SECTION XXX. SIMPLE INTEREST. INTEREST is the compensation, which the borrower of money makes to the lender. PRINCIPAL, is the sum lent. AMOUNT, is the interest added to the principal. PER CENT., a contraction of per centum, is the rate established by law; or that which is agreed on by the parties, and is so much for a hundred dollars for one 1 year. GENERAL RULE * Multiply the principal by the rate per cent. and divide by 100, and the quotient is the answer for one year; or, multiply by the per cent. and cut off two figures from the right hand, and those at the left will be the interest in dollars, and those at the right will be decimals of a dollar. SECOND METHOD. Let the per cent. be considered a decimal of a hundred dollars, and multiply the principal by it. Thus, .06 is the decimal for six per cent. and .08 is the decimal for eight per cent. NOTE. When no particular per cent. is named, 6 per cent. is to be understood as it is the legal interest in the New England States generally. In New York, the legal interest is 7 per cent. EXAMPLES. 1. What is the interest of $144 for 1 year? 2. What is the interest of $78 for 1 year? 3. What is the interest of $675 for 1 year? Ans. $4.68. Ans. $40.50. *This rule is obvious, from the fact, that the rate per cent. is such a part of every hundred. Thus, 6 per cent. is of the principal. 100 4. What is the interest of $ 1728 for 1 year ? Ans. $103.68. Ans. $2.35.6. 5. What is the interest of $ 19.64 for 2 years ? 6. What is the interest of $ 896.28 for 3 years s? Ans. $161.33. Ans. $209.55. 7. What is the interest of $ 349.25 for 10 years? 8. What is the interest of $3967.87 for 2 years ? Ans. $476.14.4. 9. What is the interest of $ 123.45 for 6 years ? Ans. $ 44.44.2. 10. What is the interest of $89.25 for 50 years? 11. What is the interest of $17.25 for 7 years Ans. $267.75. ? Ans. $7.24.5. 12. What is the interest of $ 29.19 for 9 years? Ans. $15.76.2. 13. What is the interest of $ 617.56 for 25 years ? Ans. $926.34. 14. What is the amount of $ 31.75 for 100 years? Ans. $222.25. 15. What is the amount of $76.47 for 7 years ? Ans. $108.58.7. 16. What is the amount of $716.57 for 4 years? 17. What is the amount of $178.56.5 for 18. What is the interest of $97.06 for 9 Ans. $888.54.6. 30 years? Ans. $499.98.2. 19. What is the interest of $0.75 for 75 years? Ans. $3.37.5. 20. What is the interest of $750 for 12 years ? Ans. $540. CASE 1. To find the interest for months, at six per cent. RULE.* Multiply the principal by half the number of months, and proceed as in the general rule; or, let half the number of months be considered as a decimal. It is obvious, that if the rate per cent. were 12, it would be 1 per cent. a month. If, therefore, it be 6 per cent. it will be half per cent. a month; that is, half the months will be the per cent. EXAMPLES. 1. What is the interest of $368 for 8 months? 2. What is the interest of $637 for 10 months? Ans. $31.85. 3. What is the interest of $1671.32 for 14 months? Ans. $116.99. 4. What is the interest of $891.24 for 9 months? Ans. $40.10. 5. What is the interest of $819.75 for 11 months? Ans. $45.08.6. 6. What is the interest of $3671.25 for 13 months? Ans. $238.63. 7. What is the interest of $61.18 for 15 months? Ans. $4.58. 8. What is the interest of $3181.29 for 18 months? Ans. $286.81. 9. What is the interest of $11.39 for 19 months? Ans. $1.08. 10. What is the interest of $9.98 for 23 months? Ans. $1.14. 11. What is the interest of $87.19 for 27 months? Ans. $11.77. 12. What is the interest of $32.18 for 36 months? Ans. $5.79. 13. What is the interest of $167.18 for 50 months? Ans. $41.79. 14. What is the interest of $386.19 for 100 months? Ans. $193.09. CASE II. To find the interest of any sum for months and days, at 6 per cent. RULE.