353. The principal, the rate per cent., the time, and the interest have such a relation to each other that, any three of these terms being given, the fourth can be readily found. The computations in interest, therefore, admit of the following problems among others: — I. To find the interest; II. To find the principal; III. To find the rate per cent.; IV. To find the time. 354. To find the interest of any sum for any time at 6 per cent. Ex. 1. What is the interest of $ 2640 for 2 years 7 months and 26 days, at 6 per cent.? FIRST OPERATION. Interest of $1 for 2 years cents 5 mills. Principal, $2 640 .159 23760 13200 2640 880 Interest, $420.640 Ans. Ans. $ 420.64. The interest of $2640 for 2yr. 7mo. 26d. will be 2640 times as much as the interest of $1 for the given time. The interest of $1 for 2 years will be twice as much as for 1 year, equal 12cts.; and since the interest for 2 months is 1 cent, for 7 months it will be 31 cents, or 3 And as the interest for 6 days is 1 mill, for 26 days it will be 4 mills. These several sums added together give the interest of $1 at 6 per cent. for the given time, equal $ 0.1591, which taken 2640 times, by multiplying the given principal by it, gives $ 420.64, the interest required. Ans. $ 4 2 0.6 4 Interest for 2yr. 7mo. 26d. The time, 2yr. 7mo 26d., is equal to 2yr. 1mo + 6mo. 20d. + 6d. Now, since the interest on any sum, at 6 per cent., in 200 months equals the principal, for 2yr. 1mo., or of 200 months, it will equal of the principal. We therefore take of the principal, $2640, equal $ 330, as the interest for 2yr. 1mo. Of the balance of time, 6mo. 20d., or 63mo., being of 200 months, we take of the principal, equal $88, as the interest for the 6mo. 20d.; and the 6d. being 1000 of 200 months, we take of the principal, equal $2.64, as the interest for the 6d. We add together the interest for the parts of the whole time, and obtain, as by the first operation, $420.64 as the whole interest. RULE 1. Find the interest of $1 for the given time, by reckoning 6 cents for every YEAR, 1 cent for every TWO MONTHS, and 1 mill for every 6 DAYS; then multiply the given principal by the number denoting that interest, and the product will be the interest required. Or, RULE 2. Take such fractional part or parts of the principal as the number expressing the time is of 200 months. NOTE 1. - To find the amount, add the principal to the interest. In computing interest for a fractional part of a month, the month is considered as consisting of 30 days. This has the sanction of general usage and the decisions of the courts, though not entirely accurate. NOTE 3.- Questions in interest, like other exercises in percentage, may be solved by proportion. The foregoing example admits of a statement and solution by the rule of compound proportion (Art. 340). NOTE 4. It is customary among merchants to reject the mills in the results of their computations of interest, increasing, however, the number of cents by 1 when the decimal of a cent exceeds 5. EXAMPLES. 2. What is the interest of $ 675 for 1 year? Ans. $40.50 3. What is the interest of $3967.87 for 2 years? Ans. $ 476.144 4. What is the interest of $ 896.28 for 3 years? Ans $161.33 5. What is the amount of $716.57 for 4 years? 6. What is the amount of $76.47 for 7 years? Ans. $108.587 7. What is the interest of $123.45 for 6 years? Ans. $44.442 8. What is the interest of $750 for 12 years? Ans. $540. 9. What is the interest of $130 for 2 months? 10. What is the interest of $85 for 3 months? Ans. $1.275. 11. What is the interest of $19.62 for 7 months? Ans. $0.6867. 12. What is the interest of $ 637 for 10 months? 13. What is the interest of $1671.32 for 14 months? Ans. $116.99. 14. What is the interest of $ 891.24 for 9 months? Ans. $ 40.10. 15. What is the interest of $ 91 for 5 days? Ans. $ 0.0758. 16. What is the interest of $324.66 for 18 days? 17. What is the interest of $3246 for 27 days? Ans. $14.607. 18. What is the interest $1364.24 for 1 day? 22. What is the interest of $0.75 for 75 Ans. $193.09. years? Ans. $3.37. 23. What is the interest of $396.15 for 1 year 1 month and 9 days? Ans. $26.343. 24. What is the interest of $36.18 for 3 months and 7 days? Ans. $0.584. 25. What is the interest of $97.15 for 2 years 11 months and 27 days? 26. What is the interest of $76.891 from January 11, 1852, to July 27, 1863? Ans. $53.262. 