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DISCOUNT, Is an allowance made for the payment of any sum em money belore it becomes clue; or upon advancing really money for notes, bills, &c. which are payable at ä liure dar. Wai reinains after the discouni iš velurred, in the present wastli, or such a sum ás, il pilt to interest: unului at tiegisen rate anul time, amount to the given yum ur deli.

RULE. As the amount of 100'. or 100 dollars, at the given rate , and time : is to the interest of 100, at the same rate and time : : so is the given sum : to the disco:!111:.

Subtract the discount from the given sur, and the remainder is the present worth.

Orails the amount of 100 : is to 100 : : so is the given sum or debt : to the present worth.

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

EXAMPLES. 1. What must be discounted for the ready payment of 100 dollars, duc a year hence at 6 per cent. a year i

8 $ $ $ ots. As 106 : 6 : : 100 : 5 66 the answer.

100,00 given suin.

5,66 discount.

894,54 the present worth. 2. What suin in ready money will stischarge a stelt of 9:25l. due 1 year and 8 months hence, at 6 per cent. i £100

19 Interest for 20 morithe.
110 Am't. £ £ £ f. 6. d.'

As 110 100 :: 925 : 870 18 2+ Ans. . 3. What is the present worth of 000 dollars, die years hence, at 5 per cent. :

us. 8.300) 4. What is the discount of 2751. 10s. for la aonths, at 6 per cent. per anuuin ? Ans. £13 25. 4iche

5. Bought goods amounting to 615 dols. 75 cents, at 7 months credit; how much ready money must I pay, dis count at 45 per cent. per annum ? : Ans. $600.

6. What sum of ready money must be received for a bill of 900 dollars, due 73 days hence, discount at 6 per cent. per annum ?

Ans. 8889, 32cts. 8m. NOTE.—When sundry sums are to be paid at different times, find the Rebate or present worth of each particular payment separately, and when so found, add them into one sum.

EXAMPLES.

7. What is the discount of 7502. the one half payable in six months, and the other half in six months after that, at 7 per cent. ?

Ans. 637 10s. 2 d. 8. "If a legacy is left me of 2000 dollars, of which 500 dols. are payable in 6 months, 800 dols. payable in 1 year, and the rest at the end of 3 years; how much ready money ought I to receive for said legacy, allowing 6 per cent. discount?

Ans. $1833, ?cts. 4m.

ANNUITIES. An Annuity is a sum of money, payable every year, or for a certain number of years, or forever.

When the debtor keeps the annuity in his own hands, beyond the time of payment, it is said to be in arrears.

The sum of all the annuities for the time they have been forborne, together with the interest due on each, is called the amount.

If an annuity is bought off, or paid all at once at the beginning of the first year, the price which is paid for it is called the present worth. To find the amount of an annuity at simple interest.

RULE. 1. Find the interest of the given annuity for 1 year. • 2. And then for 2, 3, &c. years, up to the given time, less 1.

3. Multiply the annuity by the number of years given and add the product to the whole interest, and the sum will be the amount sought.

EXAMPLES. I, If an annuity of :701. be forborne 5 years, what will for be due for the principal and interest at the end of said

lern, simp'e interest being computed at 5 per cent. per annum

lr. f. S. 1st. Interest of 701. ai 5 per cent. for 1- 3 10

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Ans. £385 0 . A house being let upon a lease of 7 years, at 400 Jol ars per alium, and the rent being in arrear for the rei whole teim, I demand the sundue at the end of the term, sup.e interest being allowed at bil. per cent. per annuir:

dus. $3304.

Tu and the present worth of an annuity at simple interests

Rl'IF. 538 Find the present worth of each vear by itself, idiscount

ing froin the time it falls due, atil the sum of all these på present worths will be the present worth required.

EXAMPLFS. 1. What is the present worth of 400 dols. per annum, to continue 4 ycars, at 6 per cent. per annum 1067

57235849 = 'Pres. worth of 1st yr 11: 26

24 vr. šŞ: 100 :: 460 : 358.98305

s! ir. 322,38064

4th yr.

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Ans. $1596,06503=$1396, Octs. 5m, 2. How much present movies is equivalent to an an nuity of 100 coiliers, tu contime 3 years; rebate bring maile at 6 per cerit.

Ans. $268, 37013. Im. 3. What is 801. yearly rent, tu coritinuc 5 years, worth m ready money, at b. per cent. Aus. £340 158.

EQUATION OF PAYMENTS, Is finding the equated time to pay at once, several debts due at different periods of time, so that no loss shall be sustained by either party.

RULE. Multiply each payment by its time, and divide the sum of the several products by the whole debt, and the quotient will be the equated time for the payment of the whole.

EXAMPLES. 1. A owes B 380 dollars, to be paid as follows-viz. 100 dollars in 6 months, 120 dollars in 7 months, and 160 dollars in 10 months : What is the equated time for the payment of the whole debt ?

100 X 6 = 600
120 X 72 840
160 x 10 = 1600

380

3040/8 months. Ins. 2. A merchant hath owing him 300l. to be paid as follows : 501. at 2 months, 1002. at 5 months, and the rest at 8 months; and it is agreed to make one payment of the whole ; I demand the equated time? Ans. 6 months.

S. F owes H 1000 dollars, whereof 200 dollars is to be paid present, 400 dollars at 5 months, and the rest at 15 months, but they agree to make one payment of the whole; I demand when that time must be ? Ans. 8 months.

4. A merchant has due to him a certain sum of money, to be paid one sixth at 2 months, one third at 3 months. and the rest at 6 months ; what is the equated time for the payment of the whole ?

Ans. 44 months.

BARTER, IS the exchanging of one commodity for another, and directs merchants and traders how to make the exchange without loss to either party.

RULE. Find the value of the commodity whose quantity is yven; then find what quantity of the other at the pre

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