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? Ans. $888.54,6. 17. What is the amount of $ 178.56,5 for 30 years ? Ans. $499.98,2. 18. What is the interest of $97.06 for 9 years? 19. What is the interest of $0.75 for 75 Ans. $52.41,2. years ? Ans. $3.37,5. 20. What is the interest of $750 for 12 years? CASE II. Ans. $540. To find the interest for months at 6 per cent. RULE. Multiply the principal by half the number of months, expressed decimally as a per cent.; that is, for 12 months multiply by .06; for 8 months multiply by .04; for 7 months, .035; for 1 month, .005; and point for decimals as in the last rule. NOTE 1. - - 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 a half per cent. a month, that is, half the months will be the per cent. NOTE 2. 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. 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. $286.31. 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? CASE III. Ans. $193.09. To find the interest of any sum for months and days, at 6 per cent. II. RULE.*. Find the interest for the number of months, as under Case Then to find it for the number of days,multiply the principal by one sixth the number of 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 dollars, 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, &c., as before. * The reason for this rule, so far as it relates to the interest for any number of months, was explained above. But the reason for the operation in the case of days is not so obvious. It will be seen, however, that it is nothing but an abridgment of the general rule for calculating interest, as given on page 164, which will appear from what follows. To find the interest for any number of years, we multiply the principal by the annual per cent., and the product thus obtained by the number of years, and cut off two figures, &c. In like manner, it is evident that to find the interest for any number of days, we have only to multiply by the daily per cent., and the product thus obtained by the number of days, and cut off as in the case of years. But 6 per cent. per annum is to per cent per diem, allowing 360 days to a year. Now, to multiply the principal by of the days, and cut off one figure from the product at the right, is the same as to multiply by (the daily per cent.), and the product thus obtained by the whole number of days. Where the principal is dollars only, the rule directs to cut off three figures. Two of them are cut off according to the general rule, on page 164, and the other, because in the operation we have multiplied by the number of days, instead of of them, which would have been the proper multiplier. 60 The above may be illustrated concisely by the following operation. Let it be required to find the interest of 75 dollars for 180 days. By the general rule we have 75 x 100 x 180 $2.25. By the rule under Case III. we have 75 × of 180 = $2.25. NOTE 1. - If one half the number of months be expressed by a single figure, we have only to annex to this figure the number of days, and multiply the principal by the number thus found, cutting off as above, and we obtain, by a single operation, the interest for the months and days. If any other per cent. than 6 is given, we may proceed as above, and then multiply by the given rate and divide by 6, and the result will be the interest sought. NOTE 2. 1. What is the interest of $68.25 for 8 months and 24 days? Ans. $3.00,3. OPERATION. $68.25 .044 The first 4 in the multiplier is half of the 8 27300 months; the second 4 is one sixth of the 24 27300 $3.00,300 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. ? 11. What is the interest of $112.50 for at 9 per cent. ? 12. What is the interest of $97.15 for days? 3 Ans. $0.23,6. months and 1 day, Ans. $2.70,1. 35 months and 27 Ans. $17.43,8. 13. What is the interest of $ 47.15 for 1 month and 19 days, at 13 per cent.? Ans. $0.86,6. 14. What is the interest of $678.75 for 87 months and 20 days? Ans. $297.51,8. 15. What is the interest of $86 for 99 months and 29 days, at 25 per cent. ? Ans. $179.10,6. 16. What is the interest of $33.35,8 for 15 months and 17 Ans. $2.59,6. days? 17. What is the interest of $ 144 for 5 days? CASE IV. Ans. $0.12,0. 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 reckoned by their ordinal number, as in Operation Second. NOTE. Many practical men prefer reckoning interest by the second method. EXAMPLES. 1. What is the interest of $84.97, from Sept. 25, 1833, to March 8, 1835 ? Ans. $7.40,6. First Method. $84.97 Yrs. m. d. 1835 3 8 .087 59479 67976 1416 $7.40,655 Second Method. 4 months, $84.97 .06 = 5.0982 1 year, 1.6994 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 1 of a month, the interest for that time is of a month's interest; and if the interest of 10 days be divided by 5, the quotient will be 2 days' interest, and 141 the half of this will be 1 day's interest. $7.40,64, interest as before. 2. What is the interest of $786.75, from Dec. 9, 1831, to May 11, 1833? Ans. $67.13,6. 3. What is the interest of $98.25, from July 4, 1826, to Oct. 19, 1829 ? Ans. $19.40,4. 4. What is the interest of $76.89,5, from Jan. 11, 1822, to July 27, 1833? Ans. $53.26,2. 5. What is the interest of $22.76,3, from Feb. 19, 1806, to July 18, 1830 ? Ans. $33.34,4. 6. What is the interest of $76.35, from August 17, 1830, to May 5, 1832 ? Ans. $7.86,4. 7. What is the interest of $97.86, from May 17, 1821, to Dec. 19, 1828 ? Ans. $44.55,8. 8. What is the interest of $1728.75, from Nov. 19,1823, to June 18, 1826 ? Ans. $267.66,8. 9. What is the interest of $99.99,9, from Jan. 1, 1800, to Feb. 29, 1832 ? Ans. $192.96,4. 10. What is the interest of $16.76, from Dec. 17, 1811, to June 17, 1822 ? Ans. $10.55,8. 11. What is the interest of $35.61, from Nov. 11, 1831, to Dec. 15, 1833 ? Ans. $4.47,4. 12. What is the interest of $786.97, from Oct. 19, 1827, to August 17, 1831, at 7 per cent. ? Ans. $225.92,5. 13. What is the interest of $96.84, from Nov. 27, 1829, to July 3, 1832, at 71⁄2 per cent. ? Ans. $18.88,3. 14. What is the interest of $11.10,5, from April 17, 1832, to Dec. 7, 1832, at 7 per cent.? Ans. $0.49,6. 15. What is the interest of $117.21, from June 19, 1806, to June 17, 1819, at 8 per cent. ? Ans. $129.46,1. 16. What is the interest of $ 17869.75, from Feb. 7, 1830, to Jan. 11, 1832, at 5 per cent.? Ans. $1722.44,5. 17. What is the interest of $71.09,1, from July 29, 1823, to June 19, 1827, at 12 per cent. ? Ans. $33.17,5. 18. What is the interest of $ 83.47, from Nov. 8, 1830, to July 11, 1833, at 8 per cent. ? Ans. $ 19.53,7. 19. What is the interest of $79.25, from Dec. 8, 1831, to July 17, 1833 ? Ans. $7.64,7. 20. What is the interest of $175.07, from Jan. 7, 1825, to Oct. 12, 1829 ? Ans. $50.04. 21. What is the interest of $12.75, from June 16, 1831, to August 20, 1833 ? Ans. $1.66,6. 22. What is the interest of $197.28,5, from Dec. 6, 1832, to Jan. 11, 1834 ? Ans. $12.98,7. 23. What is the interest of $12.69, from Jan. 2, 1833, to August 30, 1834, at 7 per cent. ? Ans. $1.47,5. 24. What is the interest of $79.15, from Feb. 11, 1831, to June 10, 1833, at 74 per cent. ? Ans. $13.37,3. |