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SECTION XIV.

INTEREST.

391. Illustrative Examples. (1) A merchant borrowed $3000 for a year, and used it in his business. At the end of the year he paid back the money and paid for its use a sum equal to 6% of the money borrowed. How much did he pay for its use? Ans. $180.

392. The price paid for the use of money is interest. The money for the use of which interest is paid is the principal.

393. The rate of interest is the fraction which a year's interest is of the principal. It is usually expressed as a rate per cent per annum.

In the example, what is the principal? the interest? the rate of interest ?

394. The rate of interest fixed by law is the legal rate. Interest at a higher rate than the legal rate is usury.

(2) If $180 is paid for the use of $3000 for one year, how much ought to be paid for the use of the same sum of money for two years? three years? half a year?

(3) If 6% of $3000 is paid for the use of $3000 one year, what per cent of that sum ought to be paid for its use two years? three years? half a year?

395. Interest is reckoned as a percentage, the principal being the base and the ratio being the rate per annum increased or diminished in proportion to the time.

Thus, in example (3) above, the rate per annum is 6%; the ratio for two years is 12%; for three years, 18%; for half a year,

3%

INTEREST FOR YEARS.

Oral Exercises.

396. a. At 5% a year, what is the ratio for 2 years? for 3 years? 4 years? a year? 11⁄2 years? 21 years? b. At 7% per annum, what is the ratio for 2 years? for 3 years? half a year ?

c. At 8% per annum, what is the ratio for 3 years?

d. At 5% per annum, what is the interest on $3000 for one year? for two years

?

e. At 7% per annum, what is the interest on $400 for one year? for 2 years ? 3 years ?

f. At 6% per annum, what is the interest of $4000 for one year? for 3 years? half a year? one third of a year? g. What is the interest on $700 for 2 years at 6% per

annum?

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397. Illustrative Example. What is the interest of $3250 for 3 years at 6% ?

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The principal, $3250, is multiplied by 0.18, the ratio for 3 years, and the product is the interest for that time.

Ans. $585.00.

The rate of interest being 6%, what is the interest

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INTEREST FOR MONTHS (6%).

398. Illustrative Examples. (1) At 6% per annum, what is the interest of $237.63 for 2 months? (2) Of $523.18 for 8 months?

(1)

WRITTEN WORK.

Principal, $237.63
Interest, $2.3763

(2)

WRITTEN WORK.

$523.18

4

Principal,

Interest,

$20.9272

(1) The ratio for 2 months, or of a year, is of 6%, or 1%; and 1% of the principal is found by moving the decimal point two places to the left. Ans. $2.38.

(2) The interest for 8 months is 4 times the interest for 2 months. Multiplying the principal by 4, and then moving the decimal point two places to the left, gives the same result as finding two months' interest (as in Ex. 1), and multiplying that by 4. Ans. $20.93.

399. From these examples we derive the following

Rule.

To find the interest, at 6%, for any number of months: Multiply the principal by half the number of months, and move the decimal point two places to the left.

Examples for Written Work.

400. At 6% a year, or 1% 9. Of $320 for 2 mo. 10. Of $430 for 4 mo. 11. Of $325.70 for 2 mo. 12. Of $526 for 10 mo. 13. Of $365 for 14 mo. 14. Of $962.75 for 16 mo. 15. Of $494.09 for 18 mo. 16. Of $500 for 20 mo. 17. Of $3000 for 16 mo. 18. Of $6000 for 6 mo.

for 2 mo., find the interest
19. Of $8000 for 8 mo.
20. Of $927 for 1 mo.
21. Of $625 for 3 mo.
22. Of $350 for 7 mo.
23. Of $763.20 for 5 mo.
24. Of $2500 for 9 mo.
25. Of $9000 for 15 mo.
26. Of $5000 for 5 mo.
27. Of $8000 for 17 mo.
28. Of $800 for 25 mo.

INTEREST FOR DAYS (6%).

401. Illustrative Examples. (1) At 6% a year, what is the interest of $2400 for 6 days? (2) Of $630 for 16 days?

(1)

WRITTEN WORK.

Principal, $2400
Interest, $2.400

(2)

WRITTEN WORK.

Principal,

Interest,

$630
16
3780

63
6)$10080

$1.680

(1) The ratio for 60 days (2 months) being 0.01, the ratio for 6 days is of 0.01, which is 0.001. One thousandth of the principal is found by moving the decimal point three places to the left. Ans. $2.40.

(2) The interest for 16 days might be found by first finding the interest for 6 days (moving the decimal point), then dividing that interest by 6, and lastly multiplying the quotient by 16. But it usually takes fewer figures to reverse the order of these steps, and the result is the same. So the principal is multiplied by 16, the product divided by 6, and the decimal point moved three places to the left. Ans. $1.68.

402. From these examples we derive the following

Rule.

To find the interest, at 6%, for any number of days: Multiply the principal by the number of days, divide by 6, and move the decimal point three places to the left.

NOTE. If the number of days happens to be divisible by 6, a step is saved by multiplying the principal by one sixth of the number of days and then moving the point three places to the left.

Examples for Written Work.

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403. At 6% a year, or 0.001 for 6 da., find the interest

29. Of $920 for 6 days. 30. Of $426 for 12 days. 31. Of $2365 for 18 days. 32. Of $3840 for 15 days. 33. Of $927 for 63 days. 34. Of $231 for 33 days.

35. Of $328 for 93 days.

36. Of $972 for 123 days.
37. Of $525 for 90 days.
38. Of $632 for 42 days.
39. Of $925.50 for 1 day.
40. Of $123.75 for 2 days.

At 6% per annum find the interest

41. Of $9280 for 3 days.

42. Of $2800 for 4 days.

43. Of $2250 for 5 days. 44. Of $92.60 for 53 days.

45. Of $32,500 for 17 days. 46. Of $426.76 for 91 days. 47. Of $625.72 for 88 days. 48. Of $237.58 for 11 days.

INTEREST FOR YEARS, MONTHS, AND DAYS (6%).

Oral Exercises.

404. a. The rate of interest being 6%, what is the ratio. for 2 years? for 3 years? for 4 years? for 5 years? for 6 years? for 8 years?

b. If the interest for 2 months is 1%, or 0.01, of the principal, what part of the principal is the interest for 4 months? for 6 months? for 8 months? for 5 months? for 7 months? for any number of months?

The interest for any number of months is one half as many hundredths of the principal as there are months.

c. If the interest for 6 days is 0.001 of the principal, what part of the principal is the interest for 12 days? 18 days? 24 days? 9 days? 15 days? 16 days? 17 days? 19 days? any number of days?

The interest for any number of days is one sixth as many thousandths of the principal as there are days.

405. Illustrative Examples. (1) What is the ratio, at 6% per annum, for 3 years, 8 months, 24 days?

(2) For 2 years, 7 months, 15 days?

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