EXPLANATION OF THE TABLE. What is the present worth of $1, to continue for 4 years at 6 per cent. per annum? Ans. 3.465106, agreeing with the tabular number opposite to 4 years at 6 per cent. per annum. First, find the present worth of $1, by discount for 1 year at 6 per ct. per annum, which is $0.943396 Tabular number for 4 years at 6 per. cent. as in table 3d. 1. What is the present worth of $50 per annum for 6 years at 6 per cent. per annum? Ans. $245.86c. 6m. CASE III. Annuities in Reversion. The annuity, time, and rate given, to find the present worth as in case 2. Multiply the number, under the rate and opposite th etime in table 3d, by the annuity, the product will be the present worth for yearly payments. If the payments are to be made half-yearly, or quarterly, the present worth so found for yearly payments, must be multiplied by the proper number in table 2d. Q. What is meant by annuities in reversion? A. Sums of money, which are paid yearly for a limited period, but which do not commence till after the expiration of a given period, are called annuities in reversion. Given the time of reversion, time of continuance and rate per cent. to find the present worth of the reversion. RULE. Take two numbers under the given rate in table 3, corresponding to the different periods of time, viz; time of reversion and time of continuance, and take the difference between the tabular numbers, answering to the times as above mentioned, and multiply that difference by the annuity, for the present worth annually, if the payments be half yearly or quarterly, we must use table 2 as above stated. 1. The reversion of a freehold is $60 per annum for 4 years, to commence 2 years hence, what is the present worth, allowing 6 per cent. for prompt payment. Illustration.-Time of continuance 6 years. Tabular number for 6 years at 6 per cent. found in table 3, is 4.917324 Time of reversion; 2 years tabular No. 1.833393 3.083931x60 = $185.03c.5m. x Answer. 3.083931 2. What is the present worth of a reversion of a lease of $100 per annum, to continue 10 years; but is not to commence till the end of 2 years at 6 per cent. 3. What is the present worth of a reversion of a lease for $120 per annum to continue 9 years, but not to commence till the end of 4 years at 5 per cent. to the purchaser? Ans. $701.71c. 4m. PERPETUITIES. Annuities which continue for ever, are called perpetu ities. CASE IV. Given the Annuity and rate per cent. to find the present worth. RULE.-Divide the annuity by the ratio less 1, for the present worth. Note.-Table 2d must be resorted to, as in temporary annuities, when the payments are half-yearly or quarterly, 1. What is the present worth of an annuity of $150 to continue for ever, allowing 5 per cent. to the purchaser? Operation.-1.05-1.05)150.00 $3000 Ans. 244 for 2. What is an estate of $260 per annum, to continne ever, worth in present money, allowing 6 per cent. to the purchaser? Ans. $4333.33.3 +. 3. A property in fee simple rents for $120 per annum, what is the present worth, allowing 5 per cent. to the purchaser? Ans. $2400. DISCOUNT BY COMPOUND INTEREST. The ratio in compound interest is the amount of $1 for one year, which is found thus: as 100: 106: : 1 = $1.06 is the amount of $1 for one year. = Example 1.-What is the present worth of 600 for 3 years; hence at 6 per cent. compound interest 1.063 1.191016)600(= $503.77 Ans. Ans. $600. per 2. What is the amount of $503.77, in 3 years at 6 cent.? 3. What is the present worth of $520, due 5 years hence, at 6 per cent. compound interest. Here 520 1,3312256)520(=390.62 answer. 1.065 = ALLIGATION, From the Latin (ad. to, and ligo to bind,) it being necessary in sundry cases to link or bind the quantities. We shall not omit the rule of Alligation, the object of which is to find the value of several things of the same kind of different values. The following examples will sufficiently demonstrate it. CASE I. When the quantities and rates of the simples are given to find the rate of a mixture compounded of these simples. RULE.--Find the value of each quantity, according to their respective costs, then divide the sum of the pro ducts by the aggregate of the quantities, and the quotient will be the average value of each quantity. 1. A wine merchant bought several kinds of wine, viz: 130 bottles which cost him 10 cents each. 75 66 at 15 cents each. 2. A grocer has 4 lbs. of tea at 90 cents per lb., 8 lbs. at 75 cents, and 6 lbs. at 110 cents. to be mixed together, what will a pound of this mixture be worth? Ans. 90c. 3. A grocer has 2 cwt. of coffee at $25 per cwt.; 4 cwt. at $20.50 per cwt. and 7 cwt. at $18.62% per cwt. which he will mix together, what will 1 cwt. of this mixture be worth? Ans. $20.18. CASE II. When the prices of all the simples, the quantity of one of them, and the mean price of the whole mixture are given to find the quantities of all the rest. RULE 1.-Place the mean rate and the several prices, link them and take their differences, as in the preceding case. 2. As the difference of the same name with the quantity given is to the differences respectively, so is the given quantity To the several required quantities. 1. What quantity of coffee at 20 cents, and at 16 cts. per lb. must be mixed with 35 lb. at 14 cents to make a 2. How much tea at 86 cents, at 94 cents, and at 105 cents per lb. ought to be mixed with 6 lbs. at 75 cts. per lb. for a mixture, to sell at 92 cts. per lb.? Ans. 18 lbs. at $1.05, 51 lbs. at 94c., 39 lbs. at 86c. CASE III. When the prices of the several simples, the quantity to be compounded, and the mean price are given to find the quantity of each simple. RULE 1.-Link the several prices and take their differences as before. 2d. As the sum of the differences is to the difference opposite each price, so is the quantity to be compounded to the quantity required. 1. A grocer has three sorts of sugar, viz: 10, 11, and 8 cents per lb. how much of each sort must he take? 2. A vintner has wine at 130 cts. at 160 cts. and at 180 cts. per gallon, and he would have 32 gallons worth 145 cents per gallon, I demand how much of each sort he must have? Ans. 20 gals. at $1.30, 6 gals. at $1.60 and 6 gals. at $1.80. |