found, that the present worth of a sum payable in fiftythree years is only one tenth of its nominal value. The rule for computing compound interest is as follows: Find the amount of the given principal to the time of the first payment, by simple interest. Consider this amount as the principal, on which calculate the interest as before, to the time of the second payment; and so on through all the payments, considering the last amount as the principal for the next payment. EXAMPLES FOR PRACTICE. 1. The amount of £320 10s. for 4 years, at 5 per cent. compound interest, is required. 2. What is the compound interest of £410, payable in 25 years, at 4 per cent. per annum; interest payable half yearly? Ans. £48 3s. 6d. 1 qr. 3. What is the amount of £721 for 21 years, at 4 per cent. per annum ? £1642 19s. 10d. 4. What will $2,12 amount to in 4 years, at 12 per cent. per annum, compound interest? Ans. $3,33 &c. 5. What is the compound interest of doll.33,33 for two years, at 10 per cent.? Ans. doll.6,99,9, &c. 3 6. What is the compound interest of £760 10s. for 4 years, at 6 per cent. per annum? Ans. £199 12s. 2d. 7. What is the compound interest of doll.500 for 4 years, at 6 per cent. per annum ? Ans. doll.131,233. 8. How much will £400 amount to in 4 years, at 6 per cent. per annum ? 9. How much will doll.680 per cent: compound interest? Ans. £504 19s. 91d. amount to in 4 years at 6 Ans. doll.858,48,3. 10. What is the compound interest of dol.840 for 3 years, at 5 per cent. per annum ? Ans. doll.132,48,5, EQUATION OF PAYMENTS. The following is the rule commonly used for performing this operation. Multiply each payment by the time, at which it becomes due; divide the sum of these products by the sum of the payments, and the quotient will be the time sought. This rule, though sufficiently accurate for business, is not strictly true; for although by keeping a debt unpaid after it is due, the interest of it is gained for that time; yet by paying a debt before it is due, the payer does not lose the interest for that time, but the discount, which is less than the interest. EXAMPLES FOR PRACTICE. 1. A owes B £190 to be paid as follows,-£50 in 6 months, £60 in 7 months, and 680 in 10 months; what is the equated time at which to pay the whole? 50× 6=300 50 2. A owes B doll.7 to be paid in 3 months, and doll.5 to be paid in 8 months; what is the equated time for the payment of the whole? Ans. 5 months. 3. G owes H doll.1000, of which doll.200 is to be paid immediately, doll.400 in 5 months, and the remainder in 15 months; if one payment is made of the whole, in what time ought it to be made? Ans. 8 months. 4. A debt is to be paid as follows, in 2 months, in 3 months, in 4 months, 1 in 5 months, and the remainder in 7 months; what is the equated time for the payment of the whole ? Ans. 4 months and 18 days. 5. G owes K £420, due 6 months hence; it is agreed that £60 shall be paid now, and that the remainder continue unpaid a longer time than 6 months; when must it be paid? Ans. in 7 months. DISCOUNT. By this rule is found the difference in value between a sum due at the expiration of a given time, and its present worth. The following is the method of operation. Find the amount of £100, or $100, for the given rate and time, and make it the first term of a proportion, which shall have £100, or $100, for its second term, and the given sum or debt for the third term. The fourth term of this proportion, when found, will be the present worths from which, subtracting the given sum, the re mainder will be the discount required. EXAMPLES FOR PRACTICE 1. What is the discount of £573 15s. due 3 years hence, at 4 per cent ? Ans. £68 4s. 101d. 2. What is the discount of $750 payable in one year? $22,50. 3. What is the present worth of $590, due in 3 years, discounting at the rate of 6 per cent. P Ans. $500. 4. What is the difference between the interest of $1204, at 5 per cent. per annum, for 8 years; and the discount of the same sum for the same time and rate per cent.? Ans. $137,60. 5. What is the present worth of $43,67, due in 19; months; discounting at 5 per cent. per annum ? Ans. $399,07. BARTER. This rule, which is an application of the rules of proportion, is used by merchants for proportioning their goods in such manner, that, on making an exchange of commodities, neither party may sustain a loss. The method of operation is as follows: Find the value of the commodity whose quantity is given, and then find what quantity of the other, at the rate proposed, may be had for the same money; and it will be the answer required. EXAMPLES FOR PRACTICE. 1. How much sugar at 9d. per lb. must be given in barter for 492lb. of rice, at 3d. per lb. Ans. 164lbs. 2. How much wheat at $1,25 per bushel is equal in per bushel. value to 50 bushels of rye at $0,70 Ans. 28 bushels. 3. A and B barter; A has 320lb. of chocolate, at 4s. 6d. per lb. for which B is to give him £30 in money, and the rest in cotton at 8d. per lb. How much cotton is B to give A ? Ans. 1260lbs. 4. Bought a sloop of 70 tons for $16 per ton; paid $500 in cash, 350 gallons of molasses at 80,64 per gallon, and the balance in New-England rum at $0,74 per gallon: how many gallons did it amount to? 37 Ans. 535 gallons. 5. R gave 189 yards of linen, at 6s. 8d. per yard, to C for 42 yards of cloth; what was the cloth per yard? Ans. 30s. LOSS AND GAIN. By this rule merchants so estimate their goods in buying and selling, as to know what they gain or lose. As the gains or losses are in proportion to the quantities of goods, questions in this rule are solved by applications of The Rules of Three. EXAMPLES FOR PRACTICE. 1. Bought 650lbs. of sugar, at 10 cents per lb. and sold it at 12 cents per lb. ; how much did I gain? * Ans. $13. 2. A merchant bought 1300lb. of coffee, at 22 cents per lb. and was afterwards obliged to sell it for 20 cents how much did he lose? per lb.; 3. If a trader gain 14d. per shilling on much does he gain per cent. ? 4. A parcel of goods were bought for diately sold for £25, at 4 months credit; ed per cent. per annum ? Ans. $26. his goods, how Ans. 124. 18 and immewhat was gain 5. A repeating watch was sold for $175, on which 17 per cent. was lost, whereas 20 per cent. ought to have been gained; what was the watch sold for under its value? 100-17; 175 :: 17+20 : $78,1, &c. Ans. $78,1, &c. COMMISSION AND BROKERAGE. Commission and Brokerage are allowances made at a certain rate per cent. to Factors and Brokers, for their services. The method of operation in these rules is the same as in Simple Interest. EXAMPLES FOR PRACTICE. 1. What is the commission on £500 13s. 6d., at 3 per cent.? Ans. £17 10s. 51⁄2d. 2. What is the brokerage on £879 18s. at 3 per cent. ? Ans. 63 5s. 112d. 3. What is the commission on $2176,50 at 2 per cent. ? per cent.? Ans. $4,86,9. 5. A factor has $3690, with which he is to purchase iron, reserving from it his commission of 21 per cent.; how much iron can he purchase at $95 per ton? Ans. 37 tons. 17cwt. 3qrs. 164lbs. |