COMPOUND INTEREST. 188. Compound Interest is interest on both principal and interest if the interest is unpaid when due. WRITTEN EXERCISES. 1. What is the compound interest of $300 for 2 yr. at 6% ? The interest for 1 yr. is $18, which, added to $300 gives $318, the principal for the second year. The interest of $318 for 1 yr. is $19.08, which added to $318 gives $337.08, the compound amount for 2 yr. Subtracting the principal $300 from $337.08 gives the compound interest, $37.08. PROCESS. 1st prin. 18 Int. for 1st yr. $300 = $318 2d prin. Comp. amt. 19.08 Int. for 2d yr. $337.08 300.00 $37.08 1st prin. Comp. int., Ans. = = = = = RULE. Find the amount of the principal for the first period of time. . Find the amount of this new principal for the second period, and thus continue until the end of the time. Subtract the first principal from the last amount, and the result will be the compound interest. If the interest is compounded semiannually, the rate is onehalf the annual rate; if quarterly, one-fourth the annual rate, etc. Find the compound interest of 2. $300 for 2 yr. at 6%. 3. $400 for 3 yr. at 5%. 4. $1000 for 4 yr. at 7%. 5. $2000 for 3 yr. at 4%. 6. If the interest on $500 is compounded annually for 3 years, at what rate per cent. would the simple interest on the same principal for the same time equal the compound interest? The work may be greatly shortened by using the table on page 208. COMPOUND INTEREST TABLE. Amount of $1 at Compound Interest from 1 to 20 Years. Yrs. 1 per cent. 2 per cent. 2 per cent. 3 per cent. 3 per cent. 4 per cent. 1.025000 1.050625 1.076891 1.484506 18 1.307341 1.428246 1.559659 1.103813 1.131408 17 18 19 20 1.312087 1.378511 1.412774 1.448298 1.604706 1.652848 1.702433 19 1.326951 1.456811 1.598650 1.753506 20 1.346855 1.485947 1.638616 1.806111 1.050000 1.060000 1.070000 1.102500 1.123600 1.144900 1.157625 1.191016 1.225043 1.215506 1.262477 1.310796 1.276282 1.338226 1.402552 1.340096 1.418519 1.500730 1.407100 1.503630 1.605781 1.477455 1.593848 1.718186 1.551328 1.689479 1.838459 10 1.628895 1.790848 1.967151 11 1.710339 1.898299 2.104852 12 1.795856 2.012197 2.252192 1.885649 2.132928 2.409845 1.979932 2.260904 2.578534 13 14 15 2.078928 2.396558 2.759031 1.586874 1.850930 1.999005 2.158925 Yrs. 5 per cent. 6 per cent. 7 per cent. 8 per cent. 9 per cent. 10 per cent. 2.331639 2.518170 2.719624 2.937194 3.172169 1.265319 1.272279 1.315932 1.316809 1.368569 1.362897 1.423312 1.410599 1.480244 1.733986 1.794676 1.857489 1.922501 1.989789 1.080000 1.090000 1.360489 1.459970 1.539454 1.511069 1.601032 1.563956 1.665074 1.618695 1.731676 1.675349 1.800944 1.040000 1.081600 1.124864 1.169859 1.216653 3.341727 3.642482 1.872981 1.947901 2.025817 2.106849 2.191123 1.411582 1.464100 1.538624 1.610510 2.182875 2.540352 2.952164 3.425943 2.292018 2.692773 3.158815 3.700018 2.406619 2.854339 3.379932 3.996019 2.526950 3.025600 3.616527 4.315701 5.141661 2.653298 3.207136 3.869684 4.660957 5.604411 1.677100 1.771561 1.828039 1.948717 1.992563 2.143589 2.171893 2.357948 2.593742 2.367364 3.970306 4.327633 4.717120 1.100000 1.210000 1.331000 2.580426 2.812665 3.065805 3.452271 3.797498 4.177248 2.853117 3.138428 4.594973 5.054470 5.559917 6.115909 6.727500 7. What is the compound interest of $500 for 5 yr. at 5% ? PROCESS. $.276282 According to the table, the compound amount of $1 for 5 yr. at 5% is $1.276282, and deducting $1 the compound interest of $1 is $.276282; $138.141000, Ans. hence the compound interest of $500 is 500 times $.276282, which is $138.141. Find the compound interest of8. $800 for 10 yr. at 6%. 9. $1200 for 8 yr. at 7%. 10. $2000 for 16 yr. at 10%. 