RULE. We find the interest of $1 for the given time to be $0.237 (Art. 197). Now, since the interest of $1 is $0.237, the interest of $926 will be 926 times as much, therefore we multiply them together. To find the amount, we add the principal to the interest. Hence the following - 1. Find the interest of $1 for the given time; then multiply the principal by this interest, and point off as in multiplication of decimal fractions. (Art. 185.) 2. To find the amount, add the principal to the interest. NOTE. If the interest of $1 contains a vulgar fraction, the fraction may be reduced to a decimal, if preferred. The interest may also be multiplied by the principal, when it is more convenient. EXAMPLES FOR PRACTICE. 2. What is the interest of $197 for 1 year ? Ans. $11.82. 3. What is the interest of $ 1728 for 3 years? Ans. $311.04. 4. What is the interest of $ 69 for 2 years? 5. What is the interest of $1728 for 1 year, 6 months? 6. What is the interest of $ 16.87 for 1 7. Required the interest of $118.15 for 8. Required the interest of $97.16 for 1 9. Required the interest of $789.87 for Ans. $155.52. year, 8 months? Ans. $1.68,7. 2 years, 6 months. Ans. $17.72,2. year, 5 months. Ans. $8.25,8. 10. Required the amount of $978.18 for 2 years, 3 months. Ans. $1110.23,4. 11. Required the amount of $87.96 for 1 month. Ans. $88.39,9. 12. Required the amount of $81.81 for 8 years, 4 months. Ans. $122.71,5. QUESTIONS. Art. 198. Explain the operation for finding the interest on any sum of money at 6 per cent. for any given time. What is the rule? How do you find the amount? 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? Ans. $0.20,5. 15. Required the interest of $100 for 8 years, 4 months, 1 Ans. $50.01,6. day. 16. Required the interest of $3.05 for 2 months and 2 days? Ans. $0.03,1. 17. What is the interest of $761.75 for 1 year, 2 months, 18 days? Ans. $55.60,7. 18. What is the interest of $1728.19 for 1 year, 5 months, Ans. $149.77,6. year, 4 months, 6 Ans. $7.20,5. month, 29 days? Ans. $1.05,7. 10 days? 19. What is the interest of $88.96 for 1 days? 20. What is the interest of $107.50 for 1 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 rate per cent. for any given time. any sum of money at any Ex. 1. What is the interest of $26.25 for 2 years, 4 months, 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 QUESTIONS. 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 days, at 7 per cent. ? Ans. $97.18. 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 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 Ans. $0.84,9. per cent.? 7 per 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 days, at 7 per cent. ? 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. 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 8 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. ? 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 RULE. - 1. First find the interest for one year by multiplying the principal 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. 20 days. 25 days. 15 days. 6. Required the interest of $ 1.95 for 15 years, 11 months, 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., for any time. Ex. 1. What is the interest of 25£. 2s. 6d. for 2 years, 6 months, at 6 per cent. ? 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.) RULE. 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. |