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50. What is the interest of $21, for 2 months, at 7 per cent. per annunı?

51. What is the interest of $4291, for 3 months, at 5 per cent. per annum?

52. At 4 per cent. per annum, what is the interest of $122.75 for 4 months? for 5 months? for 6 months? for 7 months? for 8 months? for 9 months? for 10 months? What is the amount for 11 months?

53. What is the interest of $14.50, for 1 year and 1 month, at 6 per cent.?

54. What is the interest of $19.25, for 3 years and 2 months, at 8 per cent.?

55. What is the amount of $458, for 2 years and 3 months, at 7 per cent.?

56. What is the amount of $8.75 for 5 years and 4 months, at 4 per cent.?

57. What is the amount of $91.50, for 2 years and 7 months, at 8 per cent.?

58. What is the interest of $81, from February 7, 1832, to August 7, 1835, at 6 per cent.?

59. Suppose a promissory note of $145, to be dated, January 15, 1831; what will be the amount of that note, October 15, 1834; the rate being 6 per cent.?

60. A owed B $96, on interest at 6 per cent. At the end of 2 years, A paid the interest then due, and $25 of the principal: at the end of 3 years and 11 months, he paid the whole debt. What was each payment?

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When interest is to be computed for any number of days,- First find the interest for 1 month; then take of a month's interest for 1 day; or 15 for 2 days, 35 or 16 for 3 days; or 25 for 4 days; or for 5 days; or for 6 days; and so on.

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6

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In the following operations, in this section, all fractions of a cent may be disregarded: this being the common practice in business.

61. What is the interest of $231, for 7 days, at 6 per cent. per annum ?

Direction. First find the interest for 1 year; then for 1⁄2 of a year or 1 month; and then for of a month.

62. What is the interest of $75, for 10 days, at 6 per cent. per annum ?

63. What is the interest of $254 for 21 days, at 6 per cent. per annum ?

64. What is the interest of $110, for 5 months, and 8 days, at 6 per cent. per annum ?

65. What is the interest of $34 for 1 year, 3 months, and 25 days, at 6 per cent. per annum ?

66. What is the interest of $91.18, for 3 years, 2 months, and 13 days, at 6 per cent. per annum?

Several other methods are practised by merchants, in computing interest; among which, are the following. When the rate is 5 per cent.-Divide the principal by 20, and the quotient is the interest for 1 year.

67. What is the interest of $4207, for 2 years, at 5 per cent. per annum ?

68. What is the interest of $951.17, for 4 years, at 5 per cent. per annum?

When the rate is 6 per cent.—Multiply the principal by half the number of months in the time, divide the product by 100, and the quotient is the interest.

69. What is the interest of $119, for 16 months, at 6 per cent. per annum ?

70. What is the interest of $96.48, for 10 months, at 6 per cent. per annum ?

71. What is the amount of $27.56, on interest 6 months, at 6 per cent. per annum?

72. What is the interest of $133.24, for 11 months, at 6 per cent. per annum?

To find the interest for DAYS, the rate being 6 per cent.-Multiply the principal in dollars by the number of days, divide the product by 6, and cut off one figure from the right of the quotient. The rest of the quotient figures express NEARLY the interest, in cents.

73. What is the interest of $249, for 75 days, at 6 per cent. per annum ?

74. What is the interest of $5824, for 21 days, at 6 per cent. per annum ?

5. What difference will it make to the man who pays interest on $100 for 1 year, whether it be computed by days, or according to true rule in page 165?

DISCOUNT.

Discount is an abatement of a certain part of a debt, when the debt is paid before it becomes due. For instance; suppose that A is bound to pay B $106, in one year from the present time; but B, wanting the money now, agrees to receive $100 for the debt, on condition of present payment: in this case, $100 is the present worth of the debt, and $6 is the discount.

The present worth of any debt due at a future period, is that sum of money, which, if put at interest, would amount to the debt by the time it becomes due. Therefore, when the interest is 5 per cent., that is, 15 of the principal, then the discount is 15 of the principal

RULE FOR COMPUTING DISCOUNT. Multiply the principal by the number of cents found to be the interest of one dollar for the time, and divide the product by the number which results from adding 100 to the multiplier. The quotient will be the discount.

For example, at the rate of 6 per cent., the discount on $124.25, due in 1 year and 10 months, is found thus

124.25

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111)1366.75(13.21

76. What is the discount on $48.51, due in 3 years; the rate of interest being 5 per cent. ?

77. What is the discount on $247, due in 1 year, the rate of interest being 6 per cent.?

78. What is the present worth of $150, due in 1 year. the rate of interest being 6 per cent.?

Find the discount, and subtract it from the debt.

79. What is the present worth of $1640, due in 2 years, the rate of interest being 5 per cent.?

80. Find the difference between the discount and the interest of $100 for 1 year, the rate being 6 per cent.

81. Find the present worth of $75, due in 2 years and 9 months, [23 years], interest being 6 per cent.

1. Suppose of $118.87; what is whole piece worth?

SECTION 24.

a piece of broad-cloth to be worth
of the piece worth? What is the

2. 11887 is of what number?

Then

3. If the interest of $100 be $3.50 for 72 of a year, what is the interest of $100 for 12 of a year ? what would be the interest for 1 year?

4. If of an acre of land produce 133 bushels of potatoes, how many bushels does 4 of an acre produce? How many bushels would 1 acre produce?

5. 9071 is % of what number?

6. If a man earn $190 a year by working of the time, how much could he earn by working constantly? 7. $14 is 8 per cent. or 18 of what sum of money?

SECTION 25.

CHANGE OF THE TERMS OF FRACTIONS.

The numerator and denominator of a fraction, are called the two terms of a fraction. These terms may be changed, and the fraction may still express the same quantity. For instance, the terms 2 and 3, in the frac tion, may be changed to 4 and 6, and the fraction will become, which is still equal to 3.

1. is equal to how many twenty-fourths ?

Direction. 8-eighths are equal to 24-twenty-fourths; therefore, find of 24, and this number will be the required numerator of 24.

2. is equal to how many fourteenths?

3. Change to eighteenths and add to it. 4. is equal to how many forty-fifths?

5. Chauge to fortieths, and then take

SECTION 26.

from it.

REDUCTION OF FRACTIONS TO LOWER TERMS. When a number can be found, that will divide both terms of a fraction, without a remainder, the two quotients arising from the division, will express the fractio reduced to lower terms. For example, both term

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8. Suppose a hogshead of sugar to be worth £20 4s. 3d.; what is the value of of the sugar?

9. What is of 4720 ?

In the several foregoing examples in this section, the learner has probably divided the given number by the denominator of the fraction, and multiplied the quotient by the numerator. It is, however, sometimes more convenient, to multiply the given number by the numerator, and divide the product by the denominator.

10. What is of 32? (Here are the two methods.)

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We may see why these two methods of operation produce the same result, in the following illustration. Here is of 32 units arranged in one line, and of 3 times 32 units arranged in three lines. The number of units [] in the two arrangements is the same.

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11. Find

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of 60156, by each of the above methods.

12. Find of 10849, by the second method. 13. A laborer worked of a year, at 92 cents per day. What did his wages amount to?

14. In of a pipe of wine, how many gallons?

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15. What is 10 of $1491?

After multiplying by 6 and dividing by 100, reduce the remainder to cents, and divide the cents.

16. A borrowed of B, $758, promising to pay it in one year; and, in addition thereto, he agreed to pay a sum, equal to 10 of the sum borrowed, for the use of the money. How much must B receive? 17. What is 10 of $28?

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