500 11. $480 for 4 yr. 3 mo. at 6%, payable quarterly. 13. What is the difference between the simple and the compound interest of $840 for 3 yr. 4 mo. 24 da. at 6% ? 14. Find the simple, the exact, the annual, and the compound interest of $365 for 2 yr. 6 mo. at 6%. DISCOUNT. 189. Trade Discount. Trade Discount is a reduction made in the price of an article. Frequently in trade several discounts are made; as, “10 and 5 off," meaning 10% off, and 5% off the remainder. 100% 20 80% WRITTEN EXERCISES. 1. What is due on a bill of $400, subject to a discount of 20% and 10%? PROCESS. $400 .72 $288.00, Ans. A reduction of 20% will leave 80%; a second reduction of 10% is of 80%, or 8% off, leaving 72%. 72% of $400 is .72 times $400, which is $288. 72% 2. What is due on a bill of $600 at 15% discount and 3% off for cash? 3. What is the cash value of a bill of $84 at a discount of 16%%? 4. A bought goods to the amount of $300, and obtained a discount of 20% and 5% off for cash; how much did he pay for the goods? 5. Find the net amount of a bill for $250, subject to a discount of 30% and 10% off. 6. What reduction from the price of an article is 25% and 10% off? 7. What reduction from the price of an article is 5%, 10%, and 20% off? 8. B bought goods to the amount of $240, and obtained a discount of 20% and 121%; how much did he pay for the goods? 9. What must a merchant ask for an article which cost $40, so that he may fall 20% and still gain 10%? 10. A merchant marks goods 20% above cost, and sells at 121% below the list price; what per cent. does he gain? 11. At what per cent. above cost must goods be marked so that after falling 20% there may still be a gain of 20% ? 12. A merchant marks goods 30% above cost, and then sells them at a discount of 25% from the list price; does he gain or lose, and what per cent.? 13. Find the net amount of a bill for $560, subject to discounts of 20%, 15%, 10%, and 5%. 14. At what per cent. above cost must a merchant mark an article so that he may sell at a discount of 20% from the list price and still have a profit of 40%? 15. At what per cent. above cost must goods be marked so that after falling 10% from the list price there shall still be a gain of 15% ? 16. What must I ask for an article which cost $200, so that I may fall 15% from my asking price and still have a profit of 10%? 190. True Discount. The Present Worth of a sum of money due at some future time without interest is such a sum as, being on interest for the given time, will amount to the given sum. 191. The True Discount is the difference between the given sum and the present worth. Thus, if $106 is due 1 yr. hence without interest, the present worth is $100, since $100 on interest for 1 yr. at 6% will amount to $106. The true discount is $106 $100, or $6. The true discount is, therefore, the interest of the present worth. $1.18)$413.00(350 354 WRITTEN EXERCISES. 1. What is the true discount of $413 due 3 yr. hence, at 6% ? The amount of $1 for 3 yr. at 6% is $1.18. PROCESS. Hence the present worth of $1.18 is $1, and $413 will give a present worth of as many dollars as $1.18 is contained times in $413, which is $350. 590 590 $413 63, Discount. Subtracting the present worth, $350, from the given amount, $413, leaves the true discount, $63. RULE. To find the present worth, divide the given sum by the amount of $1. To find the true discount, subtract the present worth from the given sum. Find the true discount of 2. $800 due 2 yr. hence at 6%. 3. $400 due 3 yr. 8 mo. hence at 6%. 4. $360 due 2 yr. 10 mo. hence at 5%. 5. $1200 due 4 yr. 6 mo. hence at 8%. 6. $700 due 5 mo. 18 da. hence at 6%. |