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52. What is the interest of $ 66.42 for 4 mo. 12 d. at 5% ? 53. What is the interest of $ 8000 for 3 mo. 3 d. at 7% ? 54. What is the interest of $ 130.50 for 45 days at 8% ? 55. What is the interest of $7500 for 2 mo. 21 d. at 6% ? 56. What is the interest of $225 from Feb. 3, 1880, to May 9, 1881, at 6% ?

57. What is the amount of $163.20 from Dec. 12, 1881, to March 27, 1882, at 10% ?

58. What is the amount of $900.65 from Sept. 16, 1881, to Nov. 8, 1882 ?

59. What is the interest of $4000 from May 12, 1879, to June 24, 1880, at 41% ?

60. What is the amount of $653.63 from Feb. 11, 1880, to Nov. 9, 1882, at 7 %?

61. A bill of goods amounting to $ 4498.25 was paid at the end of 60 days, with interest at 5%. What was the amount?

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265. In the computation of Exact Interest, as by the United States on its securities, for parts of a year, the actual number of days in each calendar month included in the time is counted, and each day's interest made a 365th of a year's interest. That is, to compute exact interest,

Multiply the interest of the principal for one year at the given rate by the exact number of days in the time, and divide by 365.

92. What is the interest on a United States Treasury certificate for $500 from April 1, 1881, to July 15, 1881, at 4%?

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for 105 days must be 18 of $20, which is $ 5.75, or, to the nearest

cent, $5.75.

93. What is the exact interest on a note for $3000 from Feb. 15, 1880, to June 5, 1880, at 5% ?

94. What is the exact interest on a $1000 bond from Nov. 1, 1881, to March 15, 1882, at 41%?

95. A note for $ 225.50 was given March 16, 1881, bearing exact interest from date at 6%. What sum should discharge the note Jan. 13, 1882 ?

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PROBLEMS IN INTEREST.

Principal, Interest, and Time given, to find the Rate.

96. At what rate must $450 be on interest to yield $ 81 in 3 years?

$450 x .01 X 3 = $ 13.50

$81 $13.50 = 6

Solution. As the interest of $450 for 3 years at 1% is $13.50, $81 is the interest at as many

per cent as there are times $13.50 in $81, or 6.

97. The interest of $250 for 1 year 3 months is $ 28.12. What is the rate per cent?

266. Rule to find the Rate of Interest.

Divide the given interest by the interest of the principal for the given time at 1 per cent, and the quotient will be the

rate.

Representing the principal by p, the interest by i, the time by t, and the rate by r, as in Art. 260, we have

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98. If $1400 yields $126 in 1 year 6 months, what is the rate?

99. At what rate must $1000 be on interest to yield $282 in 4 years 8 months 12 days?

100. At what rate must $416 be on interest to yield $ 88.64 in 3 years 16 days?

101. At what rate must $1600 be on interest to yield $46.20 in 66 days?

102. At what rate will $241.20 amount to $250.58 in 6 months 20 days?

103. At what rate will $ 480 yield $ 52.20 in 2 y. 5 mo. ? 104. What is the rate of interest if $640 gains $ 10.56 from August 12 to October 18 ?

105. In 1 y. 3 mo. 15 d. $ 960 amounts to $ 1084. What is the rate?

106. At what rate will $444 gain $156.695 in 6 y. 5 mo. ? 107. At what rate must I invest a trust fund of $25000 to secure a semi-annual income of $500 ?

Principal, Interest, and Rate given, to find the Time.

108. In what time will $ 450 yield $ 94.50 at 6%?

$450 × .06 = $27 $94.50 $273

31 y. 3 y. 6 mo.

=

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Solution. As $27 is the interest of $450 for 1 year at 6%, $94.50 is the interest for as many years as there are times $ 27 in $94.50, or, 31 years, equal to 3 years 6 months.

109. The interest of $ 140 is $ 49 at 7%. How long has it been on interest?

267. Rule to find the Time.

Divide the given interest by the interest of the principal for one year, and the quotient will be the time.

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110. How long must $98 be on interest to gain $ 23.48 at 8%?

111. How long must $75 be on interest to gain $ 6.25 at 6%?

112. How long must $3600 be on interest to gain $ 46.20 at 7% ?

113. How many days must $875 bear interest to gain $ 7 at 6%?

114. How long must $ 9080 be on interest to gain $794.50 at 31%?

115. In what time will $750, on interest at 6%, gain $750, or double itself?

116. I deposited $ 540 in a bank paying 4% simple interest until it amounted to $700. How long did it remain ?

117. Principal, $ 892; rate, 10 %; interest, $187. Required the time.

118. In what time will $ 12000 yield $ 2500 at 41%?

119. In what time will a trust fund of $4500 amount to $6000 at 31% ?

Interest, or Amount, Time, and Rate given, to find the Principal. 120. What principal at 6% will gain $94.50 in 3 years 6 months?

$1.06 x 3 = $ 0.21
94.50$ 0.21 = 450

Solution.

As the interest of $1 at 6% for 3 years 6 months is $0.21, $94.50 must be the in

terest of as many dollars as $0.21 is contained times in $94.50, or $450.

121. What sum of money at 7% interest will amount to $320 in 4 years ?

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122. What principal on interest at 6% will gain $ 6.25 in 1 year 4 months 20 days?

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