TABLES FOR RENEWING & PURCHASING OF THE LEASES OF Cathedral-Churches AND COLLEGES, According to several Rates of Interest; with their Construction and Use explained. Also Tables for Renewing and Purchasing of LIVES. With Tables for Purchasing the Leases of Land or Houses according to several Rates of Interest, very Necessary and Useful for all Purchasers, but especially for them who are any way concerned in Church or College Leases. CAMBRIDGE, Printed by John Hay●●, Printer to the University. 1886. The Preface. Courteous Reader, ALthough there be variety of Tables extant, and those excellent, for computing of Interest and purchasing of Annuities, etc. yet for renewing of Leases there seems to be a defect; to supply which defect this Little Book is intended, and that there may be nothing wanting to complete such a design, it will be convenient, by way of Preface, to lay down the Grounds and Reasons for Renewing, and to demonstrate the Construction of the Tables ensuing, that so as well the skilful, as unskilful may be convinced and satisfied, as to their truth and exactness. Some things in Arithmetic are indeed very mysterious, and not so easily apprehended by them who are not acquainted with that sort of Learning, yet I hope they will not be so uncharitable as to condemn all as false, which falls not within the verge of their knowledge, or may seem to deviate from those erroneous Rules which they have espoused upon false grounds. But without any further Apology, I shall proceed to show both the Construction and Use of a Table of Reversions, calculated for several Rates of Interest, and how the Tables following for Renewing, are made from it, which are also made for several Rates of Interest, that so both the Landlord and Tenant may the better see when they are best dealt with. This Table of Reversions showeth the decrease of one Pound yearly, according to those several Rates of Interest; or what one Pound due at the end of any number of Years to come, not exceeding 40, is worth in ready Money, at 5, 6, 7, 8, 10, & 12 per. cent. per. Ann. First, for Example, What is one Pound, due a Year hence, worth in ready Money? For answer hereunto the Rule is this, viz. Let 100lb. with the Interest for a Year added thereunto, be the first term ●n the Rule of Three: 100lb. the second, and 1lb. the third. Examples at 6lb. and 10lb. per cent. As, is to So is, to 106, 100 :: 1, 94339 or 18 s. 10 d. ¼ 110, 100 :: 1, 90909 or 18 s. 2 d. from whence it appears that 1 l. in a years time at 6 l. per cent. decreaseth to 18 s. 10 d. ¼, but at 10 lb. per cent. it decreaseth to 18 s. 2 d. so that 18 s. 10 d. ¼. ready Money, is worth 20 s. to be paid a Year hence, reckoning the Interest at 6lb. per cent. per Ann. so 18 s. 2 d. ready Money is worth 20 s. to be paid a Year hence, at 10 lb. per cent. and so by a continual Geometrical proportion decreasing it comes to pass that 20 s. to be paid 21 Years hence is worth but 5 s. 10 d. ½. ready Money, that is, 5 s. 10 d. ½, paid now, will in 21 Years at 6 lb. per cent. per Ann. compound Interest, increase to 20 s. but at 10 lb. per cent. 20 s. in 21 Years decreaseth to 2 s. 8 d. ½ so that 2 s. 8 d. ½ paid now, will amount to 20 s. in 21 Years, at 10 lb. per cent. per Ann. compound Interest; and at 12 lb. per cent. 1. s. 10 d. paid now, is worth 20 s. to be paid 21 Years hence; now, to renew a Lease of 21 Years that hath but one Year lapsed according to the rate of 10lb. per cent. per Ann. I look in the Table of Reversions against 21, and under the rate mentioned, and find in the Common Angle of meeting, 2 s. 8 d. ½, which is the Fine to be given to renew one year Lapsed in the said Lease, supposing the Rent to be one Pound per An. for it is 21 years ere this year is completed, but in 21 years' time 2 s. 8 d. ½. will amount to 20 s. as was said before, and therefore by giving 2 s. 8 d. ½. ready Money, the Lease is made up again for 21 years, according to the rate mentioned: now suppose again that there be 2 years lapsed in the same Lease allowing the same rate of Interest, then by the Table of Reversions I find that 20 s. to be paid 20 years hence is worth 2 s. 11 d. 2 q. ready Money, according to the aforesaid rate; now the Sum of these two reversions, viz. 2 s. 11 d. 2 q. and 2 s. 8 d. 2 q. is 5 s. 8 d. which is the Fine to be paid to make up the Lease 21 years again, supposing the yearly Rent to be 1 l. for 5 s. 8 d. paid now will countervalue the 2 years' Rent, which the Landlord was to receive the 2 years after 19, had not the Lease been made up, from whence the reason very plainly appears why such a Fine should be given to renew such a number of years lapsed, according to such a rate of Interest. Now although the following Tables for Renewing, are only for Leases of 21, 20, 40, and 10 years, yet by this Table of Reversions may be made Tables for Renewing of Leases for any number of years under 41, as by an Example will appear; as suppose in a Lease of 31 years, I am to renew 7 years lapsed, allowing 6lb. per cent. profit; to do this I take the Sum of the Reversions for 7 years from 31 upwards, counting that as 1, etc. and so I find the Sum to be 1 l. 12 s. 6 d. 1 q. that is 1 Year, 2 Quarters, 1 Month, & 5 Decimal Parts purchase, which is the Fine to be paid for renewing the 7 years lapsed required; this being understood it will not be difficult to do the like for any other Number of years lapsed, either in this or in any other Lease, and according to any other rate of Interest, and therefore I think it needless to multiply Examples. The reason and also truth of the Tables for Renewing will further appear, if you consider the Value of the whole Lease, and from it Subtract the Value of the years Lapsed, the Remainder, if right, is the value of a Lease for so many years as there are years remaining in the Lease, as if 7 years are Lapsed, in a Lease for 21 years, than there are 14 in esse. Example. Y. q. m. d. ps. The Value of a Lease for 21 years at 6lb. per c. is 11 3 0 1 The Value of 7 years lapsed in that Lease is which subtract 2 1 2 6 Remains 9 1 0 5 which remainder is the Value of a Lease for 14 years at 6lb. per cent. as by the Table for Purchasing appears; from whence also it is evident, that if the Value of the years in esse be Subtracted from the Value of the whole Lease, the Remainder is the Value of the years in Reversion. The Table of Reversions is also useful for purchasing the Reversion of an Estate. Example. Suppose an Estate whose Fee-Simple, or real Value is 100lb, and it be Mortgaged or Leased out for 20 years, What's the Reversion thereof Worth at 6lb. per cent? Then for Answer, I find by the Table the present Worth of 1 l. to be paid 20 years hence is at 6lb. per cent. 6 s. 2 d. 3 q. l. s. d. Then 100 times 6 s. is 30 0 0 And 100 times 2 d. or 200 d. is 0 16 8 And 100 times 3 q. or 300 q. make 0 6 3 Sum 31 2 11 So that 31 l. 2 s. 11 d. is the present Value of 100lb. to be paid 20 years hence, which is the Answer to the Question. A Table of Reversions showing what 1 lb. due any number of Years hence under 41 is worth in ready Money at 5, 6, 7, 8, 10, and 12 lb. per cent. Years. 