tiply the interest for 1 month by the number of months and fractions of a month. Thus, in 2 years, 7 months, there are 31 months, and in 12 days there are 12 or of a month. Therefore, the entire interest may be found by multiplying $1.1713 by 31.4, which is $36.78. Since there are 30 days in a month, one-third of the number of days will be tenths of a month. RULE.-I. Find the interest for 1 year and multiply this by the time expressed as years and fractions of a year. Or, II. Find the interest for 1 month and multiply this by the time expressed as months and fractions of a month. 14. What is the interest of $25.16 for 1 yr. 6 mo. at 6% ? 15. What is the interest of $36.24 for 2 yr. 4 mo. at 7% ? 16. What is the interest of $48.20 for 2 yr. 4 mo. at 8% ? 17. What is the interest of $2000 for 3 yr. 7 mo. at 9% ? 18. Find the amount of $590.50 for 3 yr. 6 mo. at 7%. 19. Find the amount of $640.82 for 2 yr. 7 mo. at 8%. 20. Find the amount of $725.83 for 3 yr. 6 mo. at 10%. 21. Find the amount of $618.24 for 2 yr. 5 mo. at 8%. 22. Find the amount of $312.29 for 3 yr. 5 mo. at 6%. 23. Find the interest of $718.24 for 5 mo. 10 da. at 5%. 24. Find the interest of $127.46 for 3 mo. 15 da. at 7%. 25. Find the interest of $364.18 for 2 mo. 12 da. at 81%. 26. Find the interest of $318.29 for 9 mo. 10 da. at 74%. 27. Find the interest of $312.24 for 2 mo. 20 da. at 8%. 28. Find the interest of $1614.25 for 20 da. at 7%. 29. Find the interest of $1318.29 for 24 da. at 10%. 30. Find the interest of $4684.68 for 11 da. at 121%. 31. If you lend $500, how much will be due you in 3 yr. 6 mo. 21 da., interest at 7%? 32. What is the interest on $784.25 from Aug. 7, 1874, to July 19, 1877, at 8%? What is the amount? 33. How much interest is due on $500, that has been loaned at interest since Jan. 1, 1876? OTHER METHODS. ALIQUOT PARTS. 336. 1. What is the interest and amount of $520.32 for 2 yr. 5 mo. 15 da. at 7%? ANALYSIS. Since the interest is 7% of the principal, we find .07 of $520.32, which is $36.4224, the interest for 1 year. Twice $36.4224 gives the interest for 2 years, which is $72.8448. One-third of the interest for 1 year is $12.1408, the interest for 4 months. One-fourth of the interest for 4 months is $3.0352, the interest for 1 month. One-half the interest for 1 month is $1.5176, the interest for 15 days. The sum of these amounts is the interest for 2 years 5 months 15 days, which is $89.5384. This sum, added to the principal, gives the amount. Solve the following by aliquot parts: 2. What is the interest of $324.22 for 3 yr. 4 mo. at 6%? 3. What is the interest of $218.90 for 2 yr. 7 mo. at 7%? 4. What is the interest of $36.48 for 2 yr. 5 mo. 15 da. at 6%? 5. What is the interest of $40.28 for 1 yr. 7 mo. 20 da. at 6%? 6. What is the interest of $56.24 for 2 yr. 5 mo. 18 da. at 7%? 7. What is the interest of $24 96 for 3 yr. 1 mo. 6 da. 8. What is the interest of $48.72 for 2 yr. 2 mo. 16 da. at 8%? 9. What is the interest of $36.18 for 2 yr. 5 mo. 21 da. at 10%? 10. What is the interest of $20.25 for 3 yr. 1 mo. 16 da. at 121%? 11. What is the interest of $30.24 for 2 yr. 8 mo. 15 da. at 8%? SIX PER CENT. METHOD. 337. The interest on $1, at 6% per annum, 1. What is the interest of $125 for 2 yr. 3 mo. 16 da. at 6%? PROCESS. $125 .1374 $17.208 ANALYSIS.-Int. of $1 for 2 yr. at 6% is .12. Int. of $1 for 3 mo. at 6% is .015. Int. of $1 for 16 da. at 6% is .002. The sum of these, .1374, is the interest of $1 for the given time at the given rate, and since the interest of $1 is .1374, the interest of $125 will be 125 times that sum, which is $17.208. 1. When it is required to find the interest at any other rate than 6%, first find it at 6%, then increase or decrease this result by such a part of it as the given rate is greater or less than 6%. Thus, if the rate is 7%, increase the interest at 6% by of it; if the rate is 5%, decrease it by of it; if the rate is 8%, increase it by, or of it; if the rate is 9%, increase it by of it, etc. 2. Exact or Accurate interest requires that the year should be considered 365 days, for a common year, and 366 days for a leap year, instead of the ordinary method of considering 12 months of 30 days each, or 360 days a year. Find the interest on the following: 6%? 6%? 18 da. at 6%? 17 da. at 6%? 18 da. at 6%? 15 dar at 5%? 7% 2. On a note for $185.26 for 1 yr. 4 mo. 13 da. at 3. On a note for $368.18 for 3 yr. 5 mo. 22 da. at 4. On a note for $284.25 for 2 yr. 7 mo. 5. On a note for $183.17 for 1 yr. 8 mo. 6. On a note for $215.25 for 3 yr. 2 mo. 7. On a note for $204.37 for 2 yr. 5 mo. 8. On a note for $186.15 for 3 yr. 7 mo. 23 da. at 9. On a note for $315.30 for 1 yr. 9 mo. 27 da. at 10. On a note for $379.15 for 1 yr. 8 mo. 11 da. at 11. On a note for $685.31 for 4 yr. 1 mo. 15 da. at 12. On a note for $516.28 for 3 yr. 6 mo. 28 da. at 13. On a note for $423.15 for 2 yr. 7 mo. 10 da. at 6%? 14. On a note for $304.27 for 1 yr. 3 mo. 21 da. at 10%? 15. On a note for $516.24 for 2 yr. 1 mo. 13 da. at 12%? Find the amount of the following notes when due: 16. $150.15. 8%? 6%? 7%? 5%? CINCINNATI, O., Jan. 31, 1877. Three months after date, for value received, I promise to pay John T. Jones, or order, One Hundred Fifty 15 Dollars, with interest at 6%. 17. $328.35. CHARLES C. THOMSON. ST. PAUL, MINN., Oct. 1, 1877. On the 15th day of January, 1878, for value received, I promise to pay to S. E. Hoyt, or order, Three Hundred Twenty-Eight 35 Dollars, with interest at 8%.. 1.0.0 18. $315.75. J. W. RAY. BUFFALO, N. Y., May 3, 1876. For value received, on demand I promise to pay to J. C. Coe, or order, Three Hundred Fifteen5 Dollars, with interest. HENRY B. ROBESON. Paid, June 5th, 1877. How much was due? COMPOUND INTEREST. 338. Compound Interest is interest upon the principal and its unpaid interest, combined at regular intervals. It is usually compounded annually, semi-annually, or quarterly. Unless some other condition is mentioned in the written obligation, the interest is understood to be compounded annually. WRITTEN EXERCISES. 1. Find the compound interest of $250 for 2 yr. 3 mo. at 6%. inal principal, and obtain $35.11, the compound interest required. RULE.-Find the interest of the principal for the first period of time at the end of which interest is due. Add this interest to the principal, and compute the interest upon this amount for the next period, and so continue. Subtract the given principal from the last amount, and the remainder will be the compound interest. 1. If the interest is compounded semi-annually, the rate is considered as one-half the annual rate; if quarterly, one-fourth, etc. |