CHAPTER XVII. INTEREST AND DISCOUNT. 352. Interest is the payment made for the use of money. The interest to be paid for a given sum differs from the payments considered in the last chapter, in that it depends on the time for which the sum is loaned as well as on the rate per cent charged. 353. The sum loaned is called the principal. The principal and interest, added together, are called the amount. SIMPLE INTEREST. 354. If 100 be taken as the representative of the principal, the rate will represent the interest for one year; the product of the rate per cent by the number of years will represent the whole interest, and this added to 100 will represent the amount. Thus, if the time be 3 years and the rate per cent 6, the interest will be represented by 18, and the amount by 118. (1) Find the interest on $1024, for 2 yrs. 8 mos., at 51%. (2) Find the interest for $750, from Mar. 13 to Aug. 28, at 6%. August is the eighth month and March the third month. In computing interest the month is reckoned as 30 days, and the year at 12 months, or 360 days. (3) Find the interest of $1020, for 5 yrs. 11 mos. 18 dys., at 6%. The interest at 6% for 1 year is .06 of the principal. The interest for 1 month is of .06 = .005 of the principal. of .005 of .001 of the principal. = The method employed in the last example may be employed for any rate per cent, by first finding the interest at 6%, and then taking such a part of the interest as the given rate is of 6%. Thus, the in 44 == of the interest at 6% interest at 6% - of itself. The interest at 8% is 6%+ of itself. Find the interest of: EXERCISE LXXI. 1. $680.40 for 2 yrs. 4 mos. 6 dys., at 6%. 3. $85.85 for 1 yr. 7 mos. 21 dys., at 6%. 4. $1100 for 3 yrs. 4 mos., at 5%. 5. $1275 for 3 yrs. 2 mos. 15 dys., at 8%. 6. $475.16 for 27 dys., at 41%. 7. $1290.50 for 63 dys., at 7%. 8. $125 for 1 yr. 2 mos. 2 dys., at 9%. 9. $250.80 for 10 mos. 10 dys., at 3%. 10. $258.85 from Mar. 6, to June 24, at 5%. 11. $380 for 2 yrs. 11 mos. 27 dys., at 41%. 12. $475.05 for 1 yr. 9 mos. 14 dys., at 7%. 13. $725.40 for 11 mos. 24 dys., at 51%. 14. $680.50 for 2 yrs. 6 dys., at 5%. 15. $630.50 for 93 dys., at 61%. 16. $547.60 from Feb. 20 to Dec. 5, at 6%. 17. $875 from May 5, 1880, to June 21, 1881, at 51%. 18. $758.50 from Jan. 5 to July 1, at 41%. 19. $342.42 from Feb. 5, 1879, to Mar. 15, 1881, at 7%. 20. $540 from Mar. 5 to Sept. 21, at 31%. Find the amount of: 21. $431.50 for 2 yrs. 8 mos., at 41%. 22. $476.50 from July 5, 1880, to Feb. 9, 1881, at 4%. 23. $319.20 from April 7 to Aug. 31, at 3%. 24. $6460 from June 15, 1878, to May 7, 1880, at 41%. 25. $150 from Aug. 5, 1879, to Mar. 17, 1881, at 7%. 26. $527.20 from Jan. 1 to Nov. 20, at 43%. 27. $1250 from Nov. 15, 1880, to Mar. 1, 1881, at 5%. 28. $624.36 from Mar. 5 to Dec. 20, at 7%. 29. $12,260 from May 6 to Oct. 24, at 3%. 30. $11,216 from Oct. 20 to Dec. 31, at 1% a month. NOTE. In business a year is reckoned at 360 days in computing interest for a time less than a year expressed in months and days; hence, the interest is or too great. But general governments take the number of days between the two given dates, and reckon for the interest such a part of a year's interest as this number of days is of 365 days. 355. It is often required to find the rate, time, or principal, when two of these and the interest (or amount) are given. (a) When the principal, interest (or amount), and time are given, to find the rate per cent. (1) At what rate per cent will $480 produce $ 72 in three years? Interest on $480 for 3 years is $72; on $480 for 1 year is of $72; on $1 for 1 year is of } of $72 = $.05. Therefore, rate required is 5% (2) At what rate per cent will $8432 amount to $9437.516 in 2 yrs. 7 mos. 24 dys.? The interest is $9437.516 - $8432 = $1005.516. Interest on $8432 for 2.65 yrs. is $1005.516; $1005.516 2.65 on $1 for 1 yr. is $.041. 2.65 X 8432 Hence, rate required is 41% The rate may also be found by forming a proportion with the representative numbers. Thus, == Hence, the interest, which rate time, is represented by 11.925. Find the rate per cent: 31. When the interest on $326 for 15 yrs. is $220.05. 32. When the interest on $372.50 for 18 yrs. is $301.725. 33. When $245 amount to $252.96 for 9 mos. yrs. 34. When the interest on $235.25 is $ 70.575 for 5 35. When $363.125 amount to $371.598 for 7 mos. 36. When the interest on $249.43 is $49.88 for 5 yrs. 4 mos. 37. When $350 amount to $406.70 for 3 yrs. 7 mos. 6 dys. 38. When the interest on $6875 is $72.05 for 90 dys. 39. When the interest on $642 is $10.70 for 5 mos. 40. When the interest on $8432 for 2 yrs. 7 mos. 23 dys. is $1339.28. 41. When a sum of money is doubled in 14 yrs. 42. When an investment for 5 yrs. 2 mos. produces a sum equal to of the capital. 43. When an investment for 3 yrs. 1 mo. 15 dys. produces a sum equal to of the capital. (b) When the principal, interest (or amount), and rate per cent are given, to find the time. Ex. In what time will the interest on $8432 amount to $1005.516, at 41% ? Interest on $8432, at 41%, for 1 yr. is .045 of $ 8432 = $379.44. Therefore, the number of years will be $1005.516 $379.44 2.65. And 2.65 yrs. = 2 yrs. 7 mos. 24 dys. Ans. Find the time in which: 44. The interest on $450 will amount to $72, at 4%. 45. The interest on $487.50 will amount to $39, at 4%. 46. The interest on $238.75 will amount to $64.46, at 44%. 47. The sum of $793.875 will amount to $805.84, at 51%. 48. A sum of money will double itself at 4%. |