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EXAMPLES.

1. What is the commission on 300 dollars, at 4 per cent.

300

Ans. $12,00 2. Required my commission on laying out 750 dollars, at 45 per cent.?

Ans. 33 dollars 75 cents. 3. What must I charge my employer on laying out 1260 dollars on his account, at 2} per cent. ?

Ans, 31 dollars 50 cents. 4. What is my commission on 2176 dollars 50 cents, at cent.?

Ans. 54 dollars 41} cents. 5. How much am I indebted to my correspondent, on laying out for me 950 dollars 75 cents, when I allow hima 24 per cent. commission? Ans. 26 dolls. 143cts.

2) per

INSURANCE Is a premium given for insuring property of all kinds from fire, the dangers of the sea, even insuring lives, &c. The instrument of agreement between the parties, is called the policy of insurance.

Rule. As in commission, being all at so much per cent.

EXAMPLES.

per cent..

1. What is the premium of insuring 800 dollars, at 11

Ans. 10 dollars. 2. What is the insurance on 1240 dolls, at 10

o per

cent.?

Ans. 124 dollars. 3. What will the insurance of 2800 dollars come to, at 124 per cent.

Ans. 350 dollars. 4. How much is the insurance of a house, in which there is spiritous liquors, gunpowder and vitriol, (such goods doubly hazardous,) amounting to 89840 dollars, at 31 per cent.

Ans. 27850 dollars 40 cents. 5. What sum must a policy be taken out for, to cover 1000 dollars, when the premium is 10 per cent.?

100 per cent.

10 premium A. 90 : 100 ::

1111 dolls. 11 cts. 11 m. 6. What sum will it require to cover a policy of insurance, for 4500 dollars, at 20 per cent.!

100-20=80 As 80 : 100 :: 4500 : $ 5625 answer:

1000

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BROKERAGE Is an allowance of so much per cent. to persons, for assisting merchants to sell their goods, or procuring customers; and they are generally terned brokers, factors, and by some commission merchants. Their per centage is scarcely 1 per cent. but often t, ., , , &c. This is performed the same as simple interest, commission, &c.

Rule. Multiply the given sum by the rate per cent. and cut off two figures of that product to the right hand, and the left-hand figures will be dollars, and the right-hand figures will be cents. Or, by the Rule of Three, say, as 100 dolls. is to the rate per cent, so is the given sum to the answer, in the same as the rate per cent. is.

EXAMPLES.

1. What is the brokerage on 400 dollars, at : per cent.? *)400

dolls. cts. dolls. Ans. $ 2,00

As 100 : 50 : : 400 : 2 dollars. 2. How much must I pay my factor for obtaining customers for me, who purchased 1200 dollars worth tobacco of me, the factorage being $ per cent.

Ans. 7 dollars 50 cents. 3. What is the brokerage on 1000 dolls. at 1) per cent.!

Ans. 15 dollars. 4. How much must I pay factorage at 14 per cent. on 2000 dollars ?

Ans. 25 dollars.

REBATE OR DISCOUNT Is an allowance made of any sum of money before it be comes due, or upon advancing ready money on bonds and notes, which are payable at a future date. 'What remains after the rebate is deducted, is the present worth, or such a sum, as if put to interest, would, at the given rate and time, amount to the given sum or debt.

RULE. As the amount of 100 dollars, at the given rate and time, is to the interest of 100 dolls. at the same rate and time, so is the given sum to the rebate required. Subtract this rebate from the given sum,

and the remainder is the present payment or worth. Or, as the amount of 100 dolls, is to 100 dollars, so is the given sum to the present worth, which subtract from the debt, and the remainder is the rebate.

Proof. Find the amount of the present worth, at the given time and rate, and if the work is right, that will be equal to the given sum or debt.

EXAMPLES.

at 6
per cent.

per annum

1. What is the rebate on 200 dollars, which is not due. for a year,

dolls. dolls. dolls. dolls. cts, m. 100+-6=106 As 106 : 100 :: 200 : 188 67 9+

dolls. cts. m. dolls. cts. m. $200-188 67 9+ equal 11 32 0+ answer. 2. What is the interest on 188 dollars 67 cents 93mills for one year, at 6 per cent. per annum?

Ans. 11 dollars 32 cents of mill. NOTE. Rebate and interest are often supposed to be the same thing, and the interest for the time is often taken in business for the rebate, and both parties allow that peither of them sustain a loss. This is not correct, as you may see by the two questions above; for the interest on 200 dollars for a year, at o per cent. is 12 doilars, whereas the rebate on the same sum, and at the same rate and time, is 11 dollars 32-to cents, making a difference of 67 cents 9+ mills, on every 200 dollars, for a year. On a large supa, for six or seven years, the difference would be very considerable...