5 per cent. 6 per cent. 7 per cent. 8 per cent. 10 per cent. 12 per cent. s. d. q. s. d. q. s. d. q. s. d. q. s. d. q. s. d. q. 1 19 0 2 18 10 1 18 8 0 18 6 0 18 2 0 17 10 1 2 18 1 2 17 9 1 17 5 2 17 1 3 16 6 1 15 11 1 3 17 3 1 16 9 2 16 3 3 15 10 1 15 0 0 14 3 0 4 16 5 1 15 10 0 15 3 0 14 8 1 13 8 0 12 8 2 5 15 8 0 14 11 1 14 3 1 13 7 1 12 5 0 11 4 0 6 14 11 0 14 1 0 13 4 0 12 7 0 11 3 2 10 1 3 7 14 2 2 13 3 2 12 5 1 11 8 0 10 3 0 9 0 3 8 13 6 1 12 6 2 11 7 2 10 9 2 9 4 0 8 1 0 9 12 10 2 11 10 0 10 10 2 10 0 0 8 5 3 7 2 2 10 12 3 1 11 2 0 10 2 0 9 3 0 7 8 2 6 5 0 11 11 8 0 10 6 1 9 6 0 8 6 3 7 0 0 5 9 0 12 11 1 2 9 11 1 8 10 2 7 11 1 6 4 2 5 1 2 13 10 7 1 9 4 2 8 3 2 7 4 0 5 9 2 4 7 0 14 10 1 0 8 10 0 7 9 0 6 9 2 5 3 0 4 1 0 15 9 7 2 8 4 0 7 3 0 6 3 2 4 9 1 3 7 3 16 9 2 0 7 10 2 6 9 1 5 10 0 4 4 1 3 3 0 17 8 8 2 7 5 0 6 4 0 5 4 3 3 11 1 2 11 0 18 8 4 0 7 0 0 5 11 0 5 0 0 3 7 0 2 7 0 19 7 11 ● 6 7 ● 5 6 1 4 7 1 5 3 0 2 4 1 20 7 6 1 6 2 3 5 2 0 4 3 2 2 11 2 2 1 0 21 7 2 0 5 10 2 4 10 0 3 11 3 2 8 2 1 10 0 22 6 10 0 5 6 2 4 6 0 3 8 0 2 5 2 1 8 0 23 6 6 0 5 3 0 4 2 2 3 4 3 2 2 3 1 5 2 24 6 2 1 4 11 1 3 11 1 3 1 3 2 0 1 1 3 3 25 5 10 3 4 8 0 3 8 1 2 11 0 1 10 0 1 2 0 26 5 7 1 4 4 3 3 5 1 2 8 1 1 8 0 1 0 2 27 5 4 1 4 1 3 3 1 2 2 6 0 1 6 1 11 0 28 5 1 0 3 10 3 3 0 0 2 3 3 1 4 2 10 0 29 4 10 1 3 8 1 2 9 2 2 1 3 1 3 0 9 0 30 4 7 2 3 6 1 2 7 2 1 11 3 1 1 3 8 0 31 4 5 1 3 3 1 2 5 1 1 10 0 1 1 0 7 0 32 4 2 1 3 0 2 2 3 2 1 8 1 11 1 6 1 33 4 0 0 2 10 1 2 1 2 1 6 3 10 1 5 2 34 3 9 2 2 8 3 2 0 0 1 5 1 9 1 5 1 35 3 7 2 2 6 2 1 10 2 1 4 0 8 2 4 2 36 3 5 1 2 5 1 1 9 0 1 3 0 7 3 4 0 37 3 3 1 2 3 2 1 7 2 1 2 0 7 0 3 1 38 3 1 2 2 2 0 1 6 2 1 1 0 6 1 3 0 39 2 11 3 2 0 0 1 5 0 1 0 0 5 3 3 0 40 2 10 0 1 11 0 1 4 0 0 11 0 5 1 2 2 AN ADVERTISEMENT TO THE READER. SEeing Mr. Æcroid's Tables have been for a long time made use of for Renewing of Leases, which Tables do a little differ from the Tables for Renewing in this Book, I thought it convenient to show the reason of that Difference, that so the truth being cleared, nothing might remain as an Objection against the use of the Tables following, for I know that whatsoever doth offer itself contrary or different from that which Men are most used to, cannot by some be entertained without the imputation of Falsehood or Error. These Tables of Æcroid's for Renewing of Leases are not indeed to be esteemed erroneous, but are exact enough according to the Rate of Interest for which they were Calculated, which was at 11 l. 3 s. 6 d. 6/17 per cent. (as is intimated in the use of those Tables) but the Table contained in this Book for Renewing a Lease of 21 years is Calculated at 11 l. 11 s. 8 d. ¼, 3/10, and at 5 l. 6 l. 8 l. and 10 l. per cent. and the Fine for Renewing 7 years Lapsed in a Lease of 21 years, by Æcroid's Tables is 1 l. 1 s. 3 d. that is 1 Year's, and 3 Weeks purchase, whereas by the Table for Renewing in this Book, it is but one Year's value at 11 l. 11 s. 8 d. ¼, 3/10, per cent. and the reason is, because the rate of Interest is greater, but when the rate of Interest is lesser, the Fine is greater, as at 10 l. per cent. the Fine for Renewing 7 years lapsed is 1 Year's, 1 Quarter's, and 1 Week's value; but at 8 l. per cent. the Fine for Renewing 7 years lapsed, is 1 Year's, and above 3 Quarter's value, and at 6 l. per cent. the Fine is 2 years and almost an halfs value. So in the Table for Renewing a Lease of 20 years, at 12 l. 6 s. per cent. the Fine for Renewing 7 years lapsed, is but 1 years' value: whereas by Æcroid's Tables it is 1 l. 3 s. 8 d. that is 1 year and above 2 months' value, but at 5 l. 6 l. 8 l. and 10 l. per cent. the Fine is greater, because the rate of Interest is less, as was said before. And that this is true it will appear if you consider that the Tables for Renewing of Leases consist of the Sums of the Tables of Reversion, or Decrease of Money; now it is evident that the greater the rate of Interest is, the greater is the decrease of Money in Reversion, and so consequently the lesser are the Sums of those Reversions, which are the Fines for Renewing. Therefore, etc. An Example will better explain it; Thus in the Table of Reversions, I find that 1 l. or 20 s. in 40 years, decreaseth to 2 d. at 12 lb. per cent. Compound Interest; and at 10 l. per cent. 20 s. in 40 years, decreaseth to 5 d. 1 q. now the Sum of these Reversions for 7 years counting 40 as 1, 39 as 2, etc. at 12 l. per cent. is but 2 s. 1 d. 2 q. but at 10 l. per cent. the Sum for 7 years is 4 s. 1 d. 3 q. which are the Fines for Renewing 7 years lapsed in a Lease of 40 years, at the rates of 12 l. and 10 l. per cent. from whence it is evident that the lesser the rate of Interest is, the greater must be the Fine for Renewing; and the greater the rate is, the lesser must be the Fine: and therefore the Difference between Æcroid's Tables for Renewing, and these in this Book, proceeds only from the different rate of Interest for which they were Calculated. The Tables following for Renewing, and also for Purchasing of Leases, showing the values in Years, Quarters, Months, and Decimal Parts of a Month, I think it convenient a little to explain them, and to show how to Add, and Subtract those sort of Valuations; in order to which, I shall show first, that the Year is divided into 4 parts or Quarters, every Quarter into 3 Months, and a Month into 10 parts, called Decimal parts, so that at 1 l. per An. Rent, it will be 5 s. a Quarter, 1 s. 8 d. a Month, and 2 d. the tenth part of a Month, and because a Month contains 4 Weeks, it will be 5 d. a Week, so that 5 Decimal parts of a Month, being equal to 10 d. are equal to 2 