On this note are the following indorsements: Sept. 9, 1890, $114.20; May 15, 1891, $78.28; Aug. 6, 1892, $244.38. What was due Feb. 7, 1894 ? $586.96. (113.) Ans. $191.02. ANDOVER, May 12, 1892. On demand, we, jointly and severally, promise to pay Abel Stevens, or order, five hundred eighty-six dollars and ninety-six cents, with interest. Value received. JAMES CARTER. INDORSEMENTS: Jan. 24, 1893, $154.87; Dec. 6, 1893, $75.18; Aug. 15, 1894, $124.87; Dec. 6, 1894, $100. What was due April 24, 1895 ? $163.42. (114.) PROVIDENCE, April 15, 1891. Six months after date, I promise to pay Asa Brewer, or order, one hundred sixty-three and dollars, with interest. Value received. CALVIN DUNSTER. INDORSEMENTS: May 24, 1892, $42.18; July 17, 1893, $6.25; Sept. 6, 1893, $48.16; Jan. 25, 1894, $27.47. What was due April 15, 1895 ? $572.76. (115.) NEW YORK, June 4, 1889. Six months after date, I promise to pay Walter Willis, or his order, five hundred seventy-two dollars and seventy-six cents, with interest at 7%. Value received. SAMUEL JOHNSON. INDORSEMENTS: April 10, 1890, $125.85; Nov. 28, 1890, $133.72; April 15, 1891, $223.08. What was due Nov. 13, 1891 ? (For Connecticut and Vermont Rules, and the rule for Annual Interest, see Appendix, pp. 349–354.) 364. The following is a common rule when settlement is made within a year after the interest begins. Rule. From the amount of the note subtract the amount of the payments. $387.75. (116.) NEW YORK, May 15, 1893. On demand, I promise to pay Samuel Adams, three hundred eighty-seven and dollars, with interest from date. Value received. HENRY PHILLIPS. 100 INDORSEMENTS: July 21, 1893, $75; Oct. 10, 1893, $125; Feb. 24, 1894, $50. What was due at the time of settlement, May 15, 1894? Amount of $387.75 from May 15, 1893, to May 15, 1894, $411.015 On demand, I promise to pay Robert Chase, or order, seventeen hundred eighty-five dollars, with interest. Value received. SALMON FRENCH. INDORSEMENTS: July 3, 1894, $300; Sept. 10, 1894, $275; Nov. 6, 1894, $317; Jan. 2, 1895, $453. What was due March 27, 1895 ? (118.) A note of $2450, dated June 4, 1895, has the following INDORSEMENTS: Sept. 4, 1895, $562.50; Dec. 24, 1895, $846.37; Feb. 18, 1896, $362.63. What was due May 12, 1896? COMPOUND INTEREST. 365. Compound Interest is interest on both principal and interest. 366. The interest may become due and be added to the principal at the end of each year, or half-year, or any other period of time that may be agreed upon. 119. What is the amount at compound interest of $100 for 3 yr. 3 m. at 6 % per annum? 367. Hence, to find the amount of any sum of money at compound interest, Rule. Find the amount of the given principal for the first period of time. With this amount as a principal, find the amount for the next period; and so on to the end of the given time. 368. To find the compound interest, Subtract the given principal from the last amount. NOTE 1. In Ex. 119 the compound interest is $120.888-$100, or $20.888. NOTE 2. If there is a fraction of a period of time, find the amount for the complete periods, and then the amount of this amount for the remaining fraction of a period. 120. What is the amount at compound interest of $300 for 2 yr. 8 m., at 4% per annum? 121. What is the compound interest of $400 for 3 years, at 7%? 122. What is the amount of $6000 at compound interest for 4 yr. 10 m. 12 d. ? 123. What is the amount of $5000 at compound interest for 2 yr. 6 m. 18 d.? 124. What is the compound interest of $12000 for 2 yr. 6 m. 18 d., at 6 % ? 125. What is the amount at compound interest of $12000 for 2 yr. 6 m. 18 d., at 4 %? 126. What is the amount at compound interest of $12000 for 2 yr. 6 m. 18 d., at 8 % ? NOTE 3. Four per cent of any number is, and 8% is, of 6% of the same number; but the compound interest of any sum of money at 4% is less than of the compound interest of the same sum for the same time at 6%, and the compound interest at 8% is more than of the compound interest at 6%, as may be seen by examples 123, 124, and 125. The compound interest at 4% is less than half the compound interest of the same sum at 8%, because the base (that is, the principal), after the 1st year, is less in computing interest at 4% than in computing it at 8%; thus, in computing interest at 4% and 8% the 1st year the base is the same, and one interest is just half of the other; but the 2d year one base is $104 and the other $108; hence, the compound interest at 4% is less than half of that at 8%. 127. What is the amount of $ 350 for 2 yr. 6 m., at 3% for each 6 m., compounding the interest semi-annually? 128. What is the amount of $ 56 for 1 yr. 9 m., at 2 % a quarter, compounding the interest quarterly? 129. What is the compound interest of $824.75 for 3 yr. 8 m. 15 d., at 6 % ? 369. Compound interest may be calculated more expeditiously by means of the following TABLE, Showing the Amount of $1, interest compounded annually at 4, 5, 6, 7, and 8 per cent, from 1 to 20 years. 12345 4 1.169859 5 11 1.070000 1.360489 1.216653-1.276282-1.338226-1.402552-1.469328+ 6 1.265319+ 1.340096- 1.418519+ 1.500730+ 1.586874+ 7 1.315932- 1.407100+ 1.503630+ 1.605781+ 1.713824+ 8 1.368569+ 1.477455+ 1.593848+ 1.718186+ 1.850930+ 9 1.423312-1.551328+ 1.689479- 1.838459+ 1.99900510 1.480244+ 1.628895- 1.790848- 1.967151+ 2.158925- 10 1.539454+ 1.710339+ 1.898299-2.104852-2.331639-| 11 12 1.601032+ 1.795856+ 2.012196+ 2.252192- 2.518170+ 12 13 1.665074- 1.885649+ 2.132928+ 2.409845+ 2.719624- 13 14 1.731676+ 1.979932-2.260904- 2.578534+ 2.937194- 14 15 1.800944- 2.078928+ 2.396558+ 2.759032-3.172169+ 15 16 1.872981+ 2.182875-2.540352— 2.952164- 3.425943-16 17 1.947900+ 2.292018+ 2.692773- 3.158815+ 3.700018+ | 17 18 2.025817- 2.406619+ 2.854339+ 3.379932+3.996019+ 18 19 2.106849+ 2.526950+ 3.025600-3.616528- 4.315701+ 19 20 2.191123+ 2.653298- 3.207135+ 3.869684+ 4.660957+ | 20 NOTE. The interest is $1 less than the amount in the above table. 130. What is the compound interest of $600 for 20 yr. at 6% ? Int. of $1 for 20 yr. at 6 % by the table... $ 2.207135 Interest of $600 for 20 yr. at 6 % 600 $1324.281, Ans. 131. What is the amount at compound interest of $30 for 5 yr. 6 m. at 4 % ? Amount of $1 for 5 yr. at 4 % by the table... $1.216653 30 Amount of $30 for 5 yr. at 4 % $36.499590 1.02 Amount of $30 for 5 yrs. 6 m. at 4 %......$37.2295818, Ans. |