewable 33 Term Insurance, Ten- Year Renewable 33 Term Insurance, Yearly Renewable 33 Term Plan, Full Preliminary 124 Term Plan, Modified Preliminary 124 Term Policy 32 xi PAGE Term Policy, Determining Premium of 33 Term, The Preliminary 119 The Exact Net Premimn 42 Thirty- Year Endowment 37 Thirty- Year Term Policy 32 To Ascertain the Loading 78 To Find the Net Annual Premium 23 Tontine' Distribution 107 Tontine Method 108 Topics, Sundry 129 Total and Permanent Disability 137 Total Insurance Fund 18 To Whom the Profits Go 36 Twenty-Payment Life 30 Twenty- Year Endowment 37 Twenty- Year Term Policy 32 U Ultimate Table 126 V Valuation, Legal Standard of 83 Valuation, Minimum Legal Standard of 81 Valuation, Net 81 Valuation, Level Net Premium 122 Valuation, Select and Ultimate 125 Value of An Annuity 21, 24> Value, The Commuted 131 Value, The Net 81 Verification Table 41, 45, 46, 47 Vie Probable ; 73 W What Becomes of the Over-charge ? 113 When Mortality Saving is Greatest 99 Withdrawals, Effect of 26 Y Yearly Dividend 107 Yearly Renewable Term Insurance 33 xii No. 2008-5M-11-20 59 HG 8773 M99 1920 Author Vol. tfiitual life insurance co of NY Title Copy Educational leaflets Date Borrower's Name