of 60l. to continue 4 years, at 61. per cent. compound intereft? Under 61 per cent. and oppofite 4, we find Multiply by 60-Annuity. 262,47660=Amount of 60l. for 4 years. Then oppofite 4 years and under 61. per cent. in Table 11. we have,792093 and ,79209;X262,7466= (208,1197+ Or, oppofite 4 years, and under 61. per cent. in Table I. we have 1,2624the amount of 11. for 4 years : Then, 262,7466+1,26247 208,0219=2081. 2s 5d. the answer. By TABLE IV. Multiply the tabular number, under the rate, and oppofite the time, into the annuity, and the product will be the prefent worth. Thus, in Example ift. What ready money will purchafe 6ol. annuity, to continue 4 years, at 61 per cent. compound intereft? Under 61 per cent. and even with 4 years, We have 3.4651-prefent worth of 11. for 4 years. Anf. 207,9060=2071. 18s. 14d. CASE CASE II. When the prefent worth,time and rate are given, to find the annuity, rent, &c. RULE I. From that power of the ratio, denoted by the number of years plus 1, fubtract that power of it, denoted by the number of years. 2. Divide the remainder by that power of the ratio, fignified by the time made lefs by unity. 3. Multiply the prefent worth into this quotient, and the product will be the annuity, penfion, rent, &c. Or, 1. Multiply that power of the ratio, denoted by the number of years, plus 1, by the present worth. 2. Multiply that power of the ratio, denoted by the sime, by the prefent worth, and fubtract this product from the former. 3. Divide the remainder by that power of the ratio, denoted by the time made lefs by unity, and the quotient will be the annuity. EXAMPLE. 1. What annuity, to continue 4 years, will 207,9041. purchase, compound interet, at 61. per cent. ? First Method. From 1,06×1,06 X 1,06×1,06×1,06=1,3382255776 Divide by 1,064-1,26247696), 0757486176(,2885896 Second Method. From 1,06×1,06×1,06×1,068 1.06 × 207,9— 278,217097573 Take 1,96X1,06.X1,06X1,c6X207,9 = 262,468959984 Divide by 1,0641,26247696) 15.748137589 59,998-460 DD EXAMPLES. 1. What annuity, being forborne 4 years, will amount to 262,47696, at 61 per cent. compound intereft? 262,47696X1,06-262,47696 1,06X1,06X1,06X1,06-1 Or, By TABLE III. =60 Divide the amount by the tabular number under the rate, and oppofite to the time, and the quotient will be the annuity. 2. What annuity being forborne 20 years, will amount to 2207,354, at 61 per cent compound intereft ? Tabular amount 36,78559)2207,13540(60 Anf.~* 2207,13540 CASE III. When the annuity, amount and ratio are given, to find the time. RULE Multiply the amount by the ratio, to this product add the annuity, and from the fum fubtract the amount this remainder being divided by the annuity, the quotient will be that power of the ratio fignified by the time, which being divided by the amount of L for year and this quotient by the fame. till, nothing re main, the number of thofe divifions, will be equal to the time Or, look for this number under the given råte in Table I. and in a line with it you will fee the time. EXAMPLE, In what time will 6ol. per annum, payable yearly, amount to 262, 47696 allowing 61. per cent. compound intereft for the forbearance of payment? In Table I. under the given rate, you will find 1,262476, and in a line under years, you will find 4. PRESENT WORTH OF ANNUITIES, &c. AT COMPOUND INTEREST. CASE I. When the annuity, &c. rate and time are given, to find the prefent worth. RULE* 1. Divide the annuity by the ratio, or the amount of il. for 1 year, and the quotient will be the prefent worth of 1 year's annuity. 2 Divide the annuity by the fquare of the ratio, and the quotient will be the prefent worth for two years. 3 in like manner, find the prefent worth of each year by itself, and the fum of all these will be the prefent value of the annuity fought. Or, Divide the annuity &c. by that power of the ratio fignified by the number of years, and fubtract the quotient from the annuity: This remainder being divided by the ratio lefs 1, the quotient will be the prefent worth. EXAMPLES. 1. What ready money will purchase an annuity of The amount of an annuity may also be found for years and parts of a year, thus: "year Find the amount for the whole years, as before. 3 Add this intereft to the former account, and it will give the whole amount required. The prefent worth of an annuity for years and parts of a year may be found thus: 1. Find the prefent worth for the whole years as before. 2. Find the prefent worth of this prefent worth, discounting for the given parts of a year, and it will be the whole prefent worth required 4 Questions in this cafe may alfo be answered by first finding the amount of the given annuity by Cafe of annuities in arrears, page 308, and then the prefent worth or principal, by Cafe 2, of Compound Intereft, 305、 By TABLE V. Multiply the tabular number, correfponding with the vate and time, by the purchase money. and the product *y.ll be the annuity. Under 61 per cent. and oppofite 4 years, you will find 28 59 annuity which 1. will purchafe in 4 years; and,28859X :07,9=£60. CASE III. When the annuity, prefent worth, and ratio, are given, to find the time. RULE.-Divide the anuuity by the product of the prefent worth and ratio fubtracted from the fum of the prefent worth and annuity, and the quotient will be that power of the ratio, denoted by the number of years, which being divided by the ratio, and this quotient by the fame, until nothing remain, the number of divifions will thew the time:Or, the above quotient being fought in Table 1, under the given rate, in a line with it you will fee the time. EXAMPLE. For how long may an annuity of 6cl. per annum be purchafed for 207,906336762 at 61. per cent. compound intereft? 60 207 906336762+60-207.906336762X1.06 =1,26247696 which being fought in Table I, under the given rate in a line with it, is 44 years. ANNUITIES, LEASES, &c. taken in REVER SIÓN, at COMPOUND INTEREST. When the annuity, time and ratio are given, to find the prefent worth of the annuity in reverfion. RUL-Divide the annuity by that power of the ratio, denoted by the time of its continuance. 2. Subtrac |