Weeks, 3 Decimal parts are but 1 d. above a Week, so that it is easy to convert the Decimal parts of a Month, into Weeks. The reason why I used this way of Valuation, was because I thought it most familiar to those who were concerned in Purchasing; and although this way of expressing the Values is not so exact, as if they were expressed in Decimals, or in Pounds, Shillings, and Pence, etc. yet is the difference very inconsiderable, although there may be sometimes a Decimal part of a Month, or thereabouts either under or over the exact Value, yet is it not to be regarded in this sort of bargaining; seeing Men in giving or taking of Fines are not tied to any particular rate of Interest so exactly, as not to err a Penny or two, although the Rent be but 20 s. per An. and therefore when a Fine is required of any Person, either for Renewing or Purchasing of a Lease, the Tables will show exactly enough what rate of Interest is allowed: so if any have a mind to give or take a Fine according to a rate of Interest proposed, they may do it near enough by the Tables. How to Add together, the Fines given in Years, Quarters, Months, and Decimal Parts of a Month. Example. Y. Q. M. d.p. Suppose I am to Add these 3 2 1 6 Fines together, viz. 2 3 1 7 Sum 6 2 0 3 First than I begin at the least Denomination, that is at Decimal Parts of a Month, and say 7 and 6 is 13, I set down 3 and carry 1 for the 10, because 10 Decimal parts are one Month; then I come to the Months and say 1 that I carry and 1 is 2, and 1 is 3, I set down 0, and carry 1 for the 3, because 3 Months make a Quarter; then I come to the Quarters, and say, 1 that I carry and 3 is 4, and 2 is 6, I set down 2 and carry 1, for the 4, because 4 Quarters make a Year; then I come to the Years, and say, 1 that I carry and 2 is 3, and 3 is 6, which I set down, and so the Sum is 6 Years, 2 Quarters, 0 Months, and 3 Decimal Parts, as in the Example. How to Subtract one from the other, the Fines given in Years, Quarters, Months, and Decimal Parts of a Month. Example. Y. Q. M. D. pts. From 4 2 1 4 Take 2 2 2 6 Remains 1 3 1 8 First as in Addition, I begin at the least Denomination, and say 6 out of 4 I cannot, wherefore I borrow 10, because 10 Decimal Parts make 1 Month, and say 6 out of 14, and there remains 8, which I set down; then I come to the Months, and say 1 that I borrowed and 2 maketh 3, than I say 3 out of 1 I cannot, wherefore I borrow 3, because 3 Months make a Quarter, and say 3 out of 4, and there remains 1, which set down; then I come to the Quarters, and say 1 that I borrowed and 2 maketh 3, then 3 out of 2 I cannot, wherefore I borrow 4, because 4 Quarters make a Year, and say 3 out of 6, and there remains 3, which I set down; and then go to the Years, and say 1 that I borrowed and 2 maketh 3, then 3 out of 4 and there remains 1; And so there Remains 1 Year, 3 Quarters, 1 Month, 8 Decimal parts. These two Examples of Addition and Subtraction, being understood, it will not be difficult to do the like with any other of these sorts of Valuations, and therefore, I think it needless to exemplify any further. The Contents of this Book. A Table of Reversions at 5, 6, 8, 10, and 12 per cent. with its Construction and Use explained in the Preface. CHAP. I. A Table for Renewing a Lease of 21 Years according to several rates of Interest, with its use explained. CHAP. II. A Table for Renewing a Lease of 20 Years according to several rates of Interest, with its use explained. CHAP. III. A Table for Renewing a Lease of 40 Years according to several rates of Interest, with its use explained. CHAP. IU. A Table for Renewing a Lease of 10 Years according to several rates of Interest, etc. CHAP. V. A Table to Reduce the Values given in Years, Quarters, Months, and Decimal Parts of a Month, in Pounds, Shillings, etc. with its use explained. CHAP. VI Tables for Purchasing and Renewing of Lives, with their Construction and Use explained. CHAP. VII. A Table to Purchase by, according to 5, 6, 8, 10, and 12 per cent. with its use exemplified. CHAP. VIII. Tables showing the increase of Money yearly, the Value of Annuities forborn, and what Annuity 1 l. ready Money will purchase at 6l. per cent. per An. Compound Interest, with their uses exemplified. CHAP. IX. Of the Difference between Long and Short Leases, Rules concerning Free-holds, and a Table of Simple Interest. CHAP. I. THE first Table which offers itself for Renewing of Leases, is for the term of 21 Years, it shows the values in Years, Quarters, Months, and Decimal parts of a Month, as all the rest do, the first part of this Table is calculated at 11 l. 11 s. 8 d. ¼, 1/10, per cent. per An. Compound Interest, so that the Fine for Renewing 7 Years Lapsed, or the present worth of 7 Years in Reversion, not to begin till 14 are expired, is exactly 1 Years Value, which Fine, and consequently rate of Interest, Bishops, Deans and Chapters Heads and Fellows of most Colleges in both Universities, do observe in Letting and Renewing of their Leases; but at other rates of Interest, the Fine for Renewing 7 Years Lapsed, the Table shows as followeth, viz. The Fine for Renewing 7 Years Lapsed Y. Q. M. D. pts l. s. d. at 5 p. c. is 2 3 2 0 Which by the Table of Red. at 10 lb. yearly Rent is 29 3 4 at 6 p. c. is 2 1 2 6 24 13 4 at 8 p. c. is 1 3 0 3 17 15 0 at 10 p. c. is 1 1 0 3 12 15 0 The years in esse may be valued as a Lease of so many years, as in this Lease of 21 years, if 7 years are run out, then there are 14 in esse, whose value are as a Lease of 14 years, and may be found by the Table for Purchasing; or if you subtract the value of the years in Reversion from the value of the whole Lease, the remainder is the value of the years in esse. To find the value of some of the years in Reversion, as suppose 3 of the 7, I do thus, because 3 wants 4 of 7, I take the value of 4 years in Reversion, from the value of 7 in Reversion, the remainder is the value of the 3 years required. Example. Y. q. m. d.p. The value of 7 years in Reversion, at 11 lb. 11. s. 8 d. per cent. is 1 0 0 0 The value of 4 years in Reversion at the same rate is Which subtract 0 1 2 7 Remains 0 2 0 3 Which remainder being given for a Fine, will make up the Lease to 17 years, that is 3 added to 14. A Table for the Renewing of any Number of years lapsed in a Lease for 21 years. 