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36. If a cloak can be made of 4 yards wide, how many yards would it a yard wide?

of

yards of cloth that is 13
take of cloth that is
Ans. 6yd. 1qr. 3 na.

37. If a box 4 feet long, 2 feet wide, 1 feet high, contains 300 pounds of sugar, how much will a box that is 8 feet long, 4 feet wide, and 3 feet high, contain ? Ans. 2400lb.

38. How much in length, that is 12 rods in breadth, will make an acre? Ans. 12rd.

39. Sound, uninterrupted, moves 1142 feet in a second; how long, after a cannon's being discharged at Boston, is the time before it is heard at Bradford, the nearest distance being 2521 miles ? Ans. 2 minutes. sold of it for Ans. $93.40.

40. Bought of a ton of potash, and $46.70; what was the value of a ton?

41. If

of a lot of land be worth $97, what would the whole lot be worth? Ans. $266.75.

42. If 19 pounds of salmon be worth 50 pounds of beef, how much salmon would buy 77 pounds of beef?

43. What part of 17 is 44?

44. What part of 11s. 3d. is 15s. ?

Ans. 2913lb.
Ans. 183.
Ans..

45. What part of 74 yards is 33 ells English? Ans. 18.

SECTION XXXVII.

SIMPLE INTEREST.

INTEREST is the compensation which the borrower of money makes to the lender.

PRINCIPAL is the sum lent.

AMOUNT is the interest added to the principal.

PER CENT., a contraction of per centum, is the rate established by law, or that which is agreed on by the parties, and is so much for a hundred dollars for one year.

CASE I.

GENERAL RULE. - Let the per cent. be considered as a decimal of the place of hundreds, and multiply the principal by it, and the product is the interest for one year. But, if it be required to find the interest for more than one year, multiply the product by the number of years.

The

NOTE. The decimal for 6 per cent. is .06; for 7 per cent., .07; for 8 per cent., .08; for 94 per cent., .0925; for 2 per cent., .025, &c. decimal must be pointed off as in Multiplication of Decimal Fractions.

This rule is obvious from the fact that the rate per cent. is such a part of every hundred dollars. Thus 6 per cent, is T of the principal.

NOTE. When no particular per cent. is named, 6 per cent. is to be understood, as it is the legal interest in the New England States. See page 148.

1. What is the interest of $ 144 for 1 year? Ans. $8.64.

OPERATION.

$144

.06

$8.64 Ans.

There being two places of decimals in the multiplier, we point off two in the product.

2. What is the interest of $78.78 for 3 years ?

OPERATION.

$78.78

.06

There being two places of decimals in the 4.72,68 multiplicand, and two in the multiplier, we point 3 off four places in the product.

$14.18,04 Ans.

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NOTE. It is a custom with merchants to reject mills in their computations, but when the decimal of a cent exceeds 5 they add 1 to the number of cents. Thus, they would reckon $81.93,8 to be in value $81.94.

3. What is the interest of $675 for 1 year? Ans. $40.50. 4. What is the interest of $ 1728 for 1 year?

Ans. $103.68.

5. What is the interest of $19.64 for 2 years?

Ans. $2.35,6.

6. What is the interest of $896.28 for 3 years?

Ans. $161.33.

7. What is the interest of $349.25 for 10 years?

Ans. $209.55.

8. What is the interest of $3967.87 for 2 years?

9. What is the interest of $123.45 for 6

10. What is the interest of $89.25 for 50

Ans. $476.14,4.
years ?
Ans. $44.44,2.

years
s?
Ans. $267.75.

11. What is the interest of $17.25 for 7 years?

Ans. $7.24,5.

12. What is the interest of $29.19 for 9 years?

Ans. $15.76,2.

13. What is the interest of $617.56 for 25 years?

Ans. $926.34.

14. What is the amount of $31.75 for 100 years?

Ans. $222.25.

15. What is the amount of $76.47 for 7 years.?

Ans. $108.58,7.

16. What is the amount of $716.57 for 4 years?

Ans. $888.54,6.

17: What is the amount of $178.56,5 for 30 years?

18. What is the interest of $97.06 for 9

19. What is the interest of $0.75 for 75

Ans. $499.98,2.

years
s?
Ans. $52.41,2.

years ?
Ans. $3.37,5.

20. What is the interest of $750 for 12 years

CASE II.

s?

Ans. $540.

To find the interest for months at 6 per cent.

RULE. Multiply the principal by half the number of months, expressed decimally as a per cent.; that is, for 12 months multiply by .06 ; for 8 months multiply by .04; for 7 months, .035; for 1 month, .005; and point for decimals as in the last rule.

NOTE 1. It is obvious, that, if the rate per cent. were 12, it would be 1 per cent. a month. If, therefore, it be 6 per cent. it will be a half per cent. a month, that is, half the months will be the per cent.

NOTE 2. If any other per cent. is wanted, proceed as above, and then multiply by the given rate per cent. and divide by 6, and the quotient is the interest.

