Or, looking into Table III under the rate, 6, the quotient, 4.374616, stands against 4 years, Ans. as before. Or, in Table I. under the given rate, you will find 1.262476, and in a line, under years, you will find 4. 2. In what time will an annuity of D.60 payable yearly, amount to D.2207-1354, allowing 6 per cent. for the forbearance of payment? Ans. 20 years. PRESENT WORTH OF ANNUITIES, &c. AT COMPOUND INTEREST. When the annuity, c. rate and time are given, to find the present worth. RULE.*1. Divide the annuity by the ratio, or the amount of D.1 or £1 for 1 year, and the quotient will be the present worth of 1 year's annuity. 2. Divide the annuity by the square of the ratio, and the quotient will be the present worth for two years. 3. In Let p present worth of the annuity, and the other letters as before: Then, REST. 287 3. In like manner, find the present wort and the sum of all these will be the pres sought. o find the annuity, rent, &c. Ör, divide the annuity, &c. by that pow denoted by the number the number of years, and subtract the quoted by the number of this remainder being divided by the ratio the present worth. EXAMPLES. 1.* What ready money will purchase a f the ratio, signified by ue 4 years, at 61. per cent. compound inteuotient, and the product First Method. 1.06)60.00000 56-603-p = enoted by the number of Ratio 2 Ratio: = Ratio = 3 1.1236,60·00000(53-399 ed by the time, by the ing continually divided by r till nothing remain, the numbe be equal to t. r Let t express the number of half years, or quarters, # the half payment, and the fum of 11. and or year's intereft, then all the will be applicable to half yearly, and quarterly payments, the fame as t The amount of an annuity may also be found for years and parts a of 1. Find the amount for the whole years, as before. 2. Find the intereft of that amount for the given parts of a year. 3. Add this intereft to the former account, and it will give the whole required. --601. The prefent worth of an annuity for years and parts of a year may be found thu 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. * Questions in this cafe may also be answered by firft finding the amount of the given annuity by Cafe I. of annuities in arrears, page 280, and then the present worth, or principal, by Cafe II. of Compound Intereft, page 278. Or, in Table I. under the given rate, you will find 1-262476, and in a line, under years, you will find 4. 2. In what time will an annuity of D.60 payable yearly, amount to D.2207-1354, allowing 6 per cent. for the forbearance of payment? Ans. 20 years. PRESENT WORTH OF ANNUITIES, &c. AT COMPOUND When the annuity, &c. rate and time are given, to find the present worth. RULE.*-1. Divide the annuity by the ratio, or the amount of D.1 or £1 for 1 year, and the quotient will be the present worth of 1 year's annuity. 2. Divide the annuity by the square of the ratio, and the quotient will be the present worth for two years. 3. In * Let p prefent worth of the annuity, and the other letters as before: Then, The number of divisions by 1.06, being 4, gives the number of years 4, the answer. Annuity 60) 262-47696 amount. = = 4.374616 1. Subtract 1. 3.374616 2. Subtract 1.06 = ratio. 2.314616 3. Subtract 1.1236 = ratio. 1.191016 4. Subtract 1.191016 = ratio]* Ans. 4 years. Or, looking into Table III under the rate, 6, the quotient, 4.374616, stands against 4 years, Ans. as before. Or, in Table I. under the given rate, you will find 1·262476, and in a line, under years, you will find 4. 2. In what time will an annuity of D.60 payable yearly, amount to D.2207-1354, allowing 6 per cent. for the forbearance of payment ? Ans. 20 years. PRESENT WORTH OF ANNUITIES, &c. AT COMPOUND When the annuity, &c. rate and time are given, to find the present worth. RULE.*-1. Divide the annuity by the ratio, or the amount of D.1 or £1 for 1 year, and the quotient will be the present worth of 1 year's annuity. 2. Divide the annuity by the square of the ratio, and the quotient will be the present worth for two years. 3. In * Let p prefent worth of the annuity, and the other letters as before: Then, |