11 l. 11 s. 8 d. ¼ p.c. 5 per cent. 6 per cent. 8 per cent. 10 per cent. Years Lapsed Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts 1 0 0 1 2 0 1 1 3 0 1 0 5 0 0 2 4 0 0 1 6 2 0 0 2 5 0 2 2 8 0 2 1 2 0 1 2 0 0 1 0 4 3 0 1 1 0 1 0 1 5 0 3 2 2 0 2 1 7 0 1 2 3 4 0 1 2 7 1 2 0 5 1 1 0 4 0 3 1 7 0 2 1 5 5 0 2 1 6 1 3 2 8 1 2 1 8 1 0 2 0 0 3 0 8 6 0 3 0 6 2 1 2 3 2 0 0 6 1 1 2 5 1 0 0 4 7 1 0 0 0 2 3 2 0 2 1 2 6 1 3 0 3 1 1 0 3 8 1 0 2 6 3 1 2 1 2 3 1 9 2 0 1 4 1 2 0 5 9 1 1 2 5 3 3 2 4 3 1 1 5 2 1 2 8 1 3 1 0 10 1 2 2 7 4 2 0 1 3 3 1 5 2 3 1 5 2 0 1 8 11 2 0 0 3 5 0 1 1 4 1 1 8 3 1 0 7 2 2 0 0 12 2 1 1 3 5 2 2 5 4 3 2 5 3 3 0 2 2 3 1 6 13 2 2 2 8 6 1 1 2 5 2 0 6 4 1 0 2 3 1 0 7 14 3 0 1 8 7 0 0 3 6 0 2 1 4 3 0 7 3 3 0 3 15 3 2 1 3 7 2 2 8 6 3 1 1 5 1 1 7 4 1 0 4 16 4 0 1 5 8 1 2 8 7 2 0 6 6 0 0 2 4 3 1 2 17 4 2 2 5 9 1 0 2 8 1 0 5 6 2 2 4 5 1 2 7 18 5 1 1 3 10 0 1 1 9 0 1 0 7 1 2 2 6 0 1 9 19 6 0 0 9 10 3 2 4 9 3 2 1 8 0 2 8 6 3 1 9 20 6 3 1 5 11 3 1 3 10 3 0 8 9 0 1 1 7 2 2 8 Total Value. Total value Total value Total value Total value 7 3 0 3 12 3 0 8 11 3 0 1 10 0 0 2 8 2 1 7 CHAP. II. THE next Table is for the term of 20 years, the first part thereof is calculated according to the rate of about 12 lb. 6 s. per cent. per An. so that 1 year's value is the worth of 7 years lapsed, or in Reversion; which Fine, and consequently rate of Interest, by some is observed in a Lease for 20 years; but at other rates of Interest: The Fine for Renewing 7 years lapsed in this Lease of 20 years, you will find by the Table as followeth, viz. The Fine for Renewing 7 years lapsed Y. Q. M. D. pts. l. s. d. at 5 p. c. is 3 0 0 8 Which by the Table of Red. at 10 lb. yearly Rent is 30 13 4 at 6 p. c. is 2 2 1 4 26 3 4 at 8 p. c. is 1 3 1 9 19 1 8 at 10 p. c. is 1 1 1 8 14 0 0 The years in esse may be valued as a Lease of so many years, or their value may be found, by subtracting the value of the years lapsed, from the value of the whole Lease, as was directed before in the Lease of 21 years. The value of some of the years in Reversion may also be found in this Lease, as is directed before in the former Lease, however to make all plain, I shall give one Example: As suppose, I am to find the value of 4 of the 7 years in Reversion in this Lease; then according to the Rule given in the Lease of 21 years, I do thus, because 4 wants 3 of 7, I take the value of 3 years in Reversion, from the value of 7 in Reversion, the remainder is the value of the 4 years required. Example. Y. q. m. d.p. The value of 7 years in Reversion at 6 l. per cent. is 2 2 1 4 The value of 3 years at the same rate is Which subtract 0 3 2 9 Remains 1 2 1 5 this Remainder being given for a Fine will make up this Lease to 17 years, that is 4 added to 13. A Table for the Renewing of any Number of years lapsed in a Lease for 20 years. 12 l. 6 s. p. c. 5 per cent. 6 per cent. 8 per cent. 10 per cent. Years Lapsed. Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts 1 0 0 1 2 0 1 1 5 0 1 0 7 0 0 2 6 0 0 1 8 2 0 0 2 5 0 3 0 3 0 2 1 7 0 1 2 3 0 1 0 7 3 0 1 1 0 1 0 2 2 0 3 2 9 0 2 2 3 0 1 2 9 4 0 1 2 6 1 2 1 5 1 1 1 4 0 3 2 6 9 2 2 2 5 0 2 ● 5 2 0 1 0 1 3 0 1 1 1 0 1 0 3 1 8 6 0 3 0 6 2 2 0 8 2 0 2 1 1 2 0 8 1 0 1 7 7 1 0 0 0 3 0 0 8 2 2 1 4 1 3 1 9 1 1 1 8 8 1 0 2 6 3 2 1 2 3 0 1 0 2 1 0 3 1 2 2 3 9 1 1 2 5 4 0 1 8 3 2 1 0 2 2 2 0 2 0 0 1 10 1 2 2 9 4 2 2 8 4 0 1 3 3 0 1 2 2 1 1 3 11 2 0 0 7 5 1 1 ● 4 1 2 0 3 2 0 8 2 3 0 0 12 2 1 1 9 5 3 2 9 5 1 0 1 4 0 0 8 3 0 2 0 13 2 3 0 6 6 2 2 0 5 3 1 6 4 2 1 2 3 2 1 7 14 3 1 0 0 7 1 1 5 6 2 0 6 5 0 2 2 4 0 1 8 15 3 2 2 9 8 0 1 5 7 1 0 0 5 3 0 8 4 2 2 6 16 4 1 0 6 8 3 1 9 8 0 0 0 6 2 0 0 5 1 1 0 17 4 3 2 1 9 2 2 8 8 3 0 5 ● 0 2 8 6 0 0 2 18 5 2 1 6 10 2 1 1 9 2 1 6 8 0 0 4 6 3 0 2 19 6 1 2 2 11 2 0 0 10 2 0 3 8 3 1 7 7 2 1 2 Total value Total value Total value Total value Total value 7 1 0 8 ●● ● 2 5 11 1 2 6 9 3 0 8 8 2 0 1 CHAP. III. THE third Table for Renewing of Leases, is for the term of 40 years, it is calculated according to five several rates of Interest, and in its manner of using differs not from the other, nevertheless an Example will be convenient, which therefore I shall give; as suppose there be 14 years lapsed or run out in a Lease for 40 years, What must I give to make up this Lease again, according to those several rates of Interest signified by the Table? that is, What must I give for 14 years in Reversion, after 26 in esse? or, What's the present Worth of 14 years, beginning 26 years hence? For answer I find by the Table that the Fine for Renewing 14 years lapsed Y. q. m. d.p. lb. s. d. at 5 p. c. is 2 3 0 4 Which by the Table of Red. at 10 l. yearly Rent is 27 16 8 at 6 p. c. is 2 0 0 2 20 03 4 at 8 p. c. is 1 0 1 3 11 01 8 at 10 p. c. is 0 2 1 4 6 03 4 at 12 p. c. is 0 1 1 1 3 08 4 The years in esse, as was said before, are valued as a Lease of so many years, as in a Lease for 40 years, if 14 years are run out, then there are 26 in esse, whose Value are as a Lease of 26 years, and may be found by the Table for Purchasing, etc. The Value of some of the years in Reversion, may be found in this Lease, by the same Rules that they were found by in the foregoing Leases; as if it were required to find the Value of 6 of the 14 years in Reversion in this Lease of 40 years, then because 6 wants 8 of 14, I take the Value of 8 years in Reversion from the Value of 14 in Reversion, and the Remainder is the Value of the 6 years required, which will make the Lease up to 32 years. A Table for the Renewing of any Number of years lapsed in a Lease for 40 years. 5 per cent. 6 per cent. 8 per cent. 10 per cent. 12 per cent. Years Lapsed. Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts 1 0 0 1 7 0 0 1 1 0 0 0 5 0 0 0 2 0 0 0 1 2 0 1 0 5 0 0 2 4 0 0 1 1 0 0 0 5 0 0 0 3 3 0 1 2 3 0 1 0 6 0 0 1 8 0 0 0 8 0 0 0 4 4 0 2 1 3 0 1 2 0 0 0 2 5 0 0 1 2 0 0 0 6 5 0 3 0 4 0 2 0 4 0 1 0 2 0 0 1 6 0 0 0 8 6 0 3 2 5 0 2 2 0 0 1 1 0 0 0 2 0 0 0 1 0 7 1 0 1 8 0 3 0 6 0 1 1 9 0 0 2 5 0 0 1 2 8 1 1 1 2 0 3 2 3 0 1 2 8 0 1 0 0 0 0 1 5 9 1 2 0 7 1 0 1 1 0 2 0 9 0 1 0 5 0 0 1 8 10 1 3 0 4 2 1 0 1 0 2 2 0 0 1 1 2 0 0 2 2 11 2 0 0 2 1 1 2 2 0 3 0 2 0 1 1 9 0 0 2 6 12 2 1 0 1 1 2 1 4 0 3 1 4 0 1 2 6 0 1 0 1 13 2 2 0 2 1 3 0 8 0 3 2 8 0 2 0 4 0 1 0 5 14 2 3 0 4 2 0 0 2 1 0 1 3 0 2 1 4 0 1 1 1 15 3 0 0 7 2 0 2 9 1 1 0 0 0 2 2 4 0 1 1 7 16 3 1 1 2 2 1 2 8 1 1 1 7 0 3 0 5 0 1 2 4 17 3 2 2 0 2 2 2 7 1 2 0 6 0 3 1 7 0 2 0 2 18 3 3 2 9 2 3 2 9 1 2 2 6 1 0 0 0 0 2 1 1 19 4 1 1 0 3 1 0 2 1 3 1 8 1 0 1 5 0 2 2 1 20 4 2 2 3 3 2 0 8 2 0 1 2 1 1 0 2 0 3 0 2 21 5 0 0 8 3 3 1 5 2 1 0 8 1 1 1 9 0 3 1 4 22 5 1 2 5 4 0 2 4 2 2 0 6 1 2 0 8 0 3 2 9 23 5 3 1 5 4 2 0 6 2 3 0 5 1 3 0 0 1 0 1 4 24 6 1 0 8 4 3 2 1 3 0 0 8 1 3 2 4 1 1 0 2 25 6 3 0 3 5 1 0 8 3 1 1 3 2 0 2 0 1 1 2 1 26 7 1 0 0 5 2 2 8 3 2 2 1 2 1 1 8 1 2 1 3 27 7 3 0 1 6 0 2 1 4 0 0 1 2 2 2 0 1 3 0 7 28 8 1 0 4 6 2 1 7 4 1 1 5 2 3 2 4 2 0 0 5 29 8 3 1 1 7 0 1 7 4 3 0 3 3 1 0 3 2 1 0 6 30 9 1 2 1 7 2 2 0 5 0 2 4 3 2 1 5 2 2 1 0 31 10 0 0 5 8 0 2 7 5 2 2 0 4 0 0 1 2 3 1 9 32 10 2 2 2 8 3 0 8 6 0 2 0 4 1 2 2 3 1 0 2 33 11 1 1 3 9 1 2 3 6 2 2 5 4 3 1 8 3 2 2 0 34 12 0 0 9 10 0 1 3 7 1 0 5 5 1 1 9 4 0 1 5 35 12 3 0 8 10 3 0 8 7 3 2 0 5 3 2 7 4 2 1 6 36 13 2 1 2 11 2 0 7 8 2 1 2 6 2 1 1 5 0 2 4 37 14 1 2 0 12 1 1 2 9 1 1 0 7 1 0 4 5 3 1 0 38 15 1 0 4 13 0 2 3 10 0 1 6 8 0 0 4 6 2 0 6 39 16 0 2 3 14 0 1 0 10 3 2 9 8 3 1 3 7 1 1 1 Total Value. Total value Total value Total value Total value 17 0 1 7 15 0 0 3 11 3 2 0 9 3 0 2 8 0 2 8 CHAP. IV. A Table for the Renewing of any Number of years lapsed in a Lease for 10 years. 17 lb. 18 s. per cent. 5 per cent. 6 per cent. 8 per cent. 10 p. cent. Years Lapsed. Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts 1 0 0 2 3 0 2 1 4 0 2 0 7 0 1 2 5 0 1 1 6 2 0 1 2 0 1 1 0 1 1 0 1 8 0 3 2 6 0 3 0 7 3 0 2 2 3 1 3 2 2 1 3 0 3 2 2 0 0 1 1 0 3 4 1 0 0 0 2 2 1 7 2 1 2 3 2 0 1 0 1 3 0 4 5 1 1 1 5 3 1 1 7 3 0 1 8 2 2 2 6 2 1 1 2 6 1 3 0 9 4 0 2 1 3 3 1 7 3 1 1 7 2 3 2 7 7 2 1 1 0 5 0 0 0 4 2 2 2 4 0 1 5 3 2 1 9 8 2 3 2 3 5 3 1 3 5 2 0 3 4 3 2 1 4 1 1 9 9 3 2 2 1 6 3 0 2 6 1 2 0 5 3 0 4 5 0 2 8 Total value Total value Total value Total value Total value 4 2 0 1 7 2 2 6 7 1 1 2 6 2 2 5 6 0 1 7 THis being the last Table for Renewing of Leases, is for the term of 10 years, the first part thereof is calculated according to the rate of about 17 l. 18 s. per cent. so that the Fine for Renewing 4 years lapsed is one years' value, but at other rates of Interest, the Fine for Renewing 4 years lapsed, is by the Table as followeth, viz. the Fine for Renewing 4 years lapsed Y. q. m. d. p. lb. s. d. at 5 p. c. is 2 2 1 7 Which by the Table of Reduction at 10 l. per Ann. is 26 08 4 at 6 p. c. is 2 1 2 3 24 08 4 at 8 p. c. is 2 0 1 0 20 16 8 at 10 p. c. is 1 3 0 4 17 16 8 The years in esse are valued as before directed in the other Leases, as, if there be 4 years run out in this Lease of 10 years, than there are 6 years in esse, whose Value are as a Lease of 6 years, etc. CHAP. V. THE next Table is for the Reduction of the Values given in Years, Quarters, Months, and Decimal Parts of a Month, into Pounds, Shillings, and Pence, the use of it is very plain and easy, as by Examples will appear. Example. Suppose the Fine for Renewing any number of years lapsed, in any Lease to be 6 y. 2 q. 2 m. 4 d. p. and the yearly Rent 55 l. What is this Fine in Pounds, Shillings, and Pence? then by the Table I find lb. s. d. against 50 l. under 2 Quarters 25 00 0 against 50 l. under 2 Months 8 06 8 against 50 l. under 4 Dec. parts 1 13 4 against 5 l. under 2 Quarters 2 10 0 against 5 l. under 2 Months 0 16 8 against 5 l. under 4 Dec. parts 0 03 4 Sum of all is 38 10 0 Then for the 6 years' Value I say, 6 times 55 l. is 330 l. which added to 38 l. 10 s. 330 00 0 0 d. the Sum is 368 10 0 Which is the Value reduced into Pounds, Shillings, and Pence required. Suppose again the Fine for Renewing any number of years lapsed in any Lease, to be 2 y. 3 q. 2 m. 9 d.p. and yearly Rent 156 l. then what is this Fine in Money? For answer I say, twice 156 is 312 l. which is the 2 years' Value, then by the Table I find lb. s. d. against 100 l. under 3 Quarters 75 00 0 against 100 l. under 2 Months 16 13 4 against 100 l. under 5 Dec. parts 4 03 4 against 100 l. under 4 Dec. parts 3 06 8 against 50 l. under 3 Quarters 37 10 0 against 50 l. under 2 Months 8 06 4 against 50 l. under 5 Dec. parts 2 01 8 against 50 l. under 4 Dec. parts 1 13 4 against 6 l. under 3 Quarters 4 10 0 against 6 l. under 2 Months 1 00 0 against 6 l. under 5 Dec. parts 0 05 0 against 6 l. under 4 Dec. parts 0 04 0 Sum is 154 13 8 The 2 years' Value add, viz. 312 00 0 The Sum is 466 13 8 Which is the Fine reduced into Money required, in like manner is any other Fine reduced, at any other yearly Rent from 1 l. to 600 l. a year, or if it be more, it is but adding, after the same manner as is done in the Examples, as suppose the Rent to be 700 l. per An. then I must find the Values for 600 l. and for 100 l. and add them together, etc. A Table for the Reduction of the Values given in Years, Quarters, Months, and Decimal Parts of a Month, into Pounds, Shillings, and Pence. Yearly Rend. 3 Quarters. 2 Quarters 1 Quarter. 2 Months. 1 Month. lb. s. d. lb. s. d. lb. s. d. lb. s. d. lb. s. d. 1 0 15 0 0 10 0 0 5 0 0 3 4 0 1 8 2 1 10 0 1 0 0 0 10 0 0 6 8 0 3 4 3 2 5 0 1 10 0 0 15 0 0 10 0 0 5 0 4 3 0 0 2 0 0 1 0 0 0 13 4 0 6 8 5 3 15 0 2 10 0 1 5 0 0 16 8 0 8 4 6 4 10 0 3 0 0 1 10 0 1 0 0 0 10 0 7 5 5 0 3 10 0 1 15 0 1 3 4 0 11 8 8 6 0 0 4 0 0 2 0 0 1 6 8 0 13 4 9 6 15 0 4 10 0 2 5 0 1 10 0 0 15 0 10 7 10 0 5 0 0 2 10 0 1 13 4 0 16 8 20 15 0 0 10 0 0 5 0 0 3 6 8 1 13 4 30 22 10 0 15 0 0 7 10 0 5 0 0 2 10 0 40 30 0 0 20 0 0 10 0 0 6 13 4 3 6 8 50 37 10 0 25 0 0 12 10 0 8 6 8 4 3 4 60 45 0 0 30 0 0 15 0 0 10 0 0 5 0 0 70 52 10 0 35 0 0 17 10 0 11 13 4 5 16 8 80 60 0 0 40 0 0 20 0 0 13 6 8 6 13 4 90 67 10 0 45 0 0 22 10 0 15 0 0 7 10 0 100 75 0 0 50 0 0 25 0 0 16 13 4 8 6 8 200 150 0 0 100 0 0 50 0 0 33 6 8 16 13 4 300 225 0 0 150 0 0 75 0 0 50 0 0 25 0 0 400 300 0 0 200 0 0 100 0 0 66 13 4 33 6 8 500 375 0 0 250 0 0 125 0 0 83 6 8 41 13 4 600 450 0 0 300 0 0 150 0 0 100 0 0 50 0 0 Yearl Rent. 1 Dec. part 2 Dec. part 3 Dec. part 1 Dec. part 5 Dec. part lb. s. d. lb. s. d. lb. s. d. lb. s. d. lb. s. d. 1 0 0 2 0 0 4 0 0 6 0 0 8 0 0 10 2 0 0 4 0 0 8 0 1 0 0 1 4 0 1 8 3 0 0 6 0 1 0 0 1 6 0 2 0 0 2 6 4 0 0 8 0 1 4 0 2 0 0 2 8 0 3 4 5 0 0 10 0 1 8 0 2 6 0 3 4 0 4 2 6 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 7 0 1 2 0 2 4 0 3 6 0 4 8 0 5 10 8 0 1 4 0 2 8 0 4 0 0 5 4 0 6 8 9 0 1 6 0 3 0 0 4 6 0 6 0 0 7 6 10 0 1 8 0 3 4 0 5 0 0 6 8 0 8 4 20 0 3 4 0 6 8 0 10 0 0 13 4 0 16 8 30 0 5 0 0 10 0 0 15 0 1 0 0 1 5 0 40 0 6 8 0 13 4 1 0 0 1 6 8 1 13 4 50 0 8 4 0 16 8 1 5 0 1 13 4 2 1 8 60 0 10 0 1 0 0 1 10 0 2 0 0 2 10 0 70 0 11 8 1 3 4 1 15 0 2 6 8 2 18 4 80 