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To make a divisor for any rate per cent.
Multiply 365 days by D100, and divide by the rate per cent
Thus, 365 x 100-6=6083 divisor at 6 per cent. ; 365 x100 :5=7300 divisor ; 365 x 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
Thus, 400 x 26=10400---6083=D1.70.92 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
6 :: 26 D1.70.9%. Or 400 x 26 x7-365=D1.99.47 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 inonths; and at 7 per ct. in 52144 days, or 171 months; from which the following rule has its origin, as exemplified above:
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
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 months.
Ans. D150 x 30--240=D18.75 at 5 per cent. ; D.150 X-30-200=122.50 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 raic find à divisor as above directed (see quesi. 65).
78. What is the interest of D22 for 25 days, at 6 per cent. ? (Rule 1.)
Ans. c.9. *79. What is the interest of D58 for 29 days, at 6 per cent. ?
Ans. c 27.6. 80. What is the interest of D400 for 26 days, at 6 per cent. ?
Ans. D1.71. 81 What is the interest of D90 for 28 days, at 6 per cent. ?
Ans. c.41.4. 82. What is the interest of 150 for 9 months, at 6 per cent. ?
Ans. D2.25. 83. What is the interest of D57 for 14 months, at 6 per cent. ?
Ans. D3.93. 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 6 per cent. ?
Ans. 158.50. 86. What is the interest of D200 for 1 year and 3 months, at 6 per cent. ?
Ans. D15.00. 87. What is the interest of D500 for 1 year and 4 inonths, at 6 per cent. ?
Ans. D 10.00. 88. What is the interest of D31 for 10 years and 6 months, al 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, ar 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 x 61 x 9:365=D15.98.5. 96. What is the interest of D12896.25 for 4 months, at 4 per cent. ?
Ans. D172.42.1 +95. What is the amount of D97.21 for 1 year and 1 month, at 7 per cent. ?
Ans D101.58.3. 96: What is the interest of D319.25 for 2 years and 7 months, to at 7 per cent. ?
Ans. D57.76.6. 97. What is the amount of D205.10 for 1 year, 4 inonths, and 2 days, at 7 per cent. ?
98. What is the interest of D4008.50 for 1 year and 9 months at 7 per cent. ?
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 X 20=1378.50. 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 41 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 365), 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 365 days, at 6 per cent. per annum. (Rule 1.)
January, 31+ February, 28+ March, 31+ April, 30+ May, 31+June, 30=181 days ; 2500 x 181=442500 x 6=2715000 dividend:- 360, &c. 1st Ans. 175.41.6; 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 fol"lowing statement : Suppose I borrow D100 at 6 per cent., for 10
рау 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 endorsements 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,
and computing interest on the several endorsements by this method, the whole principal wonld be paid, and the lender would be indebted to the borrower the sum of D2.00, while in fact, the lender had received no part of the sum lent. The difference of the rules depends on the principle assumed in respect to the time when the interest becomes due, and which party has a right to receive it.
What is simple interest? How many parts are there which require attention in interest ? Name them. How do you compute interest for days ? What is the interest of D1799.89 for 1700 days, at 92 per cent. ? How can you calculate interest for months at 6 per cent. ? How can you calculate at any other rate per cent. ? How do you compute interest for years ? When interest is required for years, months, days, &c., how will you proceed ? What is the interest of D979.99 for 9 years, 9 months, 9 weeks, and 9 days, at 9.9 per cent. ? What is bank interest? What is the rule? What can you say of the correctness of the method of calculating bank interest? When the amount and rate per cent. are given to find the principal, by what rule will
work ? What is the rule when the principal, amount, and time, are given, to find the rate per cent. ? What is the rule to find the time, when the principal, amount, and rate per cent., are given ? What can you say in relation to the computation of interest on notes, &c., where partial payments are made?
INSURANCE, COMMISSION, AND BROKERAGE.
INSURANCE is an agreement by which an individual or a com pany agrees to exempt the owners of certain property from loss or hazard. The written agreement is called the policy. The premium is the amount paid by him who owns the property to those who insure it, as a compensation for their risk. It is generally so much per cent. on the value of property insured. Commission is an allowance made to a factor, or a commission merchant, for buying and selling. Brokerage is an allowance made to dealers in money or stocks. The calculations may all be made according to the rule of simple interest for one year (See rule 3.
1. Required the insurance on D60, at 21 per cent. ?
Ans. 60 X 2.5=D1.50. 2. Required the commission on D50 at 2} per cent.
Ans. D1.25. 3. Sold goods to the amount of D200 at .75 per cent. conmishow much was received ?
Ans. D1.50. 4. What is the commission on D89 at 3 per cent. ? D2.67. 5. What is the insurance on D300 at 4.5 per cent. ? D13.50. 6. What is the insurance on D700 at 5.5 per cent. ? D38.50.
7. What is the insurance on a ship and cargo valued at 1/20000 at 6 per cent. ?
Ans. D1300. 8. Á house valued at D10000 which is insured at 1.5 per cent., required the insurance.
Ans. D150.00. 9. B. collected a county tax of D10000, for which he received a commission of 33 per cent., what sum did he receive ?
Ans. D350.00. 10. A. sold to B. goods to the amount of D99, and gained 5.5 per cent. on the sale ; what was his gain? Ans. D5.44.5.
11. What sum must you pay for the use of D85 at 6 per cent?
Ans. D5.52.5. 12. If I borrow D160, and agree to pay 1.5 per cent. for the use of it, how much must I pay
Ans. D2.40. 13. Sixty-nine shares of bank stock, of which the par value is D125, is at a discount of 8 per cent. ; what is its value ?
Ans. D7935. 14. What would be the insurance on a ship valued at D47520, at ) per cent.,?. also at } per cent. ? Ans. D237.60; D158.40.
15. What would be the insurance on a house valued at D14000, at 1} per cent. ? at i per cent.? at į per cent. ? at } per cent. ? at 1 per cent. ? Ans. D210; D105; D70; D46.66 ; D35.
16. What is the insurance on a store and goods valued ai D15000, at 11 per cent. ? at 14 per cent. ? at 24 per cent. ? at 38 per cent. ? at 4 per cent. ? at 5.1 per cent. ?
17. If a policy be taken out for D781.25 to cover D625, required the premium per cent. Thus, 1781.25 : 625 :: 100 : 80 : then 100—80= Ans. 20 per ct.
18. It is required to cover D759, premium 8 per cent.; for what sum must the policy be taken?
Ans. D 100-8=92 : 100 :: 759 : 825.
What is insurance ? commission ? brokerage ? and policy?