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 × rate × time (§ 248), or I=P×R×T; therefore

principal =

interest rate x time

Thus, if the interest on $200 for 3 yr. at 6% is $36, we have

Instead of using capital letters for the initials, we may use small letters if we wish. We shall then have :

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% ?

Since $36 = x × 6% of $200, we may divide these equals by 6% of $200, and we have

x =

$36
6% of $200

3.

The same principle is involved as in the preceding solution in which T is found.

EXERCISE 150

1. Given r = 6%, i = $90, and t = 3, find p.

find r.

2. Given i

=

$64, p

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.
4. $875, 6%, 3 yr. 7 mo.; 3 yr. 7 mo. 16 da.
5. $1250, 5%, 1 yr. 10 mo.; 1 yr. 10 mo. 5 da.
6. $2500, 5%, 2 yr. 10 mo.; 2 yr. 10 mo. 7 da.
7. $2275, 51%, 3 yr. 11 mo. ; 3 yr. 11 mo. 2 da.
8. $3525, 44%, 1 yr. 11 mo.; 1 yr. 11 mo. 3 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.
24. $420, $50.40, 3 yr.
25. $121.25, $9.70, 2 yr. 32.
26. $320.50, $57.69, 3 yr. 33.
27. $275.25, $55.05, 5 yr. 34.
28. $3500, $87.50, 10 mo. 35.
29. $220, $9.35, 1 yr. 5 mo. 36.

30. $250.50, $30.06, 2 yr.
31. $480, $36, 1 yr. 6 mo.
$240, $24, 2 yr. 6 mo.
$325, $45.50, 3 yr. 6 mo.
$240, $10.50, 1 yr. 3 mo.
$160, $19.80, 2 yr. 3 mo.
$480, $26.60, 1 yr. 7 mo.
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%.

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% ?

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?