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, and the remainder will be the compound interest. 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. 2. What is the compound interest of $500 for 2 years at per cent.? Ans. $72.45. 3. What is the amount of $312 for 3 years, at 6 per cent. compound interest? Ans. $371.59+. $250 for 2 years, Ans. $31.37+. at 7 per cent. com 4. What is the compound interest of payable semi-annually, at 6 per cent.? 5. What will $450 amount to in 1 year, pound interest, payable quarterly? 6. What is the compound interest of $236 for 4 years 7 months and 6 days, at 6% ? Ans. $482.33. Ans. $72.66+. Explain operation. Give rule. 7. What is the amount of $700 for 3 years 9 months and 24 days, at 7 per cent. compound interest? Ans. $906.55+. A more expeditious method of computing compound interest than the preceding, is by means of the following TABLE, Showing the amount of $1, or £1, at 3, 4, 5, 6, and 7 per cent, compound interest, for any number of years, from 1 to 20. Yrs. 3 per cent. 4 per cent. 5 per cent. G per cent. 7 per cent. 1.. 1.030,000 1.040,000 1.050,000 1.060,000 1.07,000 1.060,990 1.081,600 1.102,500 1.123,600 1.14,490 3.. 1.092,727 1.124,864 1.157,625 1.191,016 1.22,504 1.125,509 1.169,859 1.215,506 1.262,477 1.31,079 5. 1.159,274 1.216,653 1.276,282 1.338,226 1.40,255 6.. 1.194,052 1.265,319 1.340,096 1.418,519 1.50,073 7.. 1.229,874 1.315,932 1.407,100 1.503,630 1.60,578 8.. 1.266,770 1.368,569 1.477,455 1.593,848 1.71,818 9.. 1.304,773 1.423,312 1.551,328 1.689,479 1.83,845 10.. 1.343,916 1.480,244 | 1.628,895 | 1.790,848 1.96,715 11..1.384,234 1.539,454 1.710,339 1.898,299 2.10,485 12.. 1.425,761 | 1.601,032 1.795,856 2.012,196 2.25,219 13.. 1.468,534 1.665,074 1.885,649 2.132,928 2.40,984 14.. 1.512,590 1.731,676 1.979,932 2.260,904 2.57,853 15.. 1.557,967 1.800,944 2.078,928 2.396,558 2.75,903 16.. 1.604,706 1.872,981 2.182,875 2.540,352 | 2.95,216 17.. 1.652,848 1.947,900 2.292,018 2.692,773 3.15,881 18.. 1.702,433 2.025,817 2.406,619 2.854,339 3.37,293 19.. 1.753,506 2.106,849 2.526,950 3.025,600 3.61,652 20.. 1.806,111 2.191,123 2.653,298 3.207,135 3.86,968 8. What is the amount of $800 for 6 years, at 7 OPERATION. per From the table $1.50073 Amount of $1 for the time. 800 Principal, $1200.58400, Ans. cent. f 9. What is the compound interest of $120 for 15 years, at 5 per cent.? Ans. $129.47+. Of what use is the table in computing compound interest? 10. What is the amount of $.10 for 20 years, at 7 per cent.? Ans. $.38696. DISCOUNT. 325. Discount is an abatement or allowance made for the payment of a debt before it is due. 326. The Present Worth of a debt, payable at a future time without interest, is such a sum as, being put at legal interest, will amount to the given debt when it becomes duc. 1. A owes B $321, payable in 1 year; what is the present worth of the debt, the use of money being worth 7 per cent.? OPERATION. Am't of $1 1.07 ) $321 ( $300, Present value. 321 $321 Given sum or debt. 300 Present worth. $21 Discount. ANALYSIS. The amount of $1 for 1 year is $1.07; therefore the present worth of cvery $1.07 of the given debt is $1; and the pres ent worth of $321 will be as many dollars as $1.07 is contained times in $321. $321÷1.07 $300, Ans. RULE. I. Divide the given sum or debt by the amount of $1 for the given rate and time, and the quotient will be the present worth of the debt. II. Subtract the present worth from the given sum or debt, and the remainder will be the discount. The terms present worth, discount, and debt, are equivalent to principal, interest, and amount. Hence, when the time, rate per cent. and amount are given, the principal may be found by (321); and the interest by subtracting the principal from the amount. EXAMPLES FOR PRACTICE. 