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EXAMPLES. 1. What is the present worth of 450 dollars due in 6 months, discount at 6 per cent. per annum ?
6 m. į 6
d. 103 : 100 :: 450
Ans. 436 dollars, 89 cents, How much is the discount of £ .308 15 due in 18 months, at 8 per cent. per annum ?
Anf. £ 33 1 73 3. What is the present worth of 5150 dollars due in 4 months, discounting at the rate of 8 per cent. per annum, and allowing 1 per cent. for prompt payment ?
Anf. 4950 dols. 4. A is to pay 592"; dols. on the 19th of April, 1799, and 5989 dollars 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 ? Anf. 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.
EXAMPLE. 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 ?
I= half the months.
148,50 Ans. 148 dols. so cts. 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
per cent. per annum as discount ?
935 dollars 95 cents, if calculated for go 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 fum 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 hands but if he had allowed A the discount, and not the interest, for the time, he would have received from him 94 dols. 34 cts, and this sum being put to interest, would amount to 100 dols. in one year, which shews that the discount and not the intereft, 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 fum, as calculated for a year, is the discount.
EXAMPLES, 7. How much is the discount of 853 dols. at 2 per cent ?
Ans. 1, dols. 6 cts. 8. How much money is to be received for 985 dols. 75 cts. dis. 'counting 4 per cent ?
Anf. 946 dols. 32 cents,
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 ad September, be discounted at a bank, for 30 days, the interest of that sum for 33 days being 55 cts. 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 grace—that is, though the time of the note expires on the ift 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 fame discount or inter
est 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, No. vember 4th, paying at the same time 55 cents. A note of the same date, for 100 dollars 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
In the former case the borrower sustains a loss of 5 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. ceding cases, the Bank is supposed to discount on Tuesday, Some Banks discount twice a week-but this is for the convenience of loaning and not of renewing.
In the pre
The discount of any sum, discounted for 30 or 60 days, is found by multiplying it by one fixth of the days. (See interest, Page 107.]
What is the discount of the following sums, viz.
dols. 3. 159 discounted for 30 days. Ans. 4. 273
do. 5. 683
do. 6. 789
do. 7. 2194
4 33 9 12 06 7
12. How much is the discount of a debenture of 319 dollars, payable in 210 days, discounting for 30 days ?
Note. 28 days are allowed for a month, interest being calcu. lated as if the note were renewable.
51=1 of 33 days
12,27,8 for months 140. Įmo. 877
15 cts. 5 m. 14. What is the discount of the above fum, discounting for 60
Note. As notes are renewable in 56 days, the interest of all fecurities is calculated accordingly. 56 21013 discount months
1,01=of 63 days 42 days
Anf, 12 dols. 55 cts. 8 m.' The preceding examples shew the difference between discounting for 30 and 60 days.
What is the discount of the following sums, discounting for 30 days ? dols. days,
dols, cts. m. 15. 187 for 79
90 16. .219
4 94 5 17. 658 47
7 4 2169
What is the discount of the following sums, discounting for 60 days ? dols, days.
dols. cts. m. 19. 187 for 79
Ans. 2 76 8 20. 219 115
4 72 21. 658 47
5 79 8 22. 2169 128
52 5 4
When a note is offered at a bank for discount, two endorsers are generally required, to the first of whom it is said to be payable : thus-, having occasion for a sum of money, procures B and C as endorsers to his note, and offers it for discount in the following form.
100 dollars. For value received, I promise to pay B, or crder, at the Bank, on demand, one hundred dollars, with interest after
A. When State notes, bank shares, &c. are lodged in a bank as fecu. rity for monies, a note is presented in this form,
For value received, I promise to pay the President, Directors and Company of the Bank, or their order, at said Bank on demand, dollars, with interest after days.
EQUATION OF PAYMENTS.
The design of this Rule is to find a mean time for the payment of several sums due at different times.
Rule. Multiply each sum by its time, and divide the sum of the products by the whole debt; the quotient is accounted the mean time.
EXAMPLES. 1. A owes B 200 dollars, whereof 40 dollars is to be paid in 3 months, 60 dollars in 5 months, and the remainder in 10 months, al what time may the whole be paid without any injustice to either
60 X 5
7 months and 3 days,