108 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 596 L. 18 s. 4 d., at 6 Ans. 35 L. 16 s. 3 d. per cent. ? L. S. d. 596 18 4 6 L. 3581 10 0 s. 16/30 12 d. 3/69 qr. 2/40 2. What is the commission on 1371 L. 9 s. 5 d., at 5 Ans. 68 L. 11 s. 5 d. per cent. ? 3. What is the commission on 526 L. 11 s. 5 d., at 31 L. per cent.? Ans. 18 L. 8 s. 7 d. 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 930 L. 10 s., and is to receive 34 L. per cent. commission: what sum is due to him? Ans. 30 L. 4 s. 93 d. 6. What is the insurance of 924 L., at 7 L. per cent.? Ans. 64 L. 13 s. 7 d. 7. What is the insurance of 1250 dollars, at 71⁄2 dollars per cent.? Ans. $93.75. 8. What is the insurance of an East India ship and cargo, valued at 14813 L. 15 s., at 15 L. per cent.? Ans. 2333 L. 3 s. 33 d. 9. What is the brokage on 1321 L. 11 s. 4d., at 1 L. per cent. ? Ans. 14 L. 17 s. 4 d. 10. What is the brokage on 874 L. 15 s. 3 d., at 5 s. or L. per cent. ? Ans. 2 L. 3 s. 82 d. COMPOUND INTEREST. 3 109 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. $13.891. COMPOUND INTEREST. Compound Interest is that which arises fron 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 500 L. for 3 years, at 5 per cent. ? Ans. 78 L. 16 s. 3 d. 2. What is the compound interest of 450 L. for 3 years, at 5 per cent. per annum? Ans. 70 L. 18 s. 7 d. 3. What is the compound interest of 760 L. 10 s. for 4 years, at 6 per cent. per annum ? Ans. 199 L. 12 s. 2 d. 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 400 L. amount to in 4 years, at 6 per cent. per annum? Ans. 504 L. 19 s. 9 d. 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 concorned. 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, 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? $6 rate. 18 100 118 amt. of $100. Ans. 500 dollars. 2. What is the discount of 795 L. 11 s. 2 d. for 11 months, at 6 per cent. per annum? Ans. 41 L. 9 s. 6 d. M. M L. L. s. 12: 11: 6:5 10 105 10 795 11 2 :: 100: 754 1 8 present worth. 3. What is the present worth of 672 L. due in 2 years; discount at 6 per cent. per annum? Ans. 600 L. 4. What is the present worth of 308 L. 15 s. due in 18 months; discount at 8 per cent. per annum? Ans. 275 L. 13 s. 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 112 L. 12 s. due in 20 months, at 7 per cent. per annum? Ans. 11 L. 15 s. 3 d. 7. What is the present worth of 100 L., one half due in 4 months, and the other half in 8 months; discount at 5 per cent. per annum? Ans. 97 L. 11 s. 4 d. 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 f 750 dollars, at 3 per cent. ? Ans. $22.50. 3. How much is the discount of 650 L., at 4 per cent.? Aas. 26 L. 4. Bought goods on credit, amounting to 1656 dollars; how much ready money must be paid for them, if a discount of 5 per cent. be silowod? Ans. $1573.20. 5. A holds B's note for 175 L. 10 s.; he agrees to allow B a discount of 3 per cent. for present payment: what sum must B pay? Ans. 170 L. 4 s. 8 d. EQUATION. Equation is a method of reducing several stated times, at which money is payable, to one mean or equated time. RULE. 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. Cowes D 100 dollars, of which 50 dollars is to be paid at 2 months, and 50 at 4 months; but they agree that the whole shall be paid at one time; when must it be paid? Ans. 3 months. 50 × 2 100 2. A owes B 380 L., of which 100 L. is to be paid at 6 months, 120 L. at 7 months, and 160 L. at 10 months, but they agree that the whole shall be paid at one time: when must it be paid? Ans. at 8 months. 3. A merchant has owing to him 300 L. to be paid as |