Bal. due after Apr. 1, 1860,............$253.50 Ans. NOTE. In the following examples the terms commence with the year, or on Jan. 1. 2. Allowing interest monthly at 6 % per annum, what sum will be due Sept. 1, 1860, on the book of a savings bank having the following entries? Bay State Savings Institution, in account with Jane Ladd. 116.87 Ans. $106.70. 3. Interest at 7 %, allowed quarterly, how much was due April 4, 1860, on the following savings bank account? Detroit Savings Institution, in account with R. L. Selden. Cr. 50 36 25 78 36 48 12: 50 1860. Jan. 25 160 80 423.22 Ans. $421.82. 3. 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. 4. 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. Cr. 16 March 17 66 1859. 00 78 Ans. $179.10. COMPOUND INTEREST. 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 "2d "3d 66 "4th 66 "4 years, $777.924 Amount $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. $196.857. 2. What will $250 amot to in 3 years at 7 per cent. compound interest? 3. At 7 per cent. interest, compounded debt will $1475.50 discharge in 2 years? Ans. $306.26. semi-annually, what 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. 531 A more expeditious method of computing compound interest than the preceding is by the use of the compound interest tables on the following page. TABLE, Showing the amount of $1, or £1, at 24, 3, 34, 4, 5, 6, 7, and 8 per cent., compound interest, for any number of years from 1 to 40. 6 per cent. 7 per cent. 8 per cent. Years 22 per ct. 3 per cent. 32 per ct. 4 per cent. 5 per cent. 1 2 45 1.025000 1.030000 1.035000 1.050625 1.060900 1.071225 3 1.076891 1.092727 1.108718 4 1.103813 1.125509 1.147523 5 1.131408 1.159274 1.187686 1.040000 1.050000 1.081600 1.102500 1.124864 1.157625 1.060000 1.070000 1.080000 1.123600 1.144900 1.166400 1.191016 1.225043 1.259712 1.262477 1.310796 1.360489 1.338226 1.402552 1.469328 1.169859 1.215506 1.216653 1.276282 1.159693 1.194052 1.229255 1.265319 1.340096 1.418519 1.500730 1.586874 1.188686 1.229874 1.272279 1.315932 1.407100 1.503630 1.605782 1.713824 8 1.218403 1.266770 1.316809 1.368569 1.477455 1.593848 1.718186 1.850930 9 1.248863 1.304773 1.362897 1.423312 1.551328 1.689479 1.838459 1.999005 1.280085 1.343916 1.410599 1.480244 1.628885 1.790848 1.967151 2.158925 673 26 1.900293 2.156591 2.445959 2.772470 3.555673 4.549383 5.807353 7.396353 1.947800 2.221289 2.531567 2.883369 3.733456 4.822346 6.213868 7.988062 1.996495 2.287928 2.620172 2.998703 3.920129 5.111687 6.648838 29 2.046407 2.356566 2.711878 3.118651 4.116136 5.418388 7.114257 9.317275 4.321942 5.743491 8.627106 2.097568 2.427262 2.806794 3.243398 7.612255 10.062657 33 2.258851 2.652335 3.111942 6.088101 8.145113 10.867€69 2.432535 2.898278 3.450266 4.103333 2.493349 2.985227 3.571025 4.268090 38 2.555682 3.074783 3.696011 4.438313 4.616366 2.619574 3.167027 3.825372 7.03998910 285718 14.974458 21.724522 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. com. pound 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. $1292.52/ 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 semi annually. How much was the amount paid him? 267077 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 cent, ? per ANALYSIS. Since $.24 is the interest of $1 for 4 years at 6 per cent., $87.42 must be the interest of as |