1247436 Brought over. 1871154 1871154 1871154 1663248 1663248 185-035508376-present worth of the reversion. CASE II. When the present worth of the reversion, rate and time are given, to find the annuity. RULE.-1. Multiply that power of the ratio signified by the time of reversion, by the present worth, and the product will be the amount of the present worth for the time before the annuity com mences. 2. Multiply that power of the ratio signified by the time of con tinuance plus I by the last product. 5. Multiply that power of the ratio, signified by the time, by the aforesaid product, and this last product, divided by that power of the ratio denoted by the time, minus unity, will give the annuity. Or, divide the continual product of the present worth, that power of the ratio denoted by the time of continuance, that power of it denoted by the time of reversion, and the ratio minus 1, by that pow. er of the ratio denoted by the time of continuance minus 1, and the quotient will be the annuity. EXAMPLES. 1. What annuity, to be entered upon 2 years hence, and then to continue 4 years, may be purchased for D. 185-035899, at 6 per cent.? First Method. 1·06×1.06=1·1236 = 2d power of the ratio. Multiply by 185·036 = present worth. Divide by 1.06-126247)15-7488750(60 the annuity required. 2. The present worth of a lease of an house is 4311. 15s. 7d. 2-7819 qrs taken in reversion for 20 years; but not to commence till the end of 8 years, allowing 61. per cent. to the purchaser: What is the yearly rent? Ans. £.60. PURCHASING ANNUITIES FOREVER, OR FREEHOLD ESTATES, AT COMPOUND INTEREST. CASE I. When the annuity, or yearly rent, and the rate are given, to find the present worth, or price. RULE.* As the rate per cent. is to 1001. or 100D. so is the yearly rent, to the value required. Or, The reafon of this rule is obvious; for fince a year's interest of the price, which is given for it, is the aunuity, there can neither more nor lefs be made of that Or, Divide the yearly rent by the ratio less 1, and the quotient will be the value required. EXAMPLES. 1. What is the worth of a freehold estate of 60l. per annum, allowing 61. per cent. to the purchaser ? £.£. £, 6 100: 60 60 6)6000 £1000 Ans. Or, 1.06-1-06)60.00 1000 2. An estate brings in yearly'D 75: What will it sell for, allowing the purchaser 5 per cent. compound interest? Ans. D.1500. CASE II. When the price, or present worth, and rate are given, to find the annuity, or yearly rent. RULE.-AS.100 or D.100 is to the rate so is the present worth to its rent. Or, Multiply the present worth by the ratio less 1, and the product will be the yearly rent. EXAMPLES. 1. If a freehold estate be bought for 1000l. allowing 61. per cent. to the purchaser: What is the yearly rent? £. £. 100 6: 1000 6 Or, 1000x-06=£,60. 100)6000(£. 60 Ans. 600 0 2. If an estate be sold for 1500D. and 5 per cent. allowed to the buyer; what is the yearly rent? CASE III. Ans. D.75. When the present worth, or price, and yearly rent, are given, to find the rate. RULE. As the present worth is to the rent; so is £.100 or D. to the rate. Or, that price, than of the annuity, whether it be employed at fimple or compound interest. The following Theorems fhew all the varieties of this rule. Or, Divide the rent by the present worth; add 1 to the quotient, and the sum will be the ratio of the rate per cent. Or, Divide the sum of the present worth and rent by the present worth, and the quotient will be the ratio. EXAMPLES. 1. If an estate of 601. per annum be bought for 10001. what rate of interest was allowed the purchaser for his money? 2. An estate of 75D. per annum was purchased for 1500D. what rate of interest had the buyer for his money? Ans. 5 per cent. To find at how many years' purchase an estate may be bought. CASE I. When the rate of interest is given, to find the number of years. RULE. Divide 1001. or D. by the rate, and the quotient will be the years. EXAMPLES. 1. How many years' purchase should a gentleman offer for the purchase of an estate, to have 6 per cent. for his money? 6)100 16-666+16 years. 2. How many years' purchase is an estate worth, allowing 5 per eent. to the purchaser ? Ans. 20 years. CASE II. When the number of years' purchase, at which an estate is bought, or sold, is given, to find the rate of interest. RULE.-Divide .100 or D. by the number of years, and the quo tient will be the rate. EXAMPLES. EXAMPLES. 1. A gentleman gives 163 years' purchase for a farm; what interest is he allowed? 163 16.666+)100.000(6 per cent. Ans. 2 A gentleman gives 20 years' purchase for an estate; what interest has he? Ans. 5 per cent. PURCHASING FREEHOLD ESTATES IN REVERSION. CASE I. The rate and rent of a freehold estate being given, to find the present worth of reversion. RULE.*-1. Find the present worth of the annuity or rent, (by Case 1. of purchasing Freehold Estates, page 293,) as though it were to be entered on immediately. 2. Divide the last present worth by that power of the ratio denoted by the time of reversion (by Case 1 of Discount by Compound Interest) and the quotient will be the answer required. Or, 1. Having found the present value of the estate, supposing it to be immediate: Multiply the annuity, or rent, by the present worth of 11. or D. corresponding with the time of reversion and rate in Table 4th. and the product will be the present worth of the annuity, or rent, for the time of reversion; or the value of the present possession. 2. Subtract the value of the possession from the value of the estate, and the remainder will be the value of reversion. EXAMPLES. 1. Suppose a freehold estate of 601. per annum to commence 2 years hence, be put up to sale; what is its value, allowing the purchaser 61. per cent.? First Method. 1.06-1='06)60·00 = rent per annum. 12 = 1000 present worth, if entered on immediately. 1.06-1.1236)10C0-000(889-996=£.889 19s. 11d. = present worth of 10001. for 2 years, or the whole present worth required. The following Theorems exprefs all the Cafes under this rule. Second |