14. How much is the interest on a note for $600, dated Feb. 1, 1872, and payable Sept. 25, 1875, at 6% ? 15. If a man borrow $9700 in New York, and loan it in Colorado, what will it gain at legal int. in a year? 16. Required the interest of $127.36 from Dec. 12, 1873, to July 3, 1875, at 41%. 17. A note of $250, dated June 5, 1874, was paid Feb. 14, 1875, with interest at 8%. What was the amount? 18. A note for $710.50, with interest after 3 mo., at 77%, was given Jan. 1, 1874, and paid Aug. 12, 1876. What was the amount due ? 19. A man engaged in business was making 121% annually on his capital of $16840. He quit his business and loaned his money at 71%. What did he lose in 2 yr. 3 mo. 18 da. by the change? 20. A man borrows $2876.75, which belongs to a minor who is 16 yr. 5 mo. 10 da. old, and he is to retain it until the owner is 21 years old. What will then be due at 8% simple interest? 21. A speculator borrowed $9675, at 6%, April 15, 1874, with which he purchased flour at $6.25. May 10, 1875, he sold the flour at $73 a barrel, cash. What did he gain by the transaction? 22. A man borrows $10000 in Boston at 6%, reckoning 360 da. to the year, and lends it in Ohio at 8%, reckoning 365 da. to the year. What will be his gain in 146 days? 23. A tract of land containing 450 acres was bought at $36 an acre, the money paid for it being loaned at 54% At the end of 3 yr. 8 mo. 24 da., & of the land was sold at $40 an acre, and the remainder at $384 an acre. What was gained or lost by the transaction ? PROBLEMS IN INTEREST. 576. Interest, time, and rate given, to find the principal. ORAL EXERCISES. 1. What sum of money will gain $10 in 1 yr. at 5%? ANALYSIS.—The interest of $1 for 1 yr. at 5% is .05 of the principal, and therefore $10.05, or $200, is the required sum. Or, Since $.05 is the interest of $1, $10 is the interest of as many dollars as $.05 is contained times in $10, or 200 times. Hence, etc. What sum of money will gain, 2. $20 int. in 2 yr. at 5%? | 5. 3. $25 int. in 5 yr. at 5%? 6. 4. $60 int. in 2 yr. at 6%? | 7. $84 int. in 2 yr. at 7%? WRITTEN EXERCISES. 577. 1. What sum of money, put at interest 3 yr. at 6%, will gain $346.50? OPERATION. Int. of $1 for 31 yr. at 6% = = $.21. ANALYSIS.-Same as in oral exercises. (576.) $346.50 ÷ $.21 = 1650 times; $1 × 1650 = $1650. What principal 2. Will gain $49.50 in 1 yr. 3 mo. at 6%? At 5% ? 3. Will gain $153.75 in 3 mo. 24 da. at 7%? At 8%? RULE.-Divide the given interest by the interest of $1 for the given time, at the given rate. FORMULA.-Principal = Interest ÷ (Rate × Time). 4. Will gain $213 in 5 yr. 10 mo. 20 da. at 7%? 6. A man receives semi-annually $350 int. on a mortgage at 7%. What is the amount of the mortgage? 578. Amount, rate, and time given, to find the principal. ORAL EXERCISES. 1. What sum of money will amount to $107 in 1 yr. at 7%? ANALYSIS. Since the interest is .07 of the principal, the amount is 1.07, or 187, of it. If $107 is 107 of the principal, of the principal is of $107, or $1; and 100, or the principal itself, is $100. Or, Since $1.07 is the amount of $1, $107 is the amount of as many dollars as $1.07 is contained times in $107, or $100. What sum of money will amount to WRITTEN EXERCISES. 579. 1. What sum will amount to $337.50 in 5 yr. at 7%? OPERATION. Am❜t of $1 for 5 yr. at 7% = $1.35. $337.50 $1.35 250 times; $1 × 250 = $250. What principal = ANALYSIS. Same as in oral exercises. (578.) 2. Will amount to $1028 in 4 mo. 24 da. at 7%? 3. Will amount to $1596 in 2 yr. 6 mo. at 51% ? 4. Will amount to $1531.50 in 3 mo. 18 da. at 7%? RULE.-Divide the given amount by the amount of $1 for the given time, at the given rate. FORMULA.-Prin. = Amt. ÷ (1 + Rate × Time). 5. What is the principal which in 217 days, at 54%, amounts to $918.73? 6. What principal in 3 yr. 4 mo. 24 da. will amount to $761.44 at 5%? 580. Principal, interest, and time given, to find the rate. ORAL EXERCISES. 1. At what rate will $100 gain $14 in 2 years ? ANALYSIS. Since the interest of $100 is $14 for 2 yr., it is $7 for 1 yr., and $7 is .07 of $100, the principal. Hence the rate is 7%. Or, Since the interest of $100 for 2 yr. at 1% is $2, $14 is as many per cent. as $2 is contained times in $14, or 7%. WRITTEN EXERCISES. 581. 1. At what rate per cent. will $1600 gain $280 interest in 2 years? 2. Will $2085 gain $68.11 in 5 mo. 18 da. ? exercises. RULE.-Divide the given interest by the interest of the given principal, for the given time, at 1%. FORMULA.-Rate Int. ÷ (Prin. x 1% x Time). 4. A house that cost $14500 rents for $1189. What per cent. does it pay on the investment? 5. At what rate will $1500 amount to $1684.50 in 2 yr. 18 da.? 6. At what rate per month will $2000 gain $120 in 90 da. ? 7. A man invests $15600, which gives him an annual income of $1620. What rate of interest does he receive? 8. At what rate per annum will any sum double itself in 4, 6, 8, and 10 years, respectively? At 1%, any sum will double itself in 100 yr.; hence, to double itself in 4 yr., the rate will be as many times 1% as 4 yr. are contained times in 100 yr, or 25%, etc. 9. At what rate per annum will any sum triple itself in 2, 5, 7, 12, and 20 years, respectively? 10. I invest $49500 in a business that pays me $297 a month. What annual rate of interest do I receive? 11. Which is the better investment, and how much, one of $4200, yielding $168 semi-annually, or one of $7500, producing $7124 annually? 582. Principal, interest, and rate given, to find the time. ORAL EXERCISES. 1. In what time will $200 gain $56 at 7% ? 56 ANALYSIS.-The given interest, $56, is 5%, or .28, of the principal, $200; therefore, the time is as many years as .07, the given rate, is contained times in .28, or 4 times. Hence, etc. Or, the interest of $200 at 7% for 1 yr. is $14; therefore, the time is as many years as $14 are contained times in the given interest, $56, or 4 years. Hence, etc. |