The amount, time, and rate per cent., given to find the principal.

RULE VI.

1. Find the amount of D100 for the time at the given rate per cent.

2. Then as the amount of D100 for the time required, at the given rate per cent., is to the amount given, so is D100 to the principal required.

66. What principal at interest 6 years at 6 per cent. will amount to D500? thus D6×6 years=36D interest for 6 years, +100=136D. amount of D100; then D136: D500 :: D100 : Ans. D367.65.

67. What sum being put to interest 6 years at 6 per cent. will amount to D44.88 ? Ans. D33. 68. What sum being put to interest 8 years at 6 per cent. will amount to D74?

Ans. D50. 69. What sum being put to interest 10 years at 6 per cent. will amount to D160?

Ans. D100. 70. What sum being put to interest 11 years at 6 per cent. will amount to D830? Ans. D500.

The principal, amount, and time, given to find the rate per cent.

RULE VII.

Find the interest for the whole given time, by subtracting the principal from the amount; then as the principal is to D100, so is the interest of the principal for the given time to the interest of D100, for the same time; divide the interest last found by the time, and the quotient will be the rate per cent.

71. At what rate per ct. will D500 amount to D605 in 3 years?

72. At what rate per cent. will D750 amount to D930 in 4 years? Ans. 6 per cent, 73. At what rate per cent. will D200 amount to D255 in 5 years? Ans. 5.5 per cent.

To find the time when the principal amount and rate per cent. are

given.

RULE VIII.

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

74. In what time will D400 amount to D568, at 6 per cent.?

75. In what time will D600 amount to D750 at 5 per cent.?

Ans. 5 years.

A short method to find the interest for one or more months, at any

rate per cent.

RULE IX.

Multiply the principal by the rate per cent., which will give the interest for 1 year; divide this by 12, and the quotient will be the interest for 1 month; multiply this last interest by the ▷ number of months required, &c.

To make a divisor for any rate per cent.

RULE X.

Multiply 365 days by D100, and divide by the rate per cent Thus, 365×100÷6=6083 divisor at 6 per cent.; 365×100 ÷5=7300 divisor; 365×100÷7=5214 divisor at 7 per cent. ; and so for any other rate per cent.

76. Required the interest of D400 for 26 days at 5, 6, and 7 per cent.

:

Thus, 400×26=10400÷6083=D1.70.93 at 6 per cent. Ans. 10400 7300 D1.42.44 at 5 per cent. Ans. 10400 5214 D1.99.43 at 7 per cent. Ans. Or thus, 100 rate 400 365: 6 :: 26 D1.70.93. Or 400×26×7÷365-D1.99.43 at 7 per cent.; Again, as 365 da. : 5 per ct. :: 7300 : 100 per ct., and as 12 mo. 5 per ct. :: 240 mo. : 100 per ct.

Hence it is evident, that if the rate be 5, any principal will give 100 per cent.; that is, it will double in 7300 days, or 240 months; and at 6 per cent. any sum will double in 6083 days, or 200 months; and at 7 per ct. in 52142 days, or 1713 months; from which the following rule has its origin, as exemplified above:

RULE XI.

Multiply the principal by the days, and for 6 per cent. divide by 6083; for 5 per cent. by 7300, &c., and the quotient is the answer. These being the number of days, in which any sum will double at those respective rates. For months, multiply the principal by the months, and divide by 200 for 6 per cent., or 240 for 5 per cent., &c., and the quotient is the answer.

77. Required the interest of D150 at 5 and 6 per cent. for 30 nonths.

Ans. D150 x 30÷240D18.75 at 5 per cent.; D150×30÷ 200 D22.50 at 6 per cent.

Hence, when interest is to be calculated on cash accounts, or accounts current, where partial payments are made, or partial debts contracted, multiply the several balances into the days they are at interest, which should be done at every transaction, and the sum of those products divided by 6083 and 7300 will give the interest at 6 and 5 per cent., and for any other rate find a divisor as above directed (see qucst. 65).

APPLICATION.

78. What is the interest of D22 for 25 days, at 6 per cent.? (Rule 1.)

6

79. What is the interest of D58 for 29 days, at 6

80. What is the interest of D400 for 26 days, at

81 What is the interest of D90 for 28 days, at 6

Ans. c.9. per cent.? Ans. c 27.6. 6 per cent.? Ans. D1.71.

per cent.?