0 13 4 1 6 ● 2 0 0 2 13 4 3 6 8 90 0 15 0 1 10 0 2 5 0 3 0 0 3 15 0 100 0 16 8 1 13 4 2 10 0 3 6 8 4 3 4 200 1 13 4 3 6 ● 5 0 0 6 13 4 8 6 8 300 2 10 0 5 0 0 7 10 0 10 0 0 12 10 0 400 3 6 8 6 13 4 10 0 0 13 6 8 16 13 4 500 4 3 4 8 6 8 12 1● 0 16 13 4 20 16 8 600 5 0 0 10 0 0 15 0 0 20 0 0 25 0 0 CHAP. VI THE way of Purchasing by Lives was commonly to reckon one Life as a Lease of 7 years, two Lives as a Lease of 14 years, and three Lives as a Lease of 21 years: but this way seeming unequal, there is another way which is more agreeable to reason, and it is this, viz. for every Life to decrease one year, as if one Life be reckoned as a Lease for 10 years, than two will be as a Lease of 19, and three as a Lease of 27 years, etc. so that at 7 l. per cent. one Life is reckoned worth a little above 7 years' purchase, two Lives 10 years, 1 quarter, and 1 month's purchase, etc. as the Table for Purchasing of Lives showeth. So if you reckon one Life as a Lease of 9 years, than 2 will be as a Lease of 17, three as a Lease of 24, etc. as is evident by the Table; and one Life will be worth above 6 years and 2 quarters purchase, 2 Lives 9 years and 3 quarters purchase, 3 Lives 11 years, 1 quarter, 2 months, and 6 Decimal Parts purchase, etc. So if one single Life be reckoned as a Lease of 12 years, than two will be as a Lease of 23, three as a Lease of 33 years, etc. so that at 6 per cent. one Life is worth above 8 years and a quarter's purchase, two Lives above 12 years and a quarter's purchase, etc. as the Table shows. Now suppose any of those Persons which have their Lives upon an Estate should die, to take in others to make up the Number again, is done by the Table of Reversions at the beginning of the Book: Example, suppose there be three Lives upon an Estate, which at 7 years' purchase for the first Life, are valued at almost 12 years' purchase, and as a Lease of 27 years, at 7 l. per cent. and if one of those Persons should die, what must be given to make up the Number again? then I say, one Life which is dead was as a Lease of 10 years, and therefore to take in a New Life, I may reckon 10 years of the 27 lapsed, and so take as it were a Fine for renewing A Table for the Purchasing of Lives. What they are worth at 7 lb. per cent. What they are worth at 7 lb. per cent. What they are worth at 6 lb. per cent. Number of Lives. Number of Years. Years. Quarter's Months. Dec. parts Number of Lives. Number of Years. Years. Quarter's Months. Dec. parts Number of Lives. Number of Years. Years. Quarters. Months. Dec. parts 1 10 7 0 0 3 1 9 6 2 0 2 1 12 8 1 1 6 2 19 10 1 1 0 2 17 9 3 0 1 2 23 12 1 0 6 3 27 11 3 2 6 3 24 11 1 2 6 3 33 14 1 2 6 4 34 12 3 1 1 4 30 12 1 1 8 4 42 15 0 2 7 5 40 13 1 0 9 5 35 12 3 2 2 5 50 15 2 2 7 6 45 13 2 1 2 6 39 13 1 0 1 6 57 16 0 0 8 7 49 13 3 0 2 7 42 13 1 2 4 7 63 16 0 2 8 8 52 13 3 1 3 8 44 13 2 0 6 8 68 16 1 1 2 9 54 13 3 1 6 9 45 13 2 1 2 9 72 16 1 2 0 to years lapsed in a Lease of 27 years, now to find this Fine, I take the Sum of the Reversions for 10 years in the Table under 7 l. per cent. counting 27 as 1, 26 as 2, 25 as 3, etc. and so I find the Sum to be 2 l. 4 s. 5 d. 2 q. that is 2 years, and almost one quarters purchase, which I may take for renewing or taking in a New Life; so if two Lives be dead I may reckon 19 years lapsed in a Lease of 27 years, and find the Sum of the Reversions for 19 years, for a Fine for taking in two Lives: but if there be 4 Lives upon the Estate, then at 7 l. per cent. and at 10 years for one Life, they will be reckoned as a Lease of 34 years, and so I must begin at 34 to Sum the Reversions, or at 30 if one Life be reckoned as a Lease of 9 years, and then if one Life be dead, I must reckon 9 years lapsed in a Lease of 30 years, if 2 Lives are dead I must reckon 17 years lapsed in the same Lease, and if 3 are dead I must reckon 24 lapsed: so at 6 l. per cent. reckoning 1 Life as a Lease of 12 years, 3 Lives are as a Lease of 33 years, and so if one of these Lives be dead, I may reckon 12 years lapsed in a Lease of 33 years, if 2 Lives are dead, I may reckon 23 years lapsed in the same Lease, and begin at 33 to sum the Reversions, under 6 l. per cent. because the Lives are valued according to the same rate of Interest. This being understood, it will not be difficult to do the like for any other number of Lives, and at other rates of Interest, and number of Years for one Life; for you may by the Table for Purchasing of Leases, etc. make Tables for Purchasing of Lives according to what rate of Interest you think is most convenient; as suppose you reckon one Life as a Lease of 10 years, and you would have 5 l. per cent. profit, then that will be worth 7 years and almost 3 quarters purchase, but at 8 l. per cent. it is worth but 6 years, and almost 3 quarters purchase, etc. CHAP. VII. THE Table for Purchasing is calculated for several rates of Interest, that so the Purchaser may use that which is most convenient for him, as in purchasing of Land, 5 l. per cent. may be enough, but for Copyhold or Leases of Land 6 l. per cent. for Leases of Land and Good Houses 8 l. per cent. and for Leases of Ordinary Houses 10 l. or 12 l. per cent. The use of the Table is very plain and easy, as by Example will appear, viz. Example. What is a Lease or Annuity of 20 years' worth at 5, 6, 8, 10, or 12 per cent. per Ann.? Y. q. m. d. p. lb. s. d. A Lease for 20 years at 5 p. c. is worth 12 1 2 5 Which at 20 lb. per Ann. Rent is 249 3 4 6 11 1 2 6 229 6 8 8 9 3 0 8 196 6 8 10 8 2 0 1 170 3 4 12 7 1 2 6 149 6 8 To increase the Number of Years in a Lease, do thus, suppose a Landlord would make a Lease of Land up to 40 years, wherein his Tenant hath 20 years to come, what is it worth? then I say, Y. q. m. d.p. a Lease for 40 years at 6 per cent. is worth 15 0 0 3 20 years at the same rate are worth 11 1 2 6 Which Subtract The Remainder is 3 2 0 7 Which is the Fine to be given to make the Lease up to 40 years. To buy a Lease which is not to begin until your old Lease is out, as thus suppose a Man's Lease is out within 4 years, and he desires to have a new Lease of 21 years, to begin when his 4 years are out, what is this Lease worth in ready Money? For Answer, I add 4 years which is the time he hath in his old Lease, and 21 together, the Sum is 25, than I find the worth of these 25 years, and Subtract from it the Value of the 4 years, the Remainder is the Value of the said Lease in ready Money. Example. Y. q. m. d.p. A Lease for 25 years at 6 l. per cent. is worth 12 3 0 3 The 4 years at the same rate are worth 3 1 2 6 Which Subtract The Remainder is the Value of the Lease in ready Money required, viz. 9 1 0 7 A Table showing how many Years, Quarters, Months, and Decimal Parts of a Months Purchase any Annuity or Lease of any Land or House is Worth, according to several Rates of Interest, viz. according to 5, 6, 8, 10, and 12 per cent. 5 per cent. 6 per cent. 8 per cent. 10 per cent. 12 per cent. Number of Years to be purchased. Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts Years. Quarters. Months. Decimal Parts 1 0 3 2 4 0 3 2 3 0 3 2 1 0 3 1 9 0 3 1 7 2 1 3 1 3 1 3 1 0 1 3 0 4 1 2 2 8 1 2 2 3 3 2 2 2 6 2 2 2 1 2 2 0 9 2 1 2 8 2 1 1 8 4 3 2 0 5 3 1 2 6 3 1 0 7 3 0 2 0 3 0 0 5 5 4 1 1 0 4 0 2 5 3 3 2 8 3 3 0 5 3 2 1 2 6 5 0 0 9 4 3 2 0 4 2 1 5 4 1 1 2 4 0 1 3 7 5 3 0 4 5 2 1 0 5 0 2 4 4 3 1 4 4 2 0 7 8 6 1 2 5 6 0 2 5 5 3 0 0 5 1 1 0 4 3 2 6 9 7 0 1 3 6 3 0 6 6 1 0 0 5 3 0 1 5 1 0 9 10 7 2 2 6 7 1 1 3 6 2 2 5 6 0 1 7 5 2 1 8 11 8 1 0 7 7 3 1 6 7 0 1 6 6 1 2 9 5 3 2 3 12 8 3 1 4 8 1 1 6 7 2 0 4 6 3 0 7 6 0 2 3 13 9 1 1 7 8 3 1 2 7 3 1 8 7 0 1 2 6 1 2 1 14 9 3 1 7 9 1 0 5 8 0 2 9 7 1 1 4 6 2 1 5 15 10 1 1 5 9 2 2 5 8 2 0 7 7 2 1 2 6 3 0 7 16 10 3 1 0 10 0 1 2 8 3 1 2 7 3 0 8 6 3 2 17 11 1 0 2 10 1 2 7 9 0 1 5 8 0 0 2 7 0 1 18 11 2 2 2 10 3 0 9 9 1 1 5 8 0 2 4 7 1 0 19 12 0 1 0 11 0 1 9 9 2 1 2 8 1 1 3 7 1 1 20 12 1 2 5 11 1 2 6 9 3 0 8 8 2 0 1 7 1 2 21 12 3 0 8 11 3 0 1 10 0 0 2 8 2 1 7 7 2 0 7 22 13 0 1 9 12 0 0 4 10 0 2 4 8 3 0 2 7 2 1 7 23 13 1 2 8 12 1 0 6 10 1 1 4 8 3 1 5 7 2 2 6 24 13 3 0 5 12 2 0 5 10 2 0 3 8 3 2 8 7 3 0 4 25 14 0 1 1 12 3 0 3 10 2 2 1 9 0 0 9 7 3 1 1 26 14 1 1 4 13 0 0 0 10 3 0 7 9 0 2 0 7 3 1 7 27 14 2 1 7 13 0 2 5 10 3 2 2 9 0 2 8 7 3 2 3 28 14 3 1 7 13 1 1 8 11 0 0 6 9 1 0 6 7 3 2 7 29 15 0 1 6 13 2 1 0 11 0 1 9 9 1 1 3 8 0 0 2 30 15 1 1 3 13 3 0 1 11 1 0 1 9 1 2 0 8 0 0 6 31 15 2 1 1 13 3 2 2 11 1 1 2 9 1 2 7 8 0 1 0 40 17 0 1 8 15 0 0 3 11 3 2 0 9 3 0 3 8 0 2 9 50 18 1 0 0 15 2 2 7 12 0 2 8 9 3 2 0 8 1 0 6 60 18 3 2 2 16 0 2 0 12 1 1 5 9 3 2 6 8 1 0 9 70 19 1 1 1 16 1 1 6 12 1 2 3 9 3 2 8 8 1 0 9 80 19 2 1 2 16 2 0 1 12 1 2 7 9 3 2 9 8 1 1 0 90 19 3 0 0 16 2 1 0 12 1 2 8 9 3 2 9 8 1 1 0 Fee Simple. Fee Simple. Fee Simple. Fee Simple. Fee Simple. 20 0 0 0 16 2 2 0 12 2 0 0 10 0 0 0 8 1 1 0 How to buy the Reversion of any Lease or Annuity. Although this may be done by the Table of Reversions at the beginning of the Book, yet I think it will not be amiss, if I show how it may be done by the Tables for Purchasing also. Suppose you are to buy the Reversion of a Lease after 6 years, that is if it be 6 years before you commence, what is the present worth of a Lease suppose of 30 years at 6 per cent.? then for Answer look the Value of the whole Lease, which will Y. q. m. d.p. be found to be 13 3 0 1 Then find the Value of the 6 years which will be Which Subtract 4 3 2 0 The Remainder is the Value of the Reversion required, viz. 8 3 1 1 The Value of the years lapsed or in Reversion of any Lease, may also be found by the Table for Purchasing for the Value of the years in esse, subtracted from the Value of the whole Lease, the Remainder is the Value of the years in Reversion, as is showed in the Preface; therefore suppose in a Lease of 31 years there be 12 years lapsed, what must be given to renew this Lease again at 6 per cent.? then I find the Y. q. m. d.p. value of the whole Lease to be 13 3 2 2 And because there are 12 years lapsed, there are 18 years in esse whose value is Which Subtract 10 3 0 9 The Remainder is the value of the years in Reversion required, viz. 3 0 1 3 Years. The increase of 1 lb. yearly at 6 per cent. The Value of 1 l. Annuity to be paid at the end thereof at 6 l. per cent. What Annuity 1 lb. ready Money will purchase at 6 l. per cent. lb. s. d. q. lb. s. d. q. lb. s. d. q. 1 1 1 2 1 1 0 0 0 1 1 2 0 2 1 2 5 2 2 1 2 0 0 10 6 0 3 1 3 9 3 3 3 8 0 0 7 6 0 4 1 5 3 0 4 7 5 3 0 5 9 0 5 1 6 9 0 5 12 8 3 0 4 9 0 6 1 8 4 1 6 19 6 1 0 4 2 0 7 1 10 0 3 8 7 10 1 0 3 7 0 8 1 11 10 2 9 17 11 1 0 3 2 0 9 1 13 9 1 11 9 9 3 0 2 11 0 10 1 15 9 3 13 3 7 0 0 2 18 0 11 1 17 11 2 14 19 5 0 0 2 6 1 12 2 0 3 0 16 17 4 2 0 2 4 2 13 2 2 7 3 18 17 7 2 0 2 3 0 14 2 5 2 2 21 0 3 2 0 2 1 3 15 2 7 11 0 23 5 6 0 0 2 0 2 16 2 10 9 2 25 1 5 0 0 1 11 2 17 2 13 10 0 28 4 3 0 0 1 10 3 18 2 17 1 0 30 18 1 0 0 1 10 0 19 3 0 6 0 33 15 2 0 0 1 9 1 20 3 4 2 0 36 15 8 0 0 1 8 3 21 3 7 11 3 39 19 10 0 0 1 8 3 22 3 12 0 3 43 7 10 0 0 1 7 3 23 3 16 4 2 46 19 10 0 0 1 7 1 24 4 0 11 2 50 16 3 2 0 1 7 0 25 4 5 10 0 54 17 3 1 0 1 6 2 26 4 10 11 3 59 3 1 0 0 1 6 1 27 4 16 5 1 63 14 1 0 0 1 6 0 28 5 2 2 3 68 10 6 2 0 1 5 3 29 5 8 4 0 73 12 9 1 0 1 5 2 30 5 14 10 0 79 1 2 0 0 1 5 1 CHAP. VIII. THE use of these Tables aforegoing is easy as by Examples will appear. The first is this, suppose 30 l. be put out for 20 years, what will it amount unto in that time at 6 per cent. Compound Interest? Then I look against 20 years, and find under the increase of 1 l. etc. 3 l. 4 s. 2 d. which shows that 1 l. in 20 years' time will increase to 3 l. 4 s. 2 d. which I multiply by 30 thus, 30 times 3 l. is 90 0 0 30 times 4 s. is 6 0 0 30 times 2 d. is 0 5 0 Sum 96 5 0 that is, 30 l. in 20 years' time at 6 per cent. Compound Interest will amount to 96 l. 5 s. 0 d. The use of the Second is thus, What will an Annuity of 30 l. forborn 20 years amount to in that time? then for Answer I look against 20 years, and under the value of 1 l. Annuity, etc. I find 36 l. 15 s. 8 d. which 36 l. 15 s. 8 d. is the value of 1 l. Annuity forborn 20 years, than I multiply 36 l. 15 s. 8 d. by 30 l. thus, lb. s. d. 30 times 36 l. is 1080 00 0 30 times 15 s. is 22 10 0 30 times 8 d. is 1 00 0 Sum 1103 10 0 that is, 36 l. Annuity forborn 20 years will at the end of that term amount to 1103 l. 10 s. 0 d. The use of the third Table is thus, suppose a Gentleman hath 300 l. by him with which he's willing to purchase an Annuity for 20 years, What Annuity will that purchase at 6 per cent? For Answer I look against 20 years, and find under What Annuity 1 l. ready Money, etc. 1 s. 8 d. 3 q. which shows that 1 l. ready Money will purchase an Annuity of 1 s. 8 d. 3 q. for 20 years, which I multiply by 300 lb. thus, lb. s. d. 300 Shillings are 15 00 0 300 times 8 