13. Required the amount of $0.87 for 7 years, 3 months. Ans. $1.24,8. 14. What is the interest of $1.71 for 2 years, 2 days? 15. Required the interest of $100 for 8 days? Ans. $ 0.20,5. years, 4 months, 1 Ans. $50.01,6. for 2 months and 2 Ans. $0.03,1. 17. What is the interest of $761.75 for 1 year, 2 months, 18 days? 18. What is the interest of $1728.19 for 10 days? 19. What is the interest of $88.96 for 1 days? Ans. $55.60,7. 1 year, 5 months, Ans. $149.77,6. year, 4 months, 6 Ans. $7.20,5. 20. What is the interest of $107.50 for 1 month, 29 days? Ans. $1.05,7. 21. What is the interest of $87.25 for 1 year, 8 months, 5 days? Ans. $8.79,7. 22. What is the interest of $73.16 for 1 year, 7 months, 23 days? Ans. $7.23. 23. What is the amount of $ 1371.15 for 3 years, 6 months, 10 days? Ans. $1661.37,6. ART. 199. 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 $26.25 for 2 years, 4 months, at 7 per cent. ? QUESTIONS. Ans. $4.28,75. 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. The excess is 1 per cent.; therefore we add of the interest at 6 per cent. to itself, for the answer. If the rate per cent. had been less than 6, we should have subtracted the fractional part. Hence the following Art. 199. Explain the operation for finding the interest on any sum of money at any rate per cent. RULE. - 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 6 per cent., and point off as in multiplication of decimal fractions. (Art. 185.) NOTE 1.-If the rate per cent. is 12 per cent., the interest at 6 per cent. must be doubled. NOTE 2.. If the interest is for years only, it may be found by multiplying the principal by the interest of $1 for the given time and rate. EXAMPLES FOR PRACTICE. 1. What is the interest of $ 144 for one year at 7 per cent.? Ans. $10.08. 2. What is the interest of $850 for 1 year, 7 months, 18 Ans. $97.18. days, at 7 per cent. ? 3. What is the interest of $ 865.75 for 3 years, 9 months, 24 days, at 7 per cent. ? Ans. $231.29,9. 4. What is the interest of $ 960.18 for 1 year, 2 months, at 7 per cent.? Ans. $78.41,4. 5. What is the interest of $1728.19 for 3 years, 8 months, 10 days, at 7 per cent.? Ans. $ 446.92,9. 6. What is the interest of $17.90 for 8 months, 4 days, at 7 per cent.? Ans. $0.84,9. 7. What is the interest of $ 1165.50 for 5 years, 3 months, 9 days, at 7 per cent. ? Ans. $430.36. 8. What is the interest of $ 1237.90 for 1 year, 7 months, 3 Ans. $137.92,2. 9. What is the interest of $156.80 for 3 years and 3 days, at 3 per cent. ? Ans. $ 14.15,1. -10. What is the interest of $579.75 for 1 year, 2 months, 2 days, at 5 per cent.? Ans. $33.97,9. days, at 7 per cent. ? 11. What is the interest of $7671.09 for 2 years, 8 months, 5. days, at 8 per cent. ? Ans. $1645.02. 12. What is the interest of $ 943.11 for 1 month, 29 days, at 9 per cent. ? Ans. $ 13.91. 13. What is the interest of $975.06 for 2 years, 7 months, 9 days, at 81 per cent. ? Ans. $209.82. 14. What is the amount of $1000 for 3 years, 3 months, 29 days, at 5 per cent. ? Ans. 1183.18. years, 9 months, at Ans. $21.03,7. 3 years, 2 months, Ans. $388.94. 15. What is the interest of $765 for 2 1 per cent.? 16. What is the interest of $979.15 for 4 days, at 12 per cent.? QUESTIONS. What is the rule? What is note first? Note second? ART. 200. Second method of finding the interest of any sum of money, at any rate per cent., for any time. Ex. 1. What is the interest of $26.25 for 3 years, 5 months, and 15 days, at 8 per cent. ? RULE. 2.1000 3 6.3 0 0 0 of 4mo., .1750 $7.26,25 Ans. $7.26,2. Having found the interest for 1 year and then for 3 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 15 days are of 1 month, we take of 1 month's interest for the interest of 15 days; and add the several sums together for the answer. Hence the following 1. First find the interest for one year by multiplying the prin cipal by the rate per cent., and pointing off as in multiplication of decimal fractions; and for two or more years multiply this product by the number of years, and point off as before. 2. Find the interest for the months by taking the most convenient fractional part or parts of ONE year's interest, and then of any PART of one year's interest, if necessary, denoted by the months, or any PART of the months. 