DISCOUNT. 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 would discharge a debt of $106 payable in 12 months, discount at 6 per cent. per annum, because the $100 received would, if put to interest, regain the $6 discount. RULE. AS $100, 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 due in 6 months, discount at 6 per cent. per annum? 6 m. 6 3 100 d. 103 100 :: 450 Ans. $436 89 cts. 2. How much is the discount of £308 15s. due in 18 months, at 8 per cent. per annum ? Ans. £33 1 74. due in 4 months, annum, and allowAns. $4950. and 3. What is the present worth of $5150 discounting at the rate of 8 per cent. per ing one per cent. for prompt payment? 4. A. is to pay $5927 on the 19th of April, 1799, $5989 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. $11569,43. 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, due in 60 days, allowing legal interest, or 6 per cent per annum, as discount? 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. $935,75 if calculated for 3 months. $935,95 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, payable in 12 months, for present payment of which B. allows $6, or the interest for the time, and receives $94; this sum he immediately lends to C. for the same space of time, and then receives the amount, being 99 dols. 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 cents, and this sum being put to interest, would amount to 100 dols. in one year, which shows 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 8. How much money is to be received for $985,75, dis $6,50 discounting 10 per cent. is $17,06 counting 4 per cent.? 9. 10. 2,50 16 Ans. $17,6. Ans. $946,32. $5,85. 2,10. 3,75. 13,43. 9,80 Required the interest and discount of the following sums, at 6 per cent. per annum. interest. discount. 18. $896,50 payable in 10 months. Ans. $44,821 $42,69 19. 875,00 30,62 29,59 31,84 30,611 44,13 42,23 To raise the price of goods, so as to discount without loss. RULE. AS 100, less the discount, is to 100, so is the present price, to the price required. Or as 100, less the discount, is to the discount, so is the present price or value, to the sum to be added. EXAMPLES. 1. The present worth of certain goods is $930; at what must they be valued to allow 7 per cent. discount, without loss? Ans. $1000 2. A parcel of goods is charged at £54 14 7, how inust it be valued to allow 10 per cent. without loss? BANK DISCOUNT. Ans. £60 16 24. 1. What is the Bank Dis- 2. What is the discount of count of $563,74 for 30 days $686,74 for 63 days? with grace? 563,74 + of 33= ,5 686740 281870 cts. 310,057 Ans. 3,10. 34337 cts. 721,077 Ans. $7,21. 3. Required the discount 4. What is the discount of of $567 for 129 days? 6)73,143 Ans. $12,19 7,636 Ans. $7,64 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; at what time may the whole be paid without any injustice to either ? 2. A. is indebted to B. £120, whereof one half is to be paid in 3 months, one quarter in 6 months, and the remainder in 9 months; what is the equated time for the payment of the whole ? Ans. 5 months and 7 days. 3. C. owes D. $1400, to be paid in 3 months; but D. being in want of money, C. pays him at the expiration of 2 months, $1000; how much longer than 3 months ought C., in equity, to defer the payment of the rest? Ans. 2 months. * Equal payments being at 3 and 6 months, the mean is 4 months; at 3, 4, and 6 months, the mean is 4 months, &c. 4. The sales of a consignment of goods became due, viz. $267 on the 1st of March. 216 135 162 10th of May. 4th of July. 16th of August. Required the equated, or mean time of payment. 267 due at present, or the first payment. the 1st of March, which is the 16th of May-or thus, Ans. 92 days previous to the 16th of August, which gives the mean time, May 16th as before. If the times of payment be not in regular succession, they should be so placed previous to the calculation; noting the first or earliest time of payment, and then taking the others as they become due. When there are Drs. and Crs. to an account, and the equated time of paying the balance is required, some persons find the products of each, in the usual manner of time and money, and divide the balance of products by the balance of moneys for the time required. But the general method in such case, especially in accounts between British and American merchants, is to adjust by an interest account, and in this way, show the balance at the time of furnishing the account current, |