Detroit Savings Institution, in account with R. L. Selden. Cr. 50 36 Oct. 3 66 66 25 78 4. How much was due Jan. 1, 1860, on the following account, allowing interest semi-annually, at 6 % per annum? Dr. Irvings Savings Institution, in account with James Taylor. Cr. 5. Interest at 5 %, allowed according to Note 2, how much was due, Jan. 1, 1860, on the book of a savings bank in the city of New York, having the following entries? Sixpenny Savings Bank, in account with William Gallup. 550. Compound Interest is interest on both principal and interest, when the interest is not paid when due. - NOTE. The simple interest may be added to the principal annually, semiannually, or quarterly, as the parties may agree; but the taking of compound interest is not legal. 1. What is the compound interest of $640 for 4 years, at 5 per cent. ? $740.88 x 1.05 4 years, $777.924 Amount 640. Given principal, $137.924 Compound interest. This illustration is sufficient to establish the following RULE. I. Find the amount of the given principal at the given rate for one year, and make it the principal for the second year. II. Find the amount of this new principal, and make it the principal for the third year, and so continue to do for the given number of years. III. Subtract the given principal from the last amount; the remainder will be the compound interest. NOTES.-1. When the interest is payable semi-annually or quarterly, find the amount of the given principal for the first interval, and make it the principal for the second interval, proceeding in all respects as when the interest is payable yearly. 2. When the time contains years, months, and days, find the amount for the years, upon which compute the interest for the months and days, and add it to the last amount, before subtracting. EXAMPLES FOR PRACTICE. 1. What is the compound interest of $750 for 4 years at 6 per cent.? Ans. $196.862. What will $250 amount to in 3 years at 7 per cent. compound interest? Ans. $306.26. 3. At 7 per cent. interest, compounded semi-annually, what debt will $1475.50 discharge in 2 years? Ans. $1752.43. 4. Find the compound interest of $376 for 3 yr. 8 mo. 15 da., at 6 per cent. per annum. Ans. $90.84. 551. A more expeditious method of computing compound interest than the preceding is by the use of the compound interest table on the following page. TABLE, Showing the amount of $1, or £1, at 21, 3, 31, 4, 5, 6, 7, and 8 cent., compound interest, for any number of years from 1 to 40. per Years 22 per ct. 3 per cent. 32 per ct. 4 per cent. 5 per cent. 6 per cent. 7 per cent. 8 per cent. EXAMPLES FOR PRACTICE. 1. What is the amount of $300 for 4 years at 6 per cent. compound interest, payable semi-annually? OPERATION. $1.26677 300 $380.03100 ANALYSIS. The amount of $1 at 6 per cent., compound interest payable semi-annually, is the same as the amount of $1 at 3 per cent., compound interest. payable annually. We therefore take, from the table, the amount of $1 for 8 years at 3 per cent., and multiply this amount by the given principal. 2. What is the amount of $536.75 for 12 yr. at 8 per cent. compound interest? Ans. $1351.63. 3. What sum placed at simple interest for 2 yr. 9 mo. 12 da., at 7 per cent., will amount to the same as $1275, placed at compound interest for the same time and at the same rate, payable semi-annually? Ans. $1292.51-. 4. At 8 per cent. interest compounded quarterly, how much will $1840 amount to in 1 yr. 10 mo. 20 da.? Ans. $2137.06. 5. A father at his death left $15000 for the benefit of his only son, who was 12 yr. 7 mo. 12 da. old when the money was deposited; the same was to be paid to him when he should be 21 years of age, together with 7 per cent. interest compounded semiannually. How much was the amount paid him? 6. What sum of money will amount to $2902.263 in 20 years, at 7 % compound interest? Ans. $750. PROBLEMS IN INTEREST. PROBLEM I. 552. Given, the time, rate per cent., and interest, to find the principal. 1. What sum of money will gain $87.42 in 4 years, at 6 per ANALYSIS. Since $.24 is the interest of $1 for 4 years at 6 per cent., $87.42 must be the interest of as many dollars, for the same time and at the same rate, as $.24 is contained times in $87.42. Dividing, we obtain $364.25, the required principal. Hence the RULE. Divide the given interest by the interest of $1 for the given time at the given rate. EXAMPLES FOR PRACTICE. 1. What sum of money, invested at 6 per cent., will produce $279.825 in 1 yr. 6 mo.? Ans. $2870. 2. What sum will produce $63.75 interest in 6 mo. 24 da. at 72 per cent.? #13 3. What sum will produce $12 interest in 10 days at 10 per cent.? Ans. $4500. 4. What sum must be invested in real estate paying 12 per cent. profit in rents, to give an income of $3125? 5. What is the value of a house and lot that pays a profit of 94 per cent. by renting it at $30 per month? 6. What sum of money, put at interest 6 yr. 5 mo. 11 da., at 7 per cent., will gain $3159.14? Ans. $7000. 7. What sum of money will produce $69.67 in 2 yr. 9 mo. at 6 % compound interest? Ans. $400. 8. What principal at 6% compound interest will produce $124.1624 in 1 yr. 6 mo. 15 da.? Ans. $1314.583. PROBLEM II. 553. Given, the time, rate per cent., and amount, to find the principal. 1. What sum of money in 2 years 6 months, at 7 per cent., will amount to $136.535? OPERATION. yr. 6 mo. ANALYSIS. Since $1.175 is the amount of $1 for 2 6 years months, at 7 per $1.175, amount of $1 for 2 $136.535 1.175 = $116.20, Ans. cent., $136.535 must be the amount of as many dollars, for the same time and at the same rate, as $1.175 is contained times in $136.535. Dividing, we obtain $116.20, the required principal. Hence the |