3. Find the interest for the days by taking the most convenient fractional part or parts of ONE month's interest, and then of any PART of one month's interest, if necessary, denoted by the days or any part of the days. NOTE. Many practical men prefer this method of casting interest to any other, but in most questions it is not so expeditious as the preceding. The pupil may be required to solve the questions in interest by both methods. EXAMPLES FOR PRACTICE. 2. What is the interest of $ 1775 for 7 years? Ans. $745.50. 3. What is the interest of $987 for 3 years, 6 months? Ans. $207.27. QUESTIONS. Art. 200. Explain the operation for finding the interest of any sum of money, at any rate per cent., for any time. What is the rule ? 4. Required the interest of $ 69.17 for 4 years, 9 months. Ans. $ 19.71,3. 5. Required the interest of $ 96.87 for 10 years, 7 months Ans. $61.75,4. 25 days. 15 days. 6. Required the interest of $1.95 for 15 years, 11 months, 20 days. Ans. $1.86,8. 7. Required the interest of $ 1789 for 20 years, 1 month, Ans. $2163.19,9. 8. Required the interest of $ 666.66 for 6 years, 10 months, 13 days. Ans. $274.77,5. 9. What is the amount of $ 98.50 for 5 years, 8 months? Ans. $131.99. 10. What is the amount of $ 168.13 for 8 years, 5 months, 3 days? Ans. $253.11,9. 11. What is the amount of $75.75 for 4 years, 2 months, 27 days? Ans. $95.02,8. 12. Required the amount of $ 675.50 for 30 years, 3 months, 23 days? Ans. $1904.12,1. ART. 201. To find the interest on pounds, shillings, pence, and farthings, at any rate per cent., time. for any Ex. 1. What is the interest of 25£. 2s. 6d. for 2 years, 6 months, at 6 per cent. ? RULE. Ans. 3£. 15s. 4d. 2qr. We reduce the 2s. 6d. to the decimal of a pound (Art. 188), and, annexing it to the pounds, multiply this principal by the interest of 1£. for the given time. The product is the answer in pounds and the decimal of a pound, which must be reduced to shillings, pence, and farthings. (Art. 189.) Reduce the shillings, pence, and farthings to the decimal of a pound, and annex it to the pounds; then proceed as in United States money, and reduce the decimal in the result to a compound number. EXAMPLES FOR PRACTICE. 2. What is the interest of 26£. 10s. for 2 years, 4 months, at 5 per cent.? Ans. 3£. 1s. 10d. QUESTIONS. Art. 201. How do you find the interest on pounds, shillings, pence, and farthings? Repeat the rule. 3. What is the interest of 42€. 18s. for 1 year, 9 months, 25 days, at 6 per cent. ? What is the interest of 94£. months, 7 days, at 8 per cent.? 5 What is the amount of 110£. months, at 5 per cent.? Ans. 4. 13s. 7 d. 12s. 6d. for 4 years, 6 Ans. 34£. 4s. 2 d. 7s. 6d. for 6 years, 11 Ans. 148£. 10s. 11d. MISCELLANEOUS EXERCISES IN INTEREST. 1. What is the interest of $172.50 from Sept. 25, 1840, to July 9, 1842 ? Ans. $ 18.51,5. 2. What is the interest of $169.75 from Dec. 10, 1838, to May 5, 1841 ? ? What is the interest of $17.18 from Sept. 1, 1841 ? 4. What is the interest of $67.07 from Dec. 11, 1841 ? Ans. $24.47,2. 5 Required the interest of $117.75 from Jan. 7, 1839, to Dec. 19, 1841. Ans. $20.84,1. 6. Required the interest of $847.15 from Oct. 9, 1839, to Jan. 11, 1843. Ans. $165.47,6. 7. Required the interest of $7.18 from March 1, 1841, to Feb. 11, 1842. Ans. $0.40,6. 8. What is the interest of $976.18 from May 29, 1842, to Nov. 25, 1845 ? 9. I have John Smith's note for 1839; what is due March 9, 1842 ? Ans. $204.34,7. $144, dated July 25, Ans. $166.65,6. 10 George Cogswell has two notes against J. Doe; the first is for $375.83, and is dated Jan. 19, 1840; the other is for $76.19, dated April 23, 1841; what is the amount of both notes Jan. 1, 1842 ? Ans. $499.14,1. 11. What is the interest of $ 68.19, at 7 per cent., from June 5, 1840, to June 11, 1841 ? Ans. $4.85,2. Feb. 17, 1839, to Ans. $102.11,9. 12 Required the amount of $79.15 from Dec. 30, 1842, at 7 per cent. 13. What is the amount of $89.96 from June 19, 1840, to Dec. 9, 1841, at 84 per cent. 14 A. Atwood has J. Smith's note for Ans. $100.88,6. $325, dated June 5, 1839; what is due, at 7 per cent., July 4, 1841 ? Ans. $374.02,2. 15 J. Ayer has D. How's note for $1728, dated Dec. 29 1839; what is the amount Oct. 9, 1842, at 9 per cent.? Ans. $2160. |