due, Jan. 10th 1821, on said account, allowing hs credit on the goods purchased; interest at 7 Ans. $233 68cts.

INSURANCE, COMMISSION, AND BROKAGE.

Insurance, Commission, and Brokage, are allowances made to insurers, factors and brokers, at a stipulated rate per cent. as a compensation for their services.

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 1 per cent. as the rate is of a pound, or dollar.

1. What may a broker demand for brokage, when he sells goods to the value of £500 10s. 7d. and I allow him 7s. per cent.? Ans. £1 158. 01d.+

£ S. d.

2. What is the commission on £287 10s. at 31 per cent?

Ans. £10 1s. 3d. 3. If I employ a broker to sell goods for me to the value of £2575 17s. 6d. what is the brokage at 4s. per cent. ?

Ans. £5 38. 01d.+ 4. What is the insurance of an East India ship and cargo, valued at $84713 71cts. 6m. at 153 per cent.?

Ans. $13342 41cts.3+ 5. What is the commission on $312, at 12cts. per cent. Ans. 37cts. 4m.+

1

6. If a broker is employed to buy a quantity of goods, to the value of $2175 87 cts., what is the brokage at 37 cts. per cent. Ans. $8 15cts. 9m.+

2. What is the brokage on $15734 46cts. at 1 per cent?

Ans. $236 lct. 6m. +

8. What is the insurance of a house, valued at $1853, at 75cts. per cent. ? Ans. 13 893cts.

COMPOUND INTEREST.

Compound Interest is that which arises from any principal and its interest put together, as the interest becomes due; and for this reason it is called Compound Interest.

RULE.

Find the amount of the given sum by Simple Interest for the first year, which will be the principal for the second year; then find the amount of that principal for the second year, and that will be the principal for the third year; and so on for any number of years.

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

EXAMPLES.

1. What is the compound interest of $500, for 3 years, at 7 per cent.? Ans. $112 52cts. 1m.+

2. What is the compound interest of $450, for 3 years, at y per cent. per annum ? Ans. $101 26cts. 9m.+ 3. What is the amount of $550 75cts. for 3 years, at 6 per Gent. per annum, at compound interest?

Ans. $655 95cts. 2m. +

4. What is the compound interest of $500, for 4 years, at 6

Ans. $131 23cts. 8m.+

per cent. per annum? 5. What will $1200 amount to in 4 years, at 4 per cent. at compound interest? Ans. $1417 37cts. 7m.+

6. How much will £400 amount to in 4 years, at 6 per cent. at compound interest? Ans. 504 19s. 9 d.+

DISCOUNT.

Biscount 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 bence, 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 ven,

Is to the whole debt;

So is 100 pounds or dollars,

To the present worth.

Subtract the present worth from the whole debt, and the re mainder 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, and what the discount of $500, payable in 10 months, at 5 per cent. per annum?

Ans. Discount $20.
Present worth $480.

2. Bought goods to the value of $109 64cts. to be paid in 9 months; what present money will discharge the same, if I am allowed 6 per cent. per annum discount?

Ans. $104 91cts. 8m.+ 3. What is the present worth of $161 10cts. for 19 months, discount at 5 per cent. per annum ? Ans. 149 28cts. 2m.+ 4. What is the present worth of $430 67cts. for 19 months, discount, at 5 per cent. per annum? Ans. $399 07cts. 8m.+ 5. What is the discount of £112 12s. for 20 months, at 7 per cent. per annum? Ans. £11 15s. 3'd.+ 6. What is the present worth of $240, one half payable at 4 months, and the other half at 8 months, discount at 5 per cent. per annum? Ans. $234 16cts. 2m.+ 7. What is the present worth of $100, one quarter due in 3 months, and the remaining three quarters in 5 months, discount at 7 per cent. per annum? Ans. $97 44cts. 4m. + 8. Bought goods amounting to $615 75cts. at 6 months credit; how much ready money must be paid, if a discount of 4 per cent. per annum be allowed? Ans. $602 20cts.+ 9. What is the difference between the interest of $1204 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 60cts.

EQUATION.

Equation is a method of reducing several stated times, at which money is payable, to one mean or equated time.

RULE.

Multiply each payment by its time, add the several products together, and divide the sum by the whole debt; the quotient will be the answer.

PROOF.

The interest of the sum payable at the equated time, at any given rate, will equal the interest of the several payments for their respective times, at the same rate.

EXAMPLES.

1. A owes B 380 dollars to be paid as follows, viz. $100 in 6 months, 120 dollars in 7 months, 160 dollars in 10 months: what is the equated time for the whole debt? Ans. 8 months.

2. Cowes D 100 dollars, of which 50 dollars are to be paid at 2 months, and 50 at 4 months; but they agree that the whole shall be paid at one time: when must it be paid?

Ans. 3 months. 3. A merchant hath owing to him $300 to be paid as follows, $50 at 2 months, $100 at 5 months, and the rest at 8 months: and it is agreed to make one payment of the whole, when must that be made? Ans. 6 months.

4. B owes C $800, whereof $200 are to be paid at 3 months, $100, at 4 months, $300 at 5 months, and $200 at 6 months; but they agree to make one payment of the whole; I demand what time that must be? Ans.. 4 months, 18 days.+

5. K is indebted to L a certain sum, which is to be discharged at 4 several payments; that is at 2 months, at 4 months, at 6 months, and at 8 months; but they agree to make one payment of the whole; the equated time is demanded?

Ans. 5 months.

6. A merchant purchased goods, to the amount of $2000, whereof 400 dols. are to be paid present, 800 dols. at 5 months, and the rest at 10 months; but they agree to make one payment of the whole; what is the equated time? Ans. 6 months.