cent. per annum, when he should arrive at the age of 21 years, which his guardian then found to be $2332.50-how old was the boy at his father's decease? Ans. 11 years. INSURANCE, COMMISSION, BROKERAGE, &c. INSURANCE, Commission, Brokerage, Purchasing Stock, &c., are allowances made to insurers, factors, brokers, &c. at a stipulated rate per cent., and are found as under Case 1, Simple Interest. EXAMPLES. 1. If a factor buys goods for me to the amount of $1853, and I allow him dollars per cent. for his services-what sum must I pay him? What sum 1853 $ $100 4 3 $ 400 55 59 $13.89 Answer. 2. What is the commission on $1974, at $5 per cent.? Ans. $98.70. 3. What is the commission on £596 18 s. 4 d. at 6 per cent.? Ans. £35 16 s. 3 d. 4. What is the insurance of $1250, at $7 per cent.? Ans. $93.75. 5. The value of a certain ship and cargo is $8560—what is the insurance, at 35 per cent.? Ans. $2996. 6. What is the duty on 2 cwt. 3 qrs. 18 lb. of iron, at 2 cents per pound? Ans. $8.15. 7. If a factor buys goods for me to the amount of £575 -what is his commission, at 24 per cent.? Ans. £12 18 s. 9 d. 8. What is the insurance of an East India ship and cargo valued at £7406 17 s. 6 d. at 154 per cent. ? Ans. £1166 11s. 7 d. 9. What may a broker demand on £420 12 s. 6 d. at 6 s. 4 d. per cent.? Ans. £1 6 s. 74 d. COMPOUND INTEREST. COMPOUND INTEREST, called also interest upon interest, is that which arises from the principal and its interest added together, as the interest becomes due. RULE. Find the amount of the given principal for the first year, as under Case 1, Simple Interest. With the amount thus found, as a new principal, find as above the amount for the second year, &c. From the last amount subtract the given principal, and the remainder will be the compound interest. EXAMPLES. 1. What is the compound interest of $500 for 3 years, at 5 per cent.? What amount 500 $ 2. What will $1200 amount to in cent. per annum, compound interest? 3. What is the compound interest at 6 per cent. per annum? compound interest. 4 years, at 4 per Ans. $1417.373+ of $500 in 4 years, Ans. $131.234. 3. What will $100 amount to in 1 years, at 6 per cent. compound interest, the interest payable half-yearly? What amount|100 $ 11.03 1st half year. 11.03 2d half year. 11.03 3d half year. $109.2727 Ans. 5. What will £217 amount to in 24 years, at 5 per cent. compound interest, the interest payable quarterly? Ans. £242 13 s. 4 d. DISCOUNT. DISCOUNT is an allowance made for the payment of money before it becomes due. The present worth of any debt not yet due, is so much money as, being put to interest till the debt becomes due, at a given rate per cent., will amount to a sum equal to the debt. The present worth, subtracted from the debt, will leave the discount. To find the present worth. RULE. Find the amount of any principal, as 100, at the rate and time given, and this amount will be a sum, or debt, to which the assumed principal will be its present worth. Then with this equation and the equation demanded form the statement, and proceed as taught under Equations. EXAMPLES. 1. What is the present worth of $590 due in 3 years, discount at 6 per cent. per annum? NOTE. The discount may be found directly, when the discount on any other sum at the same rate and time is known; thus, 2. What is the discount on $590 due in 3 years, at 6 per cent. per annum, the discount on $118 for the same rate and time being $18? 3. What is the present worth of $75 for 2 years, at 6 per cent. per annum? Ans. $66.96. 4. What is the discount on $75 due in 2 years, at 6 per cent. per annum?. Ans. $8.03. 5. What is the present worth of £672 due in 2 years, Ans. £600. at 6 per cent. per annum? 6. What is the present worth of $430.67 due in 19 months, interest at 5 per cent. per annum? Ans. $399.07. 7. What is the discount of £112 12 s. due in 20 months, at 7 per cent. per annum. Ans. £11 15 s. 3 d. 8. What is the difference between the interest on $600 at 6 per cent. per annum for 6 years, and the discount on the same sum at the same rate and time? Ans. $57.17. 9. Bought goods to the amount of $615.75 at 6 months' credit; how much ready money must be paid, if a discount of 4 per cent. per annum be allowed? Ans. $602.20. NOTE.-Discount for present payment is often made without regard to time. In this case it is found as in cases of Simple Interest. EXAMPLES 1. What is the discount of $853 at 2 per cent? $853 $17.06 Ans. 2. What is the value of a $20 banknote which is 24 per cent. below par? Ans. $19.50. 3. What is the discount of £650 at 4 per cent. ? Ans. £26. 4. Bought goods on credit amounting to $1656; how much ready money must be paid for them, if a discount of 5 per cent. be allowed. Ans. $1573.20. EQUATION OF PAYMENTS. EQUATION OF PAYMENTS teaches the method of finding a mean or equated time for the payment of debts which are due at different times. Multiply each payment by its time, add the several products together, and divide the sum by the whole debt; the quotient will be the equated time. PROOF.-The interest of the sum payable at the equated time, at any given rate, will equal the interest of the several payments, for their respective times, at the same rate. EXAMPLES. 1. A owes B $100, of which $50 is to be paid in two months, and $50 in four months; but they agree that the whole shall be paid at one time, when must it be paid? $50 x 2 = 100 $50 × 4200 100)300 Ans. 3 months. 2. A owes B $380, of which $100 is to be paid at 6 months, $120 at 7.months, and $160 at 10 months; but they agree that the whole shall be paid at one time: when must it be? Ans. 8 months. 3. A merchant has owing to him $300, to be paid as follows: $50 at 2 months, $100 at 5 months, and 150 at 8 months; what is the equated time if the whole be paid at once ? Ans. 6 months. 4. Cowes D $460, to be paid thus:- in 2 months, in 4 months, in 6 months, and 4 in 8 months; but they agree to make one payment of the whole: when should it be made? Ans. in 5 months. 5. A merchant bought goods to the amount of $2000, and agreed to pay $400 cash, $800 in 5 months, and the rest in 10 months; but it is preferred to make one payment of the whole: what is the equated time? Ans. 6 months. BARTER. BARTER is the exchanging of one commodity for another, according to the prices or values fixed upon them. Questions in Barter are solved by the Rule of Three, or by Practice. RULE. Find the value of that article whose quantity is given; then find what quantity of the other may be had for that value. |