82. What is the interest of D50 for 9 months, at

Ans. c.41.4. 6 per cent.? Ans. D2.25.

83. What is the interest of D57 for 14 months, at 6 per cent. ? Ans. D3.99.

84. What is the interest of D700 for 11 months, at 6 per cent.? Ans. D38.50. 85. What is the interest of D900 for 1 year and 1 month, at per cent.? Ans. D58.50.

86. What is the interest of D200 for 1 year and 3 months, at 6 per cent.?

6

Ans. D15.00.

87. What is the interest of D500 for 1 year and 4 months, at per cent. ? Ans. D40.00.

88. What is the interest of D31 for 10 years and 6 months, at 6 per cent. ? Ans. D19.53. 89. What is the interest of D500 for 14 years, at 6 per cent.?

Ans. D420.

90. What is the bank interest of D89 for 89 days, at 6 per cent. ? Ans. D1.32. 91. What is the interest of D764 for 420 days, at 5.5 per cent.? (Rule 1.)

92. What is the interest of D642.25 for 900 days, at 7.5 per ct.? In the solution of the following questions, the year will consist of 365 days, and the months of 30 days.

(Rule 1.)

93. What is the interest of D1062.80 for 2 months, at 9 per cent.? Ans. 1062.80 × 61 × 9÷365 D15.98.5. 94. What is the interest of D12896.25 for 4 months, at 4 per Ans. D172.42.1+year and 1 month,

cent. ?

95. What is the amount of D97.21 for 1

at 7 per cent. ?

96. What is the interest of D319.25 for 2

at 7 per cent. ?

97. What is the amount of D205.10 for and 2 days, at 7 per cent.?

Ans D104.58.3. years and 7 months,

Ans. D57.76.6. 1 year, 4 months, Ans. D224.33.4

156

SIMPLE INTEREST.

98. What is the interest of D4008.50 for 1

at 7 per cent.?

year and 9 months Ans. D526.73.3

99. What is the amount of D107.70 for 7 months and 5 days. at 7 per cent. ?

Ans. D112.21.3. 100. What is the interest of D1121.42 for 11 months, at 5.5 per cent.?

Ans. 56.69+ 101. What is the amount of D1428.50 for 1 year, 5 months, and 5 days, at 5 per cent.? Ans. D1438.72.4. 102. What is the interest of D1892.50 for 1 year, at 20 per cent.? Ans. D1892.50 × 20D378.50. 103. What is the amount of D1050.25 for 1 year, at 4 per cent.? Ans. D1092.26.0. 104. What is the interest of D742.18 for 120 days, at 6 per cent.? Ans. D14.64. 105. What is the amount of D19.60 for 1 year and 10 months, at 4 per cent. ? Ans. D21.21.9.

NOTE 1.-For the sake of greater exactness in calculating Interest, should any require it, the divisor, or number of days in a year may be 3651, but the difference will be unimportant; in this case the hour the note was dated and the hour of payment, should be considered.

Required the interest of D2500 for the first 6 months of the year 1841, allowing the year to consist of 360, 365, and 3651 days, at 6 per cent. per annum. (Rule 1.)

January, 31 February, 28+ March, 31+ April, 30+May, 31+June, 30=181 days; 2500 × 181=442500×6=2715000 dividend÷360, &c. 1st Ans. D75.41.6; 2d, D74.38.3; 3d, D74.33.2. It will be seen that by omitting the 5 days in the year, the difference is D1.03.3 too much.

NOTE 2.-The erroneous method of computing interest on endorsements, and then deducting those amounts from the face of the note, except in particular cases, may be seen in the folowing statement: Suppose I borrow D100 at 6 per cent., for. 10 years, and pay D6 at the end of each year, what will be due at the end of 10 years? The amount of D100 is D160. But the first endorsement of D6 has borne interest for 9 years, the second for 8 years, the third for 7 years, and so on; so that six dollars have, in fact, been drawing interest forty-five years, and thus produced D16.20 of interest. This added to the nine en

dorsements of D6 each, gives D70.20; that is, while I have paid only the annual interest of D6, the principal has actually been reduced D16.20; by paying D6 annually for 25 years,