1. What is the interest of $368 for 8 months?

$368

.04 half the months. $14.72 Answer.

2. What is the interest of $637 for 10 months?

Ans. $31.85.

3. What is the interest of $1671.32 for 14 months?

Ans. $116.99.

4. What is the interest of $891.24 for 9 months?

Ans. $40.10.

5. What is the interest of $819.75 for 11 months?

Ans. $45.08,6.

6. What is the interest of $3671.25 for 13 months?

Ans. $238.63.

7. What is the interest of $61.18 for 15 months?

Ans. $4.58.

8. What is the interest of $3181.29 for 18 months?

Ans. $286.31.

9. What is the interest of $11.39 for 19 months? .

Ans. $1.08.

10. What is the interest of $9.98 for 23 months?

Ans. $1.14.

11. What is the interest of $87.19 for 27 months?

Ans. $11.77.

12. What is the interest of $32.18 for 36 months?

Ans. $5.79.

13. What is the interest of $167.18 for 50 months?

Ans. $41.79.

14. What is the interest of $386.19 for 100 months? Ans. $193.09.

CASE III.

To find the interest of any sum for months and days, at 6 per cent.

RULE.* - - Find the interest for the number of months, as under Case II. Then to find it for the number of days,multiply the principal by one sixth the number of days, and, if the principal be dollars, cut off three figures from the right hand, and those at the left will be the interest in dollars, and those at the right will be cents and mills. But if the principal be dollars and cents, five figures must be cut off from the right hand, and those at the left will be the interest, &c., as before.

* The reason for this rule, so far as it relates to the interest for any number of months, was explained above. But the reason for the operation in the case of days is not so obvious. It will be seen, however, that it is nothing but an abridgment of the general rule for calculating interest, as given on page 164, which will appear from what follows.

To find the interest for any number of years, we multiply the principal by the annual per cent., and the product thus obtained by the number of years, and cut off two figures, &c. In like manner, it is evident that to find the interest for any number of days, we have only to multiply by the daily per cent., and the product thus obtained by the number of days, and cut off as in the case of years. But 6 per cent. per annum is to per cent per diem, allowing 360 days to a year. Now, to multiply the principal by of the days, and cut off one figure from the product at the right, is the same as to multiply by (the daily per cent.), and the product thus obtained by the whole number of days. Where the principal is dollars only, the rule directs to cut off three figures. Two of them are cut off according to the general rule, on page 164, and the other, because in the operation we have multiplied by the number of days, instead of of them, which would have been the proper multiplier.

The above may be illustrated concisely by the following operation. Let it be required to find the interest of 75 dollars for 180 days. By the general rule we have 75 × ÷ 100 × 180 = $2.25. By the rule under Case III. we have 75 × of 180 = $2.25.

NOTE 1. If one half the number of months be expressed by a single figure, we have only to annex to this figure the number of days, and multiply the principal by the number thus found, cutting off as above, and we obtain, by a single operation, the interest for the months and days. NOTE 2. -If any other per cent. than 6 is given, we may proceed as above, and then multiply by the given rate and divide by 6, and the result will be the interest sought.

1. What is the interest of $68.25 for 8 months and 24 days? Ans. $3.00,3.

OPERATION.

$68.25

.044 The first 4 in the multiplier is half of the 8 27300 months; the second 4 is one sixth of the 24 27300 $3.00,300

days.

2. What is the interest of $637.28 for 17 months and 19 days, at 8 per cent. ? Ans. $74.91,5. 3. What is the interest of $396.15 for 13 months and 9 Ans. $26.34,3. 4. What is the interest of $ 16.75 for 7 months and 17 days, at 7 per cent.? Ans. $0.73,9.

days?

5. What is the interest of $976.18 for 29 months and 23 days, at 9 per cent.? Ans. $217.93,2. months and 7 days?

6. What is the interest of $ 36.18 for 3

7. What is the interest of $51.17 for 9

at 4 per cent.?

Ans. $0.58,4. months and 29 days, Ans. $1.69,9.

8. What is the interest of $365.19 for 33 months and 4 days, at 2 per cent. ?

Ans. $20.16,6.

9. What is the interest of 125.75 for 5 months and 4 days? Ans. $3.22,7. 10. What is the interest of $35.49 for 1 month and 2 days, at 7 per cent. ? Ans. $0.23,6. 11. What is the interest of $112.50 for 3 months and 1 day, at 9 per cent. ? Ans. $2.70,1. 12. What is the interest of $97.15 for 35 months and 27 days? Ans. $17.43,8. 13. What is the interest of $47.15 for 1 month and 19 days, at 13 per cent.? Ans. $0.86,6.

14. What is the interest of $678.75 for 87 months and 20 Ans. $297.51,8.

days?

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15. What is the interest of $86 for 99 months and 29 days, at 25 per cent. ? Ans. $179.10,6.

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