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2. At what rate per cent. per annum, will 500L. amount to 725L. in 9 years?

Ans. 5L. per cent. 3. At what rate per cent. per annum, will. 600 dollars amount to 856 dols. 50 cts. in 9 years and 6 months ?

Ans. 44 per cent.

CASE 7. To find the time, when the principal, amount, and rate per cent. are given.

RULE.
As the interest of the principal for one year,
Is to one year;
So is the whole interest,
To the time required.

EXAMPLES 1. In what time will 500L. amount to 725L. at 5 per cent. per annum ? L.

L. Y. L. Y. 500 725

25 : 1 :: 225 : 9 5

500

Ans. 9 years.

L.

L. 2500

225 2. In what time will 540L. amount to 734L. Ss. at 4 per cent. per annum?

Ans. 9 years. 3. In what time will 600 dollars amount to 798 dollars,

Ans. 54 years. at 6 per cent. per annum?

INSURANCE, COMMISSION, AND BROKAGE.

Insurance, Commission, and Brokage, are allowances made to insurers, factors, and brokers, at a stipulated rate per cent.

RULE. Work as if to find the interest of the given sum for one year, at the proposed rate: or, if the rate be less than 1 per cent. take such aliquot part, or parts, of the interest at } per cent. as the rate is of a pound, or dollar.

110

INSURANCE, COMMISSION, AND BROK'AGE.

EXAMPLES
1. What is the commission on 596L. 185. 4d. at 6 per
cent. ?

Ans. 35L, 16s. 34
L,

d.
596 18 4

6

8.

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per cent. ?

per cent. ?

2. What is the commission on 1371L. 9s. 5d. at 5 per cent.?

Ans. 68L. 11s. 5 d. 3. What is the commission on 526L. 11s. 5d. at 3 L.

Ans. 18L. 8s. 7d. 4. What is the commission on 1974 dollars at 5 dollars

Ans. $98.70. 5. A factor has sold goods for a merchant, to the amount of 930L. 10s. and is to receive 3-L. per cent. commission: what sum is due to him? Äss, 30L. 4s. 9d. 6. What is the insurance of 924L. at 7L. per cent. ?

Ans, 64L. 13s: 7d. 7. What is the insurance of 1250 dollars, at 71 dollars

Ans. $.93.75. 8. What is the insurance of an East India ship and cargo, valued at 14813L., 155. at 15%L. per cent. ?

*Ans. 2333L. 35. 31d. 9. What is the brokage on 1321L. lls. 4d. at 1}L. per cent. ?

Ans. '14L. 178. 4d. 10. What is the brokage on 874L. 155. 3d. at 5s. or L.

Ans. 2 L. 3s. 80. 11. If a broker buy goods for me, to the amount of $1953, and I allow him dols, per cent. for his service, what sum must I pay him?

Ans. $13.894.

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111

COMPOUND INTEREST.

Compound Interest is that which arises from a principal increased by its interest, as the interest becomes elue.

RULE. Find the amount of the given principal for the firs year, by simple interest; this amount will be the principal for the second year, and the amount of this principal, found as before, will be the principal for the third year, and so on.

From the last amount, subtract the given principal, and the remainder will be the compound interest.

EXAMPLES. 1. What is the compound interest of 500L. for 3 years, at 5 per cent. ?

Ans. 78L. 16s. 3d.

L.
Principal 500
Interest for 1st year 25

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L. 78 16s. 3d, 2. What is the compound interest of 450L. for 3 years, at 5 per cent. per annum?

Ans. 70L. 185. 7 d. 3. What is the compound interest of 760L. 10s. for 4 years, at 6 per cent. per annum? Ans. 199L. 12s. 2d.

4. What is the compound interest of 500 dollars for 4 years, at 6 per cent per annum? Ans. $131.231.

5. How much will 400L. amount to in 4 years, at 6 per cent. per annum?

Ans. 504L. 19s. 9 d.

DISCOUNT.

Discount is an allowance made for the payment of a sum of money before it becomes due, according to a certain rate per cent. agreed on between the parties concerned.

The present worth of any sum, or debt, due some time hence, is such a sum as, if put to interest, for that time, at a certain rate per cent. would amount to the sum or debt. (See case 5, Simple Interest.)

RULE. As the amount of 100 pounds, or dollars, at the rate and time given,

Is to 100 pounds, or dollars;
So is the whole debt,
To the present worth :

Subtract the present worth, from the whole debt, and the remainder will be the discount.

PROOF. Find the amount of the present worth for the time and rate proposed, which must equal the given sum or debt.

EXAMPLES. 1. What is the present worth of 590 dollars, due in 3 years, discount at 6 per cent, per annum? Ans. 500 dols.

$ $ 6 rate

118 : 100 :: 590 3 years

100 18

118)59000(500 dols.

590

100.

00

118 amt. of $100. 2. What is the discount of 7951.. Ils. 2d. for 11 months, at 6 per cent. per annum ?

Ans. 41L. 9ş. 6d. M. L. M. L. S.

L.

d. 12 : 6 :: 11 : 5 10 795 Il 2 whole debt. 100 0

754 1 8 present worth.

Amt. of 100L. 105. 10

41 9 6 discount. L.

L. L. s. d. 105 10 : 100 :: 795 112 : 754 1 8 present worth.

L.

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3. What is the present worth of 672L. due in 2 years; discount at 6 per cent. per annum?

Ans. 600L, 4. What is the present worth of 308L. 155. due in 18 months; discount at 8 per cent. per annum?

Ans. 275L. 135. 4 d. 5. What is the present worth of $ 430.67, due in 19 months'; discount at 5 per cent. per annum?

Ans. $ 399.07. 6. What is the discount of 112L. 12s. due in 20 months, at 7 per cent. per annum?

Ans. I1L. 15s. 3 d. 7. What is the present worth of 100L. one half due in 4 months, and the other half in 8 months ; discount at 5 per cent. per annum?

Ans. 97L. 11$. 4d. 8. Bought goods amounting to 8 615.75, at 6 months credit; how much ready money must be paid, if a discount of 4 per cent. per annum be allowed ?

Ans. $ 602.20. 9. What is the difference between the interest of 1204 dollars at 5 per cent. per annum, for 8 years; and the discount of the same sum for the same time and rate per cent. ?

Ans. $137.60.' Note.-Discount for present payment is often made without regard to time; it is then found precisely as the interest of the given sum for 1 year.

EXAMPLES, i. How much is the discount of 853 dollars, at 2 per cent.)

Ans. $17.06. 853

17.06 2. How much is the discount of 750 dollars, at 3 per cent. ?

Ans. $ 22.50. 3. How much is the discount of 650L. at 4 per cent. ?

Ans. 26L. 4. Bought goods, on credit, amounting to 1656 dollars; -how much ready money must be paid for them, if a discount of 5 per cent. be allowed ?

Ans. $ 1573.20. 5. A. hoids B's. note for 175L. 10s. he agrees to allow B. a discount of 3 per cent. for present payment; what sum must B. pay?

Ans. 170L. 43. 8 d.

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