d. is 10 00 0 300 times 3 q. is 00 18 9 Sum 25 18 9 that is, 300 l. ready Money will purchase an Annuity of 25 l. 18 s. 9 d. for 20 years at 6 per cent. CHAP. IX. Of the Difference which seems to be, between Long and Short Leases. SEeing 8 years and an half's purchase is to be given for a Lease of 20 years, at 10 l. per cent. and but 10 years' purchase for a Lease of 100 years at the same rate of Interest, that is but for a year and an half's purchase more, to make the Lease 80 years more; it may seem, that he which gives 10 years' value for the Lease of 100 years, has abundantly a better Bargain than he which gives 8 years and an half's purchase for the Lease but of 20 years; but then let him consider that in 100 years' time his Money is returned but 10 times, whereas in the Lease of 20 years his Money is returned indeed but twice and 3 years over, that is twice in 17 years, but when this Lease is out, he may purchase such another, etc. and so in an 200 years he may receive his purchase Money almost 12 times, but then on the other side let him consider that but 7 of these returns are clear gains, for he gives 1 for every 20 years, whereas in the Lease of 100 years he hath 9 returns of his Principal Money clear gains, which consideration may still make for the longer Lease to be the best; but then let him that buys this long Lease further consider that although he thinks he gives but little more Money for his 100 years' Lease, than he doth, that buys the 20 years' Lease, seeing he hath 5 times as many years in his Lease, let him consider I say the increase of his Money for that time, and that he's out of his little Money for a long time; so although he which buys one after another the 5 Leases of 20 years a Lease, is out of a great deal more Money, take them altogether, yet his Money is out but 20 years at a time: from these Considerations it will appear that there is really no difference between a long Lease and a short Lease, if the same rate of Interest in both be observed; for though there may be but little difference between their values, yet the great difference of their term of years will countervalue that, for it is evident that a little Money in a longer time, will amount to as much as a greater Sum in a shorter time: but yet notwithstanding these Considerations I grant there may be other Considerations in which a long Lease may be most profitable to the Tenant, whether it be a Lease of Land or Houses, for if he improves, or repairs, or builds, in a long Lease it is certain, he hath the longer time to enjoy the fruit of his Labour: so a short Lease to the Landlord may be most profitable, or at least most convenient, as for Colleges, etc. who live upon their Fines, and are in continual expense of Money, for them it's certain that a frequent return of Fines is best. Rules concerning Free-holds. DIvide 100 by the Price of the Purchase of the Fee Simple, the Quotient shows the rate of Interest, as if the Fee Simplo be 20 years' purchase, than 100 l. divided by 20, the Quotient is 5 l. for the rate of Interest. Or if you divide 100 by the rate of Interest which you desire to have in buying any thing, the Quotient shows how many years purchase you may give for it, thus if you desire to have 8 per cent. profit, then divide 100 by 8 ½ the Quotient is 12 ½, that is 12 years and an half's purchase, and so many years' purchase may you give and make 8 l. per cent. profit. By Decimals; Divide the Annual Rent by the bare rate of Interest proposed. Example. 400 l. per An. at the rate of 6 per cent. is worth 6666. thus ,06) 400,00 (6666. If the Rent be half, yearly, or quarterly, divide by ,0296. and ,0146. which is the Interest of 1 l. for a Quarter, as ,0296. is the Interest of 1 l. for half a year at 6 per cent, Compound Interest. A Table showing the Interest of any Sum of Money from 1 s. to 100 l. from a Day to a Year, at 6 l. p. c. per An. Simple Interest. A Day A Week 1 Mon. ● Mon 6 Mon A year. d. c. s. d. c. s. d. c. l. s. d. c. l. s. d. c. l. s. d. c. Shillings. 1 0 0 0 0 1 0 0 6 0 0 0 18 0 0 0 36 0 0 0 72 2 0 0 0 0 3 0 0 12 0 0 0 30 0 0 0 72 0 0 1 44 3 0 0 0 0 4 0 0 18 0 0 0 54 0 0 1 8 0 0 2 16 4 0 0 0 0 5 0 0 24 0 0 0 72 0 0 1 44 0 0 2 88 5 0 1 0 0 7 0 0 30 0 0 0 90 0 0 1 80 0 0 3 60 6 0 1 0 0 8 0 0 36 0 0 1 8 0 0 2 16 0 0 4 32 7 0 1 0 0 10 0 0 42 0 0 1 20 0 0 2 52 0 0 5 4 8 0 1 0 0 11 0 0 48 0 0 1 44 0 0 2 88 0 0 5 76 9 0 1 0 0 12 0 0 54 0 0 1 62 0 0 3 24 0 0 6 48 10 0 2 0 0 13 0 0 60 0 0 1 80 0 0 3 60 0 0 7 20 Pounds. 1 0 4 0 0 27 0 1 20 0 0 3 60 0 0 7 20 0 1 2 40 2 0 8 0 0 55 0 2 40 0 0 7 20 0 1 2 40 0 2 4 80 3 0 12 0 0 82 0 3 60 0 0 10 80 0 1 9 60 0 3 7 20 4 0 15 0 1 10 0 4 80 0 1 2 40 0 2 4 80 0 4 9 60 5 0 19 0 1 38 0 6 0 0 1 6 0 0 3 0 0 0 6 0 0 6 0 23 0 1 65 0 7 20 0 1 9 60 0 3 7 20 0 7 2 40 7 0 17 0 1 93 0 8 40 0 2 1 20 0 4 2 40 0 8 4 80 8 0 31 0 2 21 0 9 60 0 2 4 80 0 4 9 60 0 9 7 20 9 0 35 0 2 48 0 10 80 0 2 8 40 0 5 4 80 0 10 9 60 10 0 39 0 2 76 1 0 0 0 3 0 0 0 6 0 0 0 12 0 0 20 0 79 0 5 52 2 0 0 0 6 0 0 0 12 0 0 1 4 0 0 30 1 18 0 8 28 3 0 0 0 9 0 0 0 18 0 0 1 16 0 0 40 1 38 0 11 4 4 0 0 0 12 0 0 1 4 0 0 2 8 0 0 50 1 97 1 1 80 5 0 0 0 15 0 0 1 10 0 0 3 0 0 0 60 2 36 1 4 57 6 0 0 0 18 0 0 1 16 0 0 3 12 0 0 70 2 76 1 7 33 7 0 0 1 1 0 0 2 2 0 0 4 4 0 0 80 3 15 1 10 9 8 0 0 1 4 0 0 2 8 0 0 4 16 0 0 90 3 55 2 0 85 9 0 0 1 7 0 0 2 14 0 0 5 8 0 0 100 3 94 2 3 61 10 0 0 1 10 0 0 3 0 0 0 6 0 0 0 The Use of the foregoing Table. Note that for the greater exactness a Penny is divided into 100 parts, so that 25 parts make a Farthing, 50 an Halfpenny, and 75 parts 3 Farthings. Example. What is the Interest of 100lb. for 9 Months, 2 Weeks, and one Day? lb. sh. d. parts. lb. sh. d. Intr. of 100lb. for 6 Mon. 3 0 0 0 viz. 4 14 11 4/23 Intr. of 100lb. for 3 Mon. 1 10 0 0 Intr. of 100lb. 2 week. 0 4 7 22 Intr. of 100lb. for 1 Day 0 0 3 94 Sum 4 14 11 16 Example II. What is the Interest of 150 lb. 10 sh. 〈◊〉 6 Months, 1 Week, and 1 Day? lb. s. d. p. Interest of 100 l. for 6 Mon. 3 0 0 00 Interest of 100 l. for 1 Week 0 2 3 61 Interest of 100 l. for 1 Day 0 0 3 94 Interest of 50 l. for 6 Mon. 1 10 0 00 Interest of 50 l. for 1 Week 0 1 1 80 Interest of 50 l. for 1 Day 0 0 1 97 Interest of 10 s. for 6 Mon. 0 0 3 60 Interest of 100 s. for 1 Week 0 0 0 13 Interest of 10 s. for 1 Day 0 0 0 02 Sum 4 14 3 100 Which is the Interest of 150 l. 10 s. for 6 Months, 1 Week, and 1 Day. FINIS.