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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
P X Ti

interest
principal time
interest
I
principal × rate
PX R
Thus, if the interest on $200 for 3 yr. at 6% is $36, we have
I = 3 × 6% of $200

time =

" or T =

$36,

$36 3 × 6%

$200,

$36

3 x $200

$36
6% of $200

principal

=

rate =

P:

R

T

=

=

p: =

[ocr errors]

=

[ocr errors]

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
6% of $200

=

i

pxt

I

RX T

3.

[ocr errors]

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

[ocr errors]

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

EXERCISE 150

1. Given r = 6%, i =
2. Given i = $64, p
3. Given i = $16, p = $200, and r = 4%, find t.

=

r

$90, and t = 3, find p.
$800, and t = 2, find r.

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
23. $600 5% 4 yr.
24. $500 4% x $80

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
8. x 5% 3 yr.

$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.
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, 51%, 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, 41%, 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.
26. $320.50, $57.69, 3 yr.
27. $275.25, $55.05, 5 yr. 34.
28. $3500, $87.50, 10 mo. 35.

30. $250.50, $30.06, 2 yr.
31. $480, $36, 1 yr. 6 mo.
32. $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.

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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