109 INSURANCE, COMMISSION, AND BROKAGE. 2. At what rate per cent. per annum, will 500L. amount to 725L. in 9 years? Ans. 5L. per cent. 3. At what rate per cent. per annum, will 600 dollars amount to 856dols. 50cts. in 9 years and 6 months? Ans. 4 per cent. CASE 7. To find the time, when the principal, amount, and rate per cent. are given. RULE. Find the interest of the principal for one year. Find the interest for the time required, by subtracting the principal from the amount: then, As the interest of the principal for one year, So is one year, To the time required. EXAMPLES. 1. In what will time 500L. amount to 725L. at 5 per cent. per annum? Ans. 9 years. L. 2500 225 Interest for time required. 2. In what time will 540L. amount to 734L. 8s. at 4 per cent. per annum? Ans. 9 years. 3. In what time will 600 dollars amount to 798 dollars, at 6 per cent. per annum? Ans. 5 years. INSURANCE, COMMISSION, AND BROKAGE. Insurance, Commission, and Brokage, are allowances made to insurers, factors, and brokers, at a stipulated rate per cent. RULE. Work as if to find the interest of the given sum for one year, at the proposed rate: or, if the rate be less 110 INSURANCE, COMMISSION, AND BROKAGE. than 1 per cent. take such aliquot part or parts, of the interest at 1 per cent. as the rate is of a pound, or dollar. EXAMPLES. 1. What is the commission on 596L. 18s. 4d. at 6 per cent.? Ans. 35L. 16s. 3 d. 2. What is the commission on 1371L. 9s. 5d. at 5 Ans. 68L. 11s. 5 d. per cent.? 3. What is the commission on 526L. 11s. 5d. at 34L. per cent.? Ans. 18L. Ss. 7d. 4. What is the commission on 1974 dollars, at 5 dollars per cent.? Ans. $98.70. 5. A factor has sold goods for a merchant, to the amount of 930L. 10s. and is to receive 34L. per cent. commission: what sum is due to him? Ans. 30L. 4s. 9 d. 6. What is the insurance of 924L. at 7L. per cent.? Ans. 64L. 13s. 7d. lars 7. What is the insurance of 1250 dollars, at 74 dolper cent.? Ans. $93.75. 8. What is the insurance of an East India ship and cargo, valued at 14813L. 15s. at 15L. per cent. Ans. 2333L. 3s. 34d. 9. What is the brokage on 1321L. 11s. 4d. at 1L. per cent.? Ans. 14L. 17s. 4d. 10. What is the brokage on 874L. 15s. 3d. at 5s. or L. per cent.? Ans. 2L. 3s. 84d. 11. If a broker buy goods for me, to the amount of $1853, and I allow him & dollars per cent. for his service, what sum must I pay him? Ans. $13.89. COMPOUND INTEREST. Compound Interest is that which arises from a principal increased by its interest, as the interest becomes due. RULE. Find the amount of the given principal for the first year, by simple interest; this amount will be the principal for the second year, and the amount of this principal found as before, will be the principal for the third year, and so on. From the last amount, subtract the given principal, and the remainder will be the compound interest. EXAMPLES. 1. What is the compound interest of 500L. for 3 years, at 5 Ans. 78L. 16s. 3d. cent.? per 2. What is the compound interest of 450L. for 3 years, at 5 per cent. per annum? Ans. 70L. 18s. 7 d. 3. What is the compound interest of 760L. 10s. for years, at 6 per cent. per annum? 4 Ans. 199L. 12s. 2d. 4. What is the compound interest of 500 dollars for 4 years, at 6 per cent. per annum? Ans. $131.234. 5. How much will 400L. amount to in 4 years, at 6 per cent. per annum? Ans. 504L. 19s. 94d. DISCOUNT. Discount is an allowance made for the payment of a sum of money before it becomes due, according to a certain rate per cent. agreed on between the parties concerned. The present worth of any debt, not yet due, is so much money as, being put to interest, at a given rate per cent. till the debt become payable, will amount to a sum equal to the debt. RULE. Find the amount of 100 pounds, or dollars, at the rate and time given: then, As the amount of 100 pounds, or dollars, Is to the given sum, or debt, So is 100 pounds, or dollars, To the present worth. Subtract the present worth from the debt, and the remainder will be the discount. PROOF. Find the amount of the present worth for the time and rate proposed, which must equal the given sum or debt. EXAMPLES. 1. What is the present worth of 590 dollars, due in 3 years, discount at 6 per cent. per annum? Ans. 500 dollars. 2. What is the discount of 795L. 11s. 2d. for 11 months, at 6 per cent. per annum? M. M. L. L. s. Ans. 41L. 9s. 6d. 2 whole debt. S present worth. S. L. s. d. 105 10 795 11 2:: 100: 754 1 8 present worth. 3. What is the present worth of 672L. due in 2 years; discount at 6 per cent. per annum? Ans. 600L. 4. What is the present worth of 308L. 15s. due in 18 months; discount at 8 per cent. per annum? Ans. 275L. 13s. 4 d. 5. What is the present worth of $430.67, due in 19 months; discount at 5 per cent. per annum? Ans. $399.07. 6. What is the discount of 112L. 12s. due in 20 months, at 7 per cent. per annum? 7. What is the present worth of in 4 months, and the other half in 8 months; discount at 5 per cent. per annum? Ans. 11L. 15s. 34d. 1001. one half due Ans. 97L. 11s. 4d. 8. Bought goods amounting to $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. 9. What is the difference between the, interest of 1204 dollars 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. Note.-Discount for present payment is often made without regard to time; it is then found precisely as the interest of the given sum for 1 year. EXAMPLES. 1. How much is the discount of 853 dollars, at 2 per cent.? Ans. $17.06. 853 17.06 2. How much is the discount of 750 dollars, at 3 per cent.? Ans. $22.50. |