255. Formulas in Interest. We may express the principles involved in the problems on page 285 by using initial letters to represent the elements. In this way we have convenient formulas. = Using the initial letters, and letting the time be expressed in years, we have Interest principal x rate x time (§ 248), or I=PXRXT; therefore interest rate time , or R = I interest time = " or T = $36, $36 3 × 6% $200, $36 3 x $200 $36 principal = rate = P: R T = = p: = = x = = or P = 6%, 3. Instead of using capital letters for the initials, we may use small letters if we wish. We shall then have : i i=pxrxt, rx t i px r The simple equation and the use of the unknown quantity x may profitably be used in the solution of some problems, thus: $36 is the interest on $200 for how many years at 6% ? r = $36 = i pxt I RX T 3. Since $36 = x × 6% of $200, we may divide these equals by 6% of $200, and we have The same principle is involved as in the preceding solution in which T is found. EXERCISE 150 1. Given r = 6%, i = = r $90, and t = 3, find p. Find the missing element, marked x: p p r t 4. $300 16. $375 4% 4 yr. 5% x 3 yr. $90 6% 2 yr. x 3% x $54 21. x 5% 3 yr. $30 22. $700 x 2 yr. $70 x 25. x 3% 3 yr. $36 26. $250 x 2 yr. $20 27. $900 6% x $162 t i x 4 yr. $60 5. x 4% 4 yr. $64 6. $700 3% x $42 7. $650 5% 2 yr. x $30 $36 9. $300 x 3 yr. 10. $300 3% x $36 11. $700 5% 3 yr. x. 12. x 6% 5 yr. $60 13. $400 x 2 yr. $48 14. $500 5% x $75 15. $800 4% 2 yr. x 17. x 18. $600 19. $700 20. $600 i x 2 yr. $70 28. A note for $275 at 6% runs for 3 yr. without any payments being made. What is the amount then due ? 29. A note for $300 at 6% amounts to $336. How long has the note run? 30. A note for $400 amounts in 3 yr. to $460. What is the rate of interest? 31. A note amounts to $224 in 2 yr. The face of the note is $200. What is the rate of interest? 32. Write a note for $275 due 2 yr. 6 mo. after this date, at 6%, and find the amount due at maturity. EXERCISE 151 REVIEW OF INTEREST Given the principal, rate, and time, find the interest: 1. $250, 5%, 4 mo. 10 da. ; 8 mo. 20 da. 2. $520, 6%, 2 yr. 9 mo. ; 2 yr 9 mo. 25 da. 3. $760, 5%, 4 yr. 6 mo.; 4 yr. 6 mo. 15 da. Given the principal, rate, and time, find the amount : 9. $175, 6%, 6 mo.; 8 mo.; 1 yr. 2 mo. 10. $225, 6%, 8 mo. 3 da.; 1 yr. 8 mo. 3 da. 11. $625, 5%, 4 mo. 3 da. ; 2 yr. 4 mo. 3 da. 12. $1250, 5%, 3 mo. 8 da. ; 2 yr. 3 mo. 8 da. 13. $2275, 51%, 10 mo. 14 da. ; 3 yr. 10 mo. 14 da. 14. Find the interest on $275 for 3 yr. 6 mo. at 5%. 15. Find the interest on $1250 for 7 yr. 11 mo. at 6%. 16. Find the interest on $630 for 2 yr. 4 mo. 5 da. at 6%. 17. Find the interest on $345 for 2 yr. 3 mo. 3 da. at 5%. 18. Find the interest on $290 for 1 yr. 6 mo. 5 da. at 5%. 19. Find the interest on $350 for 1 yr. 9 mo. 15 da. at 4%. 20. Find the interest on $650 for 2 yr. 8 mo. 10 da. at 6%. 21. Find the interest on $1575 for 3 yr. 1 mo. 6 da. at 51%; at 41%; at 6%. 22. What is the interest on $375 from July 4, 1915, to May 1, 1918, at 6% ? Given the principal, interest, and time, find the rate: 23. $275, $27.50, 2 yr. 30. $250.50, $30.06, 2 yr. 33. 29. $220, $9.35, 1 yr. 5 mo. 36. $480, $26.60, 1 yr. 7 mo. Given the principal, interest, 37. $240, $36, 6%. 38. $3000, $155, 2%. 39. $175, $12.25, 4%. 40. $600, $42.75, 5%. 41. $360, $19.91, 5%. 47. How long will it take a sum to double itself at 4%? 48. How long will it take $220, together with the interest, to amount to $253, at 6% ? and rate, find the time : 42. $280, $28, 4%. 43. $350, $17.50, 3%. 44. $525, $47.25, 6%. 45. $230, $20.70, 41%. 46. $2500, $37.50, 41%. 49. How long will it take $1750, together with the interest, to amount to $1968.75, at 5% ? 50. For how long must $1250 be invested at 5% so that it shall amount, together with the interest, to $1281.25? to $1385? to $1416.25? 51. A girl had $250 invested for her, at 6%, on her birthday. When she became 21 it amounted, with interest, to $400. How old was she when it was invested? 52. A father gave his son his promissory note for $225, due when the son became 21 years old. The rate of interest was 5%, and when the note became due the principal and interest together amounted to $303.75. How old was the son when the note was given? 53. Which yields the better income, $1675 at 5% or $1375 at 6%? What is the difference for 2 yr. 6 mo.? 54. A man receives $2187.50 interest in 2 yr. 6 mo. on an investment of $17,500. What is the rate of interest? 55. A man has $250 in a savings bank at 3%. He leaves the principal, but draws out the interest as it is due. How much does he draw out in four years? 56. A man having $13,500 invested at 5% reinvests $4000 of it at 51%, $5000 of it at 31%, and leaves the rest as before. What is the annual difference in income? 57. A boy has $300 given to him the day he is 14 years old. His father invests it for him in a 5% promissory note, due on the day he is 21 years old. What is the amount on the day the note is due? 58. A real estate dealer buys 360 acres of farm land at $30 an acre, and after keeping it 7 months sells it at an advance of $3.75 an acre. The money being worth to him 5% a year, how much does he gain by the transaction? 59. A man having $26,750 invested in business has found that his annual profits average 18% a year. He is offered $35,000 for the business, which he can invest at 41%. If he sells out and retires, what will be his loss in income? 60. On April 10 a coal dealer borrowed $33,250 at 5%, with which he purchased his summer's supply of coal at $4.75 a ton. He sold the coal at $5.65 a ton, the buyers paying for unloading and delivery, and paid his debt on November 16. How much did he gain? 61. On October 15 a dealer purchased $1750 worth of goods for the holiday trade on 30 days' credit. At the end of that time he gave his note for 2 months at 6% a year. He sold the goods for $2105, and paid the note when due. What per cent did he make on the original purchase price? |
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