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DISCOUNT

Is the abating of so much money to be received before it is due, as that money, if put at interest, would gain in the same time and at the same rate.

Thus 100 dollars would discharge a debt of 106 dollars payable in 12 months, discount at 6 per cent. per annum, because the 100 dollars received would, if put to interest, regain the 6 dollars discount.

RULE. As 100 dollars, with the interest for the given time, is to 100, so is the given sum to the present worth, and the difference between the present worth and the given sum is the discount.

EXAMPLES.

1. What is the present worth of 450 dols. due in 6 months, discount at 6 per cent. per annum ?

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2. How much is the discount of £.308 15s. due in 18 months,

at 8 per cent. per annum ?

Ans. £.33 77 3. What is the present worth of 5150 dols. due in 4 months, discounting at the rate of 8 per cent. per annum, and allowing 1 per cent. for prompt payment? Ans. 4950 dols.

4. A is to pay 5927 dols. on the 19th of April, 1799, and 5989 dols. the 19th of July following-It is required to know how much money will discharge both sums on the 19th of January, 1799, discounting at 8 per cent. per annum?

Ans. 11569 dols. 43 cts.

Though the discount found by the preceding method is thought to be the sum that should be deducted for present payment in justice to both parties, yet in business the interest for the time is taken for the discount.

EXAMPLES.

5. What ready money will discharge a note of 150 dollars, due in 60 days, allowing legal interest, or 6 per cent. per annum as discount?

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6. Bought goods to the amount of 950 dollars, at 90 days credit, what ready money will discharge it, allowing the interest for the time at 6 per cent. per annum as discount ?

Ans. 935 dols. 75 cts. if calculated for 3 months. 935 dols. 95 cts. if calculated for 90 days.

When the interest for the time is allowed as discount, it is presumed that neither party suffers any loss, but the following statement evinces the contrary.

A owes B 100 dollars payable in 12 months, for present payment of which B allows 6 dollars or the interest for the time, and receives 94 dollars; this sum he immediately lends to C for the same space of time, and then receives the amount, being 99 dollars 64 cents, which is 36 cents less than he would have to receive from A, had he left the money in his handsbut if he had allowed A the discount, and not the interest, for the time, he would have received from him 94 dols. 34 cents, and this sum being put to interest would amount to 100 dols. in one year, which shews that the discount and not the interest, is the just deduction for prompt payment.

But when discount is to be made for present payment, without any regard to time, the interest of the sum, as calculated for a year, is the discount.

EXAMPLES.

7. How much is the discount of 853 dols. at 2 per cent,

853
2

dols. 17,06

Ans. 17 dol.. 6 cts.

8. How much money is to be received for 985 dols. 75 cts. discounting 4 per cent. ? Ans. 946 dols. 32 cts.

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BANK DISCOUNT.

THE method used among bankers, in discounting notes, &c. is, to find the interest of the sum, from the date of the note to the time when it becomes due, including the days of grace; the interest thus found is reckoned the discount. Thus, if a note for 100 dollars, dated the 2d September, be discounted at a bank for 30 days, the interest of that sum for 33 days being 55 cents, is deducted for discount. It may be asked, why interest for 33 days is calculated on a note for 30, the answer is, that as custom has allowed the borrower three days of gracethat is, though the time of the note expires on the first of October (the day of the date being included in the 30 days) he may withhold the payment till the 4th-it is therefore reasonable that he should pay interest for it,

If a note of 100 dollars were discounted at a bank for 60 days, the interest of that sum for 63 days, being 105 cents, would be deducted for the same reason.

In case payment of a note be not convenient at the proper time, a new note must be presented on the day of discount, immediately preceding the expiration of the time, paying the same discount or interest for the time, as before stated. Thus, a note of 100 dollars, dated October 7th, 1800, for 30 days, though it is not payable till November 8th, yet must be replaced by a new note on Tuesday, November 4th, paying at the same time 55 cents. A note of the same date, for 100 dols. for 60 days, though not payable till Monday, December 8th, (including in this time the days of grace) must be replaced by a new note on Tuesday, December 2d, paying likewise 105 cents. In the former case the borrower sustains a loss of 5

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days in 30, and in the latter 7 days in 60 by renewing. All Banks have their stated times of discount, generally once in a week. In the preceding cases, the Bank is supposed to discount on Tuesday. Some Banks discount twice a week-others oftener.

The discount of any sum, discounted for 30 or 60 days, is found by multiplying it by one sixth of the days. [See interest, page 110.]

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13. How much is the discount of a debenture of 319 dols.

payable in 210 days, discounting for 30 days.

NOTE. 28 days are allowed for a month, interest being calculated as if the note were renewable.

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14.

What is the discount of the above sum, discounting for 60 days?

NOTE. As notes are renewable in 56 days, the interest of all securities is calculated accordingly.

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