3. What ready money must I pay, to discharge a debt of 600 dollars, due four years hence, at 5 per cent. per annum?

Ans. 500 dollars. 4. What is the present worth of 450 dollars, due in six months, at 6 per cent. per annum?

Ans. 436 dollars 89 cents. 5. How much ready money must I pay for a note of 615 dollars 75 cents, due seven months hence, rebate at 4. per cent. per annum ?

Ans. 600 dollars. 6. What ready money must I pay, to discharge a debt of 650 dollars, due two years hence, rebate at 7 per cent. per annum?

Ans. 570 dollars 16+ cents.

When sundry sums are to be paid at different times. RULE. Find the rebate, or present worth of each particular payment separately, and add them into one sum, and that will be the answer required.

7. What is the rebate of 1000 dollars, one-half due in six months, and the other half due in six months after, at 6 per cent. per annum?

Ans. 42 dollars 86+ cents. 8. i have a bond of 2000 dollars, of which 500 dollars is payable in six months, 800 dollars in one year, and the balance at the end of three years. How much ready money ought I to get for it at present, allowing rebate at 6 per cent. per annum?

Ans. 1833 dolls. 37 cts. A short method for finding the rebate of any given sum for

months and days. RULE. Lessen the interest of the given sum for the time, by subtracting its own interest, and this gives the rebaté very nearly.

9. What is the rebate of 50 dollars for six months, at 6 per cent. per annum?

Ans. I dol. 46 cts.
Interest on $50 for six months $150 ots.
Interest on i dol. 50 cts. six months

Ans. Si 46 10. What ready money must I pay for my bond, which has 73 days to go before it is due, for 900 dollars, rebate at 6

per cent. per annum ? Ans. 889 dolls. 32+ cts.

NOTE. When rebate is to be made for present payment, without any regard to time, the interest on the gum is calculated for a year, as the discount or rebate. 11. How much is the rebate of 750 dolls. at 4

per

cent.?

Aps. 30 dollars. 12. How much ready money must I give for 1000 dolls. et 5 per cent.?

Ans. 950 dollars.

4

ANNUITIES BY SIMPLE INTEREST.

An annuity is a sum of money, payable every year, or for a certain number of years, or for ever.

When an an. nuity is bought off, or paid all at once at the beginning of the first year, the price paid is called the present worth.

To find the amount of an annuity. RULE. Find the interest of the given annuity for one year, and for as many years up to the given time, less one; then inultiply the annuity by the given number of years, and add that product to the whole interest, and the sum will be the amount sought.

EXAMPLES.

1. If an annuity of 280 dollars be forborne five years, what will be due for principal and interest at the end of said time, simple interest being computed at 5 per cent, per annum?

Ans. 1540 dollars.

2

Interest on 280 dollars for 1 year, at 5 per cent.

819 280

28 280

42 280

56 Five years' annuity, at 280 dollars per year 1400

Ans. $1540

2. A farm being let upon a lease of four years, at 100 dollars per annum, and the rent being in arrears for the whole term, I demand the sum due at the end of the term, simple interest being allowed at 6 per cent. per annum?

Ans. 436 dollars. To find the present worth of an annuity at simple interest.

Rule. Find the present worth of each year by itself, rebating from the time it falls due, and the sum of all these will be the present worth required.

3. How much is the present worth of 400 dollars per annum, to continue four years, at 6 per cent. per annum?

Ans. 1396 dollars 64 cents. 4. If the payment of the rent of a house be omitted for seven years, what will be the amount in that time, at 6 per cent. when the rent is 224 dollars per year?

Ans.' 1850 dollars 23+ cents. 5. If the payment of a pension of 200 dollars per year be forborne seven years, what will it amount to, at 4 per cent. per annum ?

Ans. 1568 dollars. 6. Suppose a salary of 400 dolls. a year be forborne seven years, what is the amount at the expiration of that time, at 45 per cent. per annum ?

Ans. 3178 dollars. 7. What ready money will equal an annuity of 100 dollars, to continue three years, rebate being at 6 per cent. per annum?

Ans. 268 dollars 37 + cts. NOTE. Nos. 4, 5 and 6, are wrought by the first rule. When the annuity, salary or rent, are to be paid by half yearly or quarterly payments, the amount of such annuity, salary or rent, will be more than yearly, half yearly inore than yearly, and quarterly more than half yearly.

RULE for half yearly payments. Take always half of the ratio, half of the annuity, and twice the number of years; that is, reduce the years to half years, and work as before.

8. If 280 dollars annuity, payable half yearly, be forborne five years, what will it amount to in that time, at 5 per cent,

Ang. 1557 dollars 50 cents.

per annum

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