$ 1000 70 1070 75 995 99.50 1094.50 20 1.60 21.60 20 750 791.60 302.90 New Principal March 1, 1816, Interest to 4th endorsement, being 20 months, Amount to do. 2nd endorsement, Interest to 4th endorsement, Amount to do. 3d endorsement, which does not bear interest, because one year's interest has accrued on new principal. 4th endorsement, Deduct from 1094.50, New principal Nov. 1, 1817, 12.31.6 Interest to July 1, 1918, being 8 months, 15.69 3 Difference between this result and that by Rule I. Principal, Rule II. Rule III Interest to 4th endorsement Nov. 1, 1817, being 34m. 1.98.5 By Rule IV. at 7 per cent. 1000 198.331 1198-33 865 do. Amount to Sum of the first four endorsements. Interest to March 1, 1818, Amount. 5th endorsement, New principal, 5 62 59 Interest to July 1, 1816, 246.73 59 Balance due do. EXAMPLE 2. On Jan. 1, 1816, Samuel Trusty owed me. 7751, on which I was to receive interest at 7 per cent. On July 1, he paid me 1001.; on Jan. 1 1817, 251.; on Sept. 1, 251.; on March 1, 1818, 251.; on July 1, 1819, 101.; on Sept. 1, 3901; and on Jan. 1, 1821, the balance: What was the balance by the four preceding rules and what is the whole interest paid? By Rule 1. By Rule 2. { Balance due £384 508ļ. Whole interest paid £210-3544. I gave a promissory note to A. D. March 1, 1817, for $350. On Dec. 1, I paid $150; on April 1, 1818, $35; on June 1,$10; Jan. 1, 1819, $40; Dec. 1, 865; and March 1, 1820, a settlement was made. To whom was a balance due, and how much, computing interest at 6 per cent. by the last three rules? Ans. DISCOUNT IS an allowance made for the payment of any sum of money, before it becomes due, and is the difference between that sum, due some time 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 I* As the amount of £100 for the given rate and time is to £100; 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 shall become 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, I give that benefit to another; therefore we have only to inquire what discount ought to be allowed. And here, many suppose that, since by not paying 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 the supposition is false, for they cannot be said to lose that interest till the time arrives, when the debt becomes due; whereas we are to consider what would be lost, at present, by paying the debt before it becomes due; this can, in point of equity, be no other than such a sum, which being put out at interest till the debt shall become due, would amount to the interest of the debt for the same time. It is bezides plain, that the advantage arising from discharging a debt due some time hence, by a present payment, according to the principles above mentioned, is exactly the same as employing the whole sum at interest till the time when the debt becomes due, arrives: for, if the discount allowed for present payment be put out at 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 £106, due one year hence, reckoning interest at £6 per cent. will be £6, and £6 put out to interest at £6 per cent. for one year, will amount to £6 7s. 24d. which is exactly equal to the interest of £106, for one year at £6 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 (call1 here the present worth) at a certain rate per cent. and for the given time, that amount must be in the same proportion either to its principal or interest, Subtract the present worth from the given sum, and the remainder will be the discount required. Or, As the amount of £100 for the given rate and time, is to the interest of £100 for that time: so is the given sum or debt to the discount required. Or, In federal money, divide the given sum by the amount of $100 for the given time and rate; point off from the right of the quotient, two places less than in division of decimals for the present worth. Add 100 £ £ s. £ s. d. As £111: 11 :: 635 17: 63 0 2 disc. Ans. £ £ £ S. £ S. d. Or, As 111: 100 :: 635 17: 572 16 91 present worth. £ 8. £ S. d. £ s. d. And 635 17-572 16 91=63 0 21 discount. $ IN FEDERAL MONEY. C. $ c. m. 11:: 2119 50: 210 04 01 discount. Or, $ $ As 111: 2119.5×100 As 111: 100 :: 2119 50: =$1909 45c. 91⁄2m.≈ present worth; and 21195-1909 4595-210 0405 discount as 19-094595; and 1909-4595-present worth, as be payable in half a year, 2. What is the present worth of $350 discounting at 6 per cent. per annum? Ans. $339 80c. 5m. 3. What is the present worth of £65, due 15 months hence, at £6 per cent. per annum ? Ans. £60 9s. 34d. 4. What is the discount on £97 10s. due January 22, this being September 7th, reckoning interest at £5 per cent.? Ans. £1 15 11. as the amount of any other sum, at the same rate, and for the same time, to its principal or interest. In common cases, the interest is taken for the discount, the parties not attending to the real difference between discount and interest. Thus $100 discounted in this way for a year at 6 per cent. or $6 is taken out, and the person receives $94. If he were to lend the $94 on interest for a year at the same rate, he would receive of interest $5 64cts. or 36 cents less than the above discount, which is, in fact, discounting at 619 per cent, or nearly 6-4 per cent. instead of In Bank Discount, the interest is considered as the discount. 5. What ready money will discharge a debt of $1595 due 5 months and twenty days hence, at 6 per cent.? Ans. $1541 32c. 6m. 6. Bought a quantity of goods for $250, ready money, and sold them for $300 payable 9 months hence: What was the gain, in ready money, supposing discount to be made at 6 per cent.? Ans. $37 8c. 11m. 7. What is the present worth of $960, payable as follows; viz. at 3 months, at 6 months, and the rest at 9 months, supposing the discount to be made at 6 per cent. ? Ans. $936 70c. RULE II. As any sum of money, at 6 per cent. per annum, will double, at simple interest, in 200 months; therefore, To 200 add the number of months for which the discount is required, by which sum divide the product of the money and time, (in months,) and the quotient will be the discount. EXAMPLES. 1. What is the discount of $150 75c. for a year? 150.75 200 +12 Any principal to be discounted for one year, at any of the following rates, (or for any rate and time, whose product is equal to any of the following rates) being multiplied by the multiplier, (if any.) and divided by the corresponding divisor, the quotient will be the discount. |