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 incipal, 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. 18s. 7 d. 3 What is the con.pound 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. $131.23. 5. How much will 400 L. amount to in 4 years, at 6 per cent. per annum ? Ans. 504 L. 19 s. 94 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 concerned. The present worth of any debt, not yet due, is so much money as, being put to interest, at a given rate perent. till the debt become payable, will amount to a sum equal to the dent. RULE. Find the amount of 100 pounds, or dollars, at the rate and time given. then, As the amount of two 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 eq debt. EXAMPLES. 1. What is the present worth o. 3 years, discount at 6 per cent. per the given sum or 590 dollars, due in annum? 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. L. S. L. s. d. 41 9 6 discount. L. L. s. d. 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. 15s. 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 of 750 dollars, at 3 per cent.? Ans. $22,50. 3. How much is the discount of 650 L., at 4 per cent.? Ans. 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 allowed? 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. 50X2=100 1|00)3|00 3 months. 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 follows: 50 L. at 2 months, 100 L. at 5 months, and 150 L. at 8 months; it is agreed to make one payment of the whole: at what time must it be paid? Ans. 6 months. 4. F owes H 2400 dollars, of which 480 dollars are to be paid at present, 960 dollars at 5 months, and the rest at 10 months, but they agree to make one payment of the whole, and wish to know the time. Ans. 6 months. 5. A merchant has purchased goods to the amount of 2000 dollars, of which sum 400 dollars are to be paid at present, 800 dollars at 6 months, and the rest at 9 months; but it is agreed to make one payment of the whole what is the equated time? Ans. 6 months. 6. G owes K 420 L. which will be due 6 months hence it is agreed that 60 L. shall be paid now, and that the rest remain unpaid a longer time than 6 months; when must it be paid? Ans. in 7 months. BARTER. Barter is the exchanging of one commodity for another, according to the price or value agreed upon by the parties concerned. Questions relating to barter are solved either by the Rule of Three or by Practice. Note. When a given quantity of any commodity at a given price is to be bartered for another commodity at a given price, find the value, in money, of that commodity whose quantity is given; then find what quantity of the other may be had for that value. EXAMPLES. 1. Ho v much sugar, at 11 d. per lb., must be given in barter for 100 lb. of rice, at 34 d. per lb.? Ans. 350 lb. |