INTEREST. 351. INTEREST is an allowance made for the use of money, or for value received; and it is generally reckoned as a certain rate per cent. for any given time, but usually for one year. The principal is the sum lent, on which interest is computed. The amount is the interest and principal added together. Simple interest is that reckoned on the principal only; and is that meant when the term interest is used alone. Legal interest is the rate per cent. established by law. Usury is a higher rate per cent. than is allowed by law. The legal rate per cent. varies in the different States and in different countries. In Maine, New Hampshire, Vermont, Massachusetts, Rhode In Alabama and Texas, it is 8 per cent. In Louisiana, it is 5 per cent. In Canada, Nova Scotia, and Ireland, it is 6 per cent. NOTE. The legal rate, as above, in some of the States, only that which the law allows, when no particular rate is mentioned. By special agreement between parties, in Ohio, Indiana, Michigan, Illinois, Iowa, Nebraska, Missouri, Kansas, Arkansas, Louisiana, and Mississippi, interest can be taken as high as 10 per cent.; in Florida, as high as 8 per cent.; in Texas and Wisconsin, as high as 12 per cent.; and in California and Minnesota, any per cent. In New Jersey, by a special law, 7 per cent. may be taken in the city of Paterson, and in the counties of Essex and Hudson. In Vermont 7 per cent. may be taken on railroad bonds. Banks in Illinois cannot take above 7 per cent., and in Ohio, not above 6 per cent. In Mississippi, above 6 per cent. can be taken only for money lent. 352. When the rate of interest is 6 per cent. per annum, the interest for 1 year or 12 months will be 6 cents on every 100 cents on which it is reckoned, or 18 of the principal. Hence, for 2 months or of a year, it will be 1 cent on every 100 cents, or Too of the principal; and for 1 month or of 2 months it will be 5 mills, or ʊ of the principal. Now, since the interest on 100 cents for 1 month, or 30 days, is 5 mills, for 6 days, or of 30 days, it will be 1 mill, or Too of the principal; and since the interest on 100 cents for 2 months is 1 cent, or of the principal, for 100 times 2 months, or 200 months, or 16 years 8 months, it will be 100 cents, or equal the whole principal; and in the same ratio for any other length of time. The interest of $ 1, at 6 per cent., and the ratio of the interest to the principal, for 200 months, and other convenient parts of time, is shown in the following 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.? 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 3 cents, or 3 cents 5 mills. And as the interest for 6 days is 1 mill, for 26 days it will be 43 mills. These several sums added together give the interest of $1 at 6 per cent. for the given time, equal $ 0.159, which taken 2640 times, by multiplying the given principal by it, gives $ 420.64, the interest required. Ans. $ 4 2 0.64 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 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. NOTE 2. 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? 19. What is the interest of $ 6444 for, 29 days? 20. What is the amount of $18.60 for 24 days? 21. What is the interest of $386.19 for 100 months? Ans. $193.09. 22. What is the interest of $0.75 for 75 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. |