27. What is the interest of $98.25 from July 4, 1856, to October 19, 1859 ? Ans. $19.404. 28. What is the interest of $22.763 from February 19, 1836, to July 18, 1860? 29. What is the interest of $175.07 from January 7, 1855, to October 12, 1859 ? Ans. $50.04. 30. What is the interest of $197.28 from December 6, 1852, to January 11, 1854? Ans. $12.987. 31. What is the amount of $ 4377.15 for 3 years? 32. What is the interest of $444.60 for 5 years and 6 months? Ans. $146.718. 355. To find the interest of any sum of money at any rate per cent. for any given time. Ex. 1. What is the interest of $ 84.50 at 7 per cent. for 2 years 5 months and 12 days? Ans. $14.49. days; and since 2 days are of 10 days, we take for 2 days. The interest as found for the several time, added together, gives the interest required. Having found the interest for 1 year, and then for 2 years, the interest for 5 months is obtained by first taking of 1 year's interest, for 4 months, and then of this last interest for 1 month. And since 10 days are of 1 month, we take of 1 month's interest for the interest of 10 of the last interest parts of the whole We first find the interest on the given sum at 6 per cent., and then add to this interest the fractional part of itself, denoted by the excess of the rate above 6 per cent. This excess is 1 per cent.; therefore we add of the interest at 6 per cent. to that interest for the answer. 6 per cent, we should RULE 1.- First find the interest for one year by multiplying the principal by the rate per cent. expressed decimally; and for two or more years multiply this product by the number of years. Find the interest for months by taking the most convenient fractional part or parts of ONE year's interest. Find the interest for days by taking the most convenient fractional part or parts of ONE month's interest. Or, RULE 2. Find the interest of the given sum at 6 per cent., and then add to this interest, or subtract from it, such a fractional part of itself as the given rate is greater or less than cent. per cent. NOTE 1. of the interest at 6 per cent. may be taken for that at 1 per cent.;, for that at 14 per cent.; }, for that at 2 per cent.; 4, for that at 3 per From the interest at 6 per cent. may be taken of itself for that at 4 per cent.; of itself for that at 44 per cent.; and of itself for that at 5 per cent. To the interest at 6 per cent. may be added of itself for that at 7 per cent.; of itself for that at 7 per cent.; of itself for that at 8 per cent ; and of itself for that at 9 per cent. If the rate is 12 per cent., the interest at 6 per cent. may be taken twice; if 18 per cent., the interest at 6 per cent. may be taken three times, etc. NOTE 2. - When in this book the rate of interest is not given, 6 per cent. is to be understood. EXAMPLES. 2. What is the interest of $16.75 for 7 months and 17 days, at 7 per cent.? Ans. $0.739. 3. What is the interest of $11.10 from April 17, 1852, to December 7, 1852, at 7 per cent.? Ans. $0.496. 4. What is the interest of $12.69, from January 2, 1853, to August 30, 1854, at 7 per cent.? Ans. $ 1.471. 5. What is the interest of $5000 for 2 years 5 months 26 days, at 7 per cent. ? 6. What is the amount of $ 416 for 3 years 16 days, at 7 cent.? per Ans. $504.64. 7. What is the interest of $336 for 15 days, at 5 per cent.? Ans. $0.70. 8. What is the interest of $17869.75 from February 7, 1852, to January 11, 1860, at 5 per cent.? Ans. $7083.3703. 9. What is the interest of $ 300.50 for 1 year 2 months and 15 days? Ans. $21.786. 10. What is the interest of $ 37 for 29 days, at 5 per cent.? 11. What is the interest of $ 35.61 from November 11, 1861, to December 15, 1863? Ans. $ 4.474. 12. What is the interest of $ 16.76 from December 17, 1841, to January 17, 1852 ? Ans. $10.139+ 13. What is the interest of $1728.19 from May 7, 1854, to July 17, 1860, at per cent.? Ans. $26.762. 14. What is the interest of $ 397.16 for 1 year 6 months and 1 day, at 5 per cent.? 15. What is the amount of $100.25 for 2 months and 29 days, at 4 Ans. $101.241. per cent.? Ans. $32.826. 16. What is the interest of $51.17 for 9 months and 29 Ans. $1.699. days, at 4 per cent.? 17. What is the interest of $42.20 for 1 year and 16 days, at 4 per cent. ? |