Mr. James Carroll, Baltimore, in Account Current, Dr. Cr. Feb. 11, To $186.50×303*=5650950 26, To $214.75×288 =6184800 To $515.25×173 8913825 June 20, * For rightly understanding this calculation, it is necessary to consider that the account is made up till the 10th of December, and the interest calculated on it till that date. We place in a column, as above, all the sums on the debit side, and then all those on the credit side, prefixing to both their dates, and to the former the word to, and to the latter by, for the sake of distinction. We next find, successively, the number of days that elapse between Feb. 11 and Dec. 10, between Feb. 26 and Dec. 10, &c. and place them in the next column. A debit column and a credit one are thus formed, and all the sums on the debit side are multiplied by the corresponding number of days, and the products are placed in the debit column. In like manner, the products of the sums on the credit side by the days which follow them, are placed in the credit column. The sums of the two columns are then taken, and the debit side is found, by subtraction, to exceed the other side by $59028.50, which by means of the method pointed out in § 123, gives $11.32, the interest due on the entire account. This is placed on the debit side of the account; and then the sum of all on the credit side is taken from the sum of all on the debit side, and the remainder $163.32 is placed on the credit side, and is the sum due by the person to whom the account is furnished. It is scarcely necessary to say that the last two lines, in Italics, form the answer of the account, being found by the calculator. In calculating the interest on the debit side, it is the custom in some places to include both days, as in the above example. 14. Required the principal and interest due on the following account current, till the 18th of January, 1828, at 6 per cent. per annum. Ans. Interest $10.70, Principal $1296.571. Dr. 1827. Mr. J. Fox, in Account Current with A. Bell. Cr. May 19 To Goods Aug. 23 To Tea Oct. 4 To Goods 200 00 Dec. 1 By Bill $cts. 400 50 680.00 81 50 Nov. 18 To Sugar 300 00 1828. 1828. Jan. 18 By Balance to new Jan. 18 To Balance of Inte Account 134 572 rest 10 70 $1296 571 $1296 57 15. Required the principal and interest due on the following account current, till the 26th of June, 1828, at 5 per cent. per annum. Dr. 1827. Mr. Joseph Foulks, New-Orleans, in Account Cur- Sep. 3 To Balance Dec. 21 To Flour 1828. Jan. 27 To Goods Mar. 26 To Linen June 26 To Balance of Inte Mar. 20 By Tobacco 1040 50 May 25 By Cotton rest Cr. $cts. 1675 50 1236 75 912 25 838 75 June 26 By Balance to new 868 69 16. On the 5th of January, 1822, the public funded debt of Great Britain and Ireland consisted of 150. Discount is an abatement made for advancing money before it becomes due. The money which is received as the full payment of any debt or bill due some time after, is called its present worth. PROBLEM I.-To find the present worth of a bill or debt. 151. RULE. Find the interest of the debt at the given rate, and for the given time; consider this interest as discount, and subtract it from the debt to find the present worth.* * This rule for the calculation of discount is that which is always employed by merchants and bankers. It is founded, however, on a principle radically false; and always gives the discount too large, and consequently the present worth too small, by the interest of the true discount. This will appear manifest, if we consider that the true present worth of any debt is such a sum as would, if lent at interest at the assigned rate amount to that debt at the time at which it would have been due: and consequently the discount, or the difference between the present worth and S Example 1. Required the present worth of a bill of $350, due at the end of 3 months, at 6 per cent. per annum. Here, by the method already explained in interest, the discount is readily found to be $5 25, and this being taken from $350, the remainder, $344 75, is the present worth. 2. What is the present worth of a bill of £39 5s., due on the 1st of September, but paid on the 3d of July preceding, discount being allowed at 5 per cent. per annum? The time here is 60 days, for which the interest of £39 5s. is found to be 6s. 5-7d.; and by subtracting this from £39 5s. we have remaining £38 18s. 693d., the present worth.* 3. Required the present worth of a bill of $346, drawn 8th of March, at 6 months, and discounted 3d of June, at 6 per cent. per annum. By counting forward 6 months and 3 days, from the 8th of March, we find this bill to be due on the 11th of September. The number of days from the 3d of June till this date is 100, and the interest of $346 for 100 days, at 6 per cent. per annum, is found, by any of the methods formerly explained, to be $5.69; and, consequently, the present worth is $340.31. It is proper to observe, that in each of the following exercises, 3 days of grace must be allowed. Exercises.-1. Required the present worth of a bill of the debt, should be, not the interest of the debt, but the interest of the present worth; and therefore the interest of the debt will exceed the true discount, that is, the interest of the present worth, by the interest of that discount. The true present worth will be found by the rule to Problem II. of the present article. * In the United States, as well as in Great Britain and Ireland, three days, called Days of Grace, are always allowed after the time a bill is nominally due, before it is legally due: thus, suppose a bill were drawn on the 8th of April, at 4 months, it would be due, not on the 8th, but on the 11th of August. It may be remarked, that if, without the days of grace, a bill should appear to be due on the 31st of a month which contains only 30 days, the last day of that month is to be taken, and not the 1st of the next; and, consequently, the 3d of the next month will be the day on which, by the addition of the days of grace, the bill will be really due. Thus, a bill drawn on the 31st of August, at 3 months, would be due on the 3d of December. In like manner, a bill which, without the addition of the days of grace, would be due on the 29th, 30th, or 31st of February, if that month contained so many days, would be really due on the 3d of March. It may be farther remarked, that bills which fall due on Sunday, are paid, in the United States as well as in England, on Saturday, but in Ireland on Monday. $500, drawn 1st of March, at 7 months, and discounted June 9th, at 6 per cent. per annum. Ans. $489.72. 2. Required the discount of $285, for 1 year, at 6 per cent. per annum. Ans. $17.24. Ans. $247.41. 3. What is the present worth of a bill of $250, payable în 60 days, at 6 per cent. per annum? 4. What is the discount of $675.75, payable in 90 days, at 6 per cent. per annum ? Ans. $10.33. 5. What is the present worth of $175.50, payable in 30 days, at 7 per cent. per annum? Ans. $174.39. 6. Required the present worth of a bill of $500, drawn on the 20th of May, and due on the 4th of October, at 5 per cent. per annum. Ans. $489.72. 7. Required the present worth of a bill of $875.75, drawn on the 8th of September, at 5 months, and discounted on the 12th of November, at 6 per cent. per annum. Ans. $862.64. 8. Required the present worth of a bill of $670, drawn on the 8th of June, at 90 days, and discounted on the 10th of July, at 6 per cent. per annum. Ans. $663,28. 9. Required the discount of a bill of $2000, drawn on the 10th of April, at 60 days, and discounted on the 1st of May, at 6 per cent. per annum. Ans. $1986.19. 10. What is the present worth of $196.75, due at the end of 9 months, at 6 per cent. per annum. Ans. $187.80. 11. What is the present worth of a bill of $1400, drawn the 1st of August, at 18 months, and discounted on the 25th of December, at 6 per cent. per annum? Ans. $1306.56. PROBLEM II.--To find the true present worth of a bill or debt. - 152. ROLE. As the amount of $100 for the given time and proposed rate, is to $100, so is the debt to its true present worth and the present worth being subtracted from the debt, the remainder is the discount. : 100 Example 1.-Required the true present worth of $210, due at the end of a year, at 5 per cent. per annum. In this case, the amount As $105: $100:: $210: of $100 being $105, we have, by the rule, this analogy As $105 : $100 :: $210: $200, the true present worth required. : 105)21000($200 210 |