* Multiply by half the number of months and one-sixth of the days; and if the principal be dollars, cut off three figures from the right hand, and those at the left will be the interest in dol * By taking one-sixth of the days, and annexing them to half of the months, they become decimals of a month; for as days are thirtieths of a month, they will therefore be sixtieths of half months; and if one-sixth of the days be taken, they become tenths, or decimals of a month. lars, and those at the right will be cents and mills. But if the principal be dollars and cents, five figures must be cut off from the right hand, and those at the left will be the interest, as before, &c. NOTE. If any other per cent. is wanted, proceed as above, and then multiply by the given rate per cent. and divide by 6, and the quotient is the interest. EXAMPLES. 1. What is the interest of $ 68.25 for 8 months and 24 days? Ans. $3.00.3. 68.25 .0.44 27300 27300 3.00.300 The first 4 in the multiplier is half of the 3 months; the second 4 is onesixth of the 24 days. 2. What is the interest of $637.28 for 17 months and 19 days, at 8 per cent. ? Ans. $74.91.5. 3. What is the interest of $396.15 for 13 months and 9 days? Ans. $26.34.3. 4. What is the interest of $16.75 for 7 months and 17 days, at 7 per cent.? Ans. $0.73.9. 5. What is the interest of $976.18 for 29 months and 23 days, at 9 per cent. ? Ans. $217.93.2. 6. What is the interest of $36.18 for 3 months and 7 days? Ans. $0.58.4. 7. What is the interest of $51.17 for 9 months and 29 days, at 4 per cent. ? Ans. $1.69.9. 8. What is the interest of $ 365.19 for 33 months and 4 days, at 2 per cent. ? Ans. $20.16.6. 9. What is the interest of $ 125.75 for 5 months and 4 days? Ans. $3.22.7. 10. What is the interest of $35.49 for 1 month and 2 days, at 7 per cent.? Ans. $0.23.6. 11. What is the interest of $112.50 for 3 months and 1 day, at 9 per cent. ? Ans. $2.70.1. 12. What is the interest of $97.15 for 35 months and 27 days? interest of $47.15 for 1 interest of $678.75 for Ans. $17.43.8. month and 19 days, Ans. $0.86.6. 87 months and 20 Ans. $297.51.8. interest of $86 for 99 months and 29 days, 16. What is the interest of $33.35.8 for 15 months and 17 days? Ans. $179.10.6. Ans. $2.59.6. Ans. $0.12.0. 17. What is the interest of $144 for 5 days? CASE III. When the interest is required on any sum, from a certain day of the month in a year, to a particular day of a month in the same, or in another year. RULE. Find the time, by placing the latest date in an upper line, and the earliest date under it. Let the year be placed first; the number of months that have elapsed since the year commenced, at its right hand, and the day of the month next; then subtract the earlier from the latest date, and the remainder is the time for which the interest is required. Then proceed as in the last rule. Or, the months may be considered as fractional parts of a year, and the days as fractional parts of a month. EXAMPLES. 1. What is the interest of $84.97, from Sept. 25, 1833, to March 8, 1835 ? = 84.97 .06 5.0982 4 months, 1.6994 1 month, = .4248 = .1416 = 283 is It is evident, that 4 months' interest of a year's interest; and, for the same reason, 1 month's interest is of 4 months' interest; and as 10 days is of a month, the interest for that time of a month's interest; and if the interest of 10 days be divided by 5, the quotient will be 2 day's interest, and the half of this will be 1 day's interest. $7.40.64 Interest as before. 10 days, 2 days, 1 day, = 141 is 2. What is the interest of $786.75, from Dec. 9, 1881, to May 11, 1833 ? Ans. $67.13.6. 3. What is the interest of $ 98.25, from July 4, 1826, to Oct. 19, 1829 ? 4. What is the interest of $76.89.5, from July 27, 1833 ? Ans. $19.40.4. |