per cent. ? 50. What is the interest of $21, for 2 months, at 7 per cent. per annum ? 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 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. 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 ? When interest is to be computed for any number of days, First find the interest for 1 month; then take zo of a month's interest for 1 day; šo or } for 2 days, To for 3 days; 30 or 15 for 4 days; or for 5 days; 3% or } for 6 days; and so on. 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 I of a year or 1 month; and then for 7 of a month. At 3 30 or 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 Az üterest of $133.24, for 11 months, at 6 per eut. 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 of one figure from the right of the quotient. The rest of the quotient igures 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 ? 75. 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 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 the debt becomes due. Therefore, when the rate of interest is 5 per cent., that is, Too of the principal, then the discount is 165 of the principal; when the rate of interest is 6 per cent., that is, 167 of the principal, then the discount is lóg of the principal; and so on. RULE FOR COMPUTING DISCOUNT. Multiply the principal by the rate of interest; then divide the product by a number, which is to be found by adding 100 and the rate together. The quotient will be the discount. 76. What is the discount on $48.51, due in 3 years; the rate of interest being 5 per cent. per annum, and consequently the discount being 165 per annum? 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 vear, 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. What is the difference between the discount on $ 100 for 1 year, and the interest of $ 100 for 1 year; the rate of interest 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 ? SECTION 24. 1. Suppose of a piece of broad-cloth to be worth $118.87; what is of the piece worth? What is the whole piece worth? 2. 11887 is of what number? 3. If the interest of $100 be $ 3.50 for 7 of a year, what is the interest of $100 for of a year? Then what would be the interest for 1 year? 4. If ii of an acre of land produce 133 bushels of potatoes, how many bushels does 24 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 to of the tiine, how much could he earn by working constantly? 7. $ 14 is 8 per cent. or Too 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 inay be changed, and the fraction may still express the same quantity. For instance, the terms 2 and 3, in the fraction , may be changed to 4 and 6, and the fraction will become %, which is still equal to ģ. 1. is equal to how many twenty-fourths ? Direction. S-eighths are equal to 24-twenty-fourths; therefore, find á of 24, and this number will be the re quired numerator of 74 2. is equal to how many fourteenths ? SECTION 26. When a number can be found, that will divide both terms of a fraction, without a remainder, the two quolients arising from the division, will express the fraction reduced to lower terms. For example, both terms of the fraction is can be divided by 3, and the reduced fraction will be . Again, both terms of can be divided by 2, and the reduced fraction will be ž. Thus any fraction may be reduced to its lowest terms, by repeatedly dividing the terms, until no number will divide them both without a remainder. 1. Reduce each of the following fractions to its low est terms. š. g. i. is. 1. 1. 2. . 2. Reduce each of the following fractions to its lowest terms. o. o. 100. 500 100. Too Only once dividing the terms of a fraction, will reduce it to its lowest terms, if we use the greatest common divisor, that is, the greatest number that will divide both terms without a remainder. TO FIND THE GREATEST COMMON DIVISOR of two numbers,- Divide the greater number by the smaller, then divide the divisor by the remainder; and thus continue dividing the last divisor by the last remainder, till nothing remains. The divisor used last of all, will be the greatest common divisor. 3. Find the greatest common divisor of 91 and 117. 91)117(1 This operation is perform91 ed according to the direction 26)91(3 above, and 13 is found to be 78 the greatest common divisor; or the greatest number by 13)26(2 which 91 and 117 can be di26 vided without a remainder. 4. Find the greatest common divisor of 15 and 235. 5. Reduce this to its lowest terms, by using the greatest common divisor of the two terms. 6. Reduce to their lowest terms, 14, 15, and m. SECTION 27. COMPOUND FRACTIONS. A compound fraction arises from dividing a unit into ą certain number of equal parts, and then dividing one of these parts into other equal parts 156 |