A System of Arithmetic

DISCOUNT.

DISCOUNT is an allowance, made for the payment of any sum of money before it becomes due; and is the différence between that sum, due sometime hence, and its present worth.

The present worth of any sum, or debt, due some time hence, is such a sum, as, if put to interest, would in that time and at the rate per cent. for which the discount is to be made, amount to the sum or debt then due.

RULE.*

1. As the amount of 1001. for the given rate and time is to 1001. so is the given sum or debt to the

present worth.

*That an allowance ought to be made for paying money before it becomes due, which is supposed to bear no interest till after it is due, is very reasonable; for, if I keep the money in my own hands till the debt becomes due, it is plain I may make an advantage of it by putting it out to interest for that time; but if I pay it before it is due, it is giving that benefit to another; therefore we have only to inquire what discount ought to be allowed. And here some debtors will be ready to say, that since by not paying the money till it becomes due, they may employ it at interest, therefore by paying it before due they shall lose that interest, and for that reason all such interest ought to be discounted but that is false, for they cannot be said to lose that interest till the time, when the debt shall become due; whereas we are to consider what would properly be lost at present, by paying the debt before it becomes due; and this can, in point of equity or justice, be no other than such a sum, as, being put out to interest till the debt becomes due, would amount to the in

2. Subtract the present worth from the given sum, and the remainder is the discount required.

Or,

As the amount of 1001. for the given rate and time is to the interest of 1001. for that time, so is the given sum ör debt to the discount required.

EXAMPLES.

1. What is the discount of 5731. 15s. due 3 years hence, at 4 per cent. ?

terest of the debt for the same time. It is beside plain, that the advantage arising from discharging a debt, due sometime hence, by a present paymemt, according to the principles we have mentioned, is exactly the same as employing the whole sum at interest till the time, when the debt becomes due; for, if the discount allowed for present payment be put out to interest for that time, its amount will be the same as the interest of the whole debt for the same time: thus the discount of 1051. due one year hence, reckoning interest at 5 per cent. will be 51. and 51. put out to interest at 5 per cent. for one year, will amount to 51. 5s. which is exactly equal to the interest of 1051. for one year at 5 per cent.

The truth of the rule for working is evident from the nature of Simple Interest; for since the debt may be considered as the amount of some principal, called here the present worth, at á certain rate per cent. and for the given time, that amount must be in the same proportion, either to its principal or interest, as the amount of any other sum, at the same rate, and for the same time, is to its principal or interest.

2. What is the present worth of 1501. payable in of a year, discount being at 5 per cent.?

Ans. 1481. 2s. 11 d.

3. Bought a quantity of goods for 150l. ready money, and sold them again for 2001. payable at of a year hence; what was the gain in ready money, supposing discount to be made at 5 per cent. ? Ans. 421. 15s. 5d.

4. What is the present worth of 1201. payable as follows, viz. 50l. at 3 months, 50l. at 5 months, and the rest at 8 months, discount being at 6 per cent.?

Ans. 1171. 5s. 51d.

DISCOUNT BY DECIMALS.

RULE.*

As the amount of 11. for the given time is to 11. so is the interest of the debt for the said time to the discount required.

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

* Let m represent any debt, and n the time of payment; then will the following Tables exhibit all the variety, that can happen with respect to present worth and discount.

OF THE PRESENT WORTH OF MONEY PAID BEFORE IT IS DUE AT SIMPLE INTEREST.

The present worth of any sum m.