2. What is the present worth of $180, payable in 3 years 4 months, discounting at 6% ? Ans. $150. Define discount. Present worth. Give analysis. Rule. 3. What is the present worth of a note for $1315.389, due in 2 years 6 months, at 7 per cent.? Ans. $1119.48. 4. What is the present worth of a note for $866.038, due in 3 years 6 months and 6 days, when money is worth 8 per cent.? What the discount? Ans. $190.15+, discount. 5. What is the present worth of a debt for $1005, on which $475 is to be paid in 10 months, and the remainder in 1 year 3 months, the rate of interest being 6% ? When payments are to be made at different times without interest, find the pres. cnt worth of each payment separately, and take their sum. 6. I hold a note against C for $529.925, due Sept. 1, 1859; what must I discount for the payment of it to-day, Feb. 7, 1859, money being worth 6%? Ans. $17.425. 7. A man was offered $3675 in cash for his house, or $4235 in 3 years, without interest; he accepted the latter offer; how much did he lose, money being worth 7 per cent.? Ans. $175. 8. A man, having a span of horses for sale, offered them for $480 cash in hand, or a note of $550 due in 1 year 8 months, without interest; the buyer accepted the latter offer; did the seller gain or lose thereby, and how much, interest being 6%? Ans. Seller gained $20. 9. What must be discounted for the present payment of a debt of $2637.72, of which $517.50 is to be paid in 6 months, in $793.75 in 10 months, and the remainder in 1 year 6 months, the use of money being worth 7 per cent.? Ans. $187.29+. 10. What is the difference between the interest and discount of $130, due 10 months hence, at 10%? Ans. $.834. PROMISCUOUS EXAMPLES IN PERCENTAGE. 1. A merchant bought sugar in New York at 61 cents per pound; the wastage by transportation and retailing was 5 per cent., and the interest on the first cost to the time of sale was 2 per cent.; how much must he ask per pound to gain 25 per cent.? Ans. 8+ cents. 2. A person purchased 2 lots of land for $200 each, and sold one at 40 per cent. more than cost, and the other at 20 per cent. less; what was his gain ? Ans. $40. 3. Sold goods to the amount of $425, on 6 months' credit, which was $25 more than the goods cost; what was the true profit, money being worth 6%? Ans. $12.62+. 4. Bought cotton cloth at 13 cents a yard, on 8 months' credit, and sold it the same day at 12 cents cash; how much did I gain or lose per cent., money being worth 6 per cent.? 5. A farmer sold a pair of horses for $150 each; on one he gained 25 per cent., on the other he lost 25 per cent.; did he gain or lose on both, and how much? Ans. Lost $20. 6. A man invested of all he was worth in the coal trade, and at the end of 2 years 8 months sold out his entire interest for $3100, which was a yearly gain of 9 per cent. on the money invested; how much was he worth when he commenced trade? 7. In how many years will a man, per cent. on a debt for land, pay the interest? Ans. $3750. paying interest at 7 face of the debt in Ans. 14 years. 8. Two persons engaged in trade; A furnished g of the capital, and B ; and at the end of 3 years 4 months they found they had made a clear profit of $5000, which was 121 per cent. per annum on the money invested; how much capital did each furnish? Ans. A, $7500; B, $4500. 9. Bought $500 worth of dry goods, and $800 worth of groceries; on the dry goods I lost 20 per cent., but on the groceries I gained 15 per cent.; did I gain or lose on the whole investment, and how much? Ans. Gained $20. 10. What amount of accounts must an attorney collect, in order to pay over $1100, and retain 8 per cent. for collecting? Ans. $1200 T. A merchant sold goods to the amount of $667, to be paid in 8 months; the same goods cost him $600 one year previous to the sale of them; money being worth 6 per cent., what was his true gain? Ans. $5.346+. |