10. Required the commission on $649 75c. at 13 per cent. 649.75 162.4375 1137 0625 Ans. $11 37c. 0m. BROKERAGE Is an allowance of so much per cent. to a person called a Broker, for assisting merchants in purchasing or selling goods. 11. Required the Brokerage on £911 12s. at 5s. or per cent. 58.1911 12 12. Required the Brokerage on $876 21c. at 33 cents, or at per cent. 1876.21 292.07 Ans. $2 92c. 0m. BUYING AND SELLING STOCKS. Stock is a general name for the capitals of trading companies, or, of a fund established by government, the value of which is variable. 13. Required the amount of £375 159. bank stock, at £75 per cent? 50375 15 Or thus: 251 375 15 Subtract 93 18 9 |25|1|187 17 6 93 18 9 Ans. £281 16 3 As before, £281 16 3 14. Required the amount of $2195 50c. bank stock, at 125 per cent. 12512195-50 Ans. $2744-375 15. What is the value of $6950 at 105 per cent? Ans. $7297 50cts. 16. Value of £225 of stock at 95 per cent.? Ans. £213 15. 1 TO CALCULATE INTEREST FOR DAYS. RULE I. Multiply the principal by the days, and that product by the rate, and divide the last product by 365×100.* 15. Required the interest of £360 10s. for 175 cent. 360.5X175X6 100X365 = £10.17 days, at 6 per £10 7s. 4 d. Rule for making a divisor for any Rate. Multiply 365 by 100, and divide by the rate. Thus, for 6 per * This rule is the result of a statement in the Double Rule of Three, as follows. £ Rate. Prin. As 100 And as 365: to the Rule we have 6: 360-5: the interest for 1 year. Days. :: 175: the interest for 175 days. Wrought according 360-5X175X6 The rule for finding a divisor for any Rate, is a contraction of this result. 360-5X175X6 X175X =360.5 X 175X; 6 But dividing both parts of the 1 =360·5 × 175 X6083 6 Therefore 360-3 In the same way divisors 6 365 X 100 are formed for any other rate. Hence too, the 2d Rule is obvious, for 360.5 X 175 6083 the interest, and is the product of the principal and days divided by the divisor formed as above. When the time is given in months, the divisor is formed in a similar manner. Suppose in the last example the time had been 11 months. Then, As 1006: 360-5: the interest for a year, and as 12: Note. As 365 days: 5 per cent. :: 7300 days : 100 per cent. And as 12 months: 5 per cent. :: 240 months: 100 per cent. Hence it is evident that if the Rate be 5, any principal will gain 100 per cent. that is, will double in 7300 days or 240 months. And at 6 per cent. any sum will double in 6083 days, or 200 months, and at 7 per cent. in 52143 days, or 1712 months. RULE II. Multiply the principal by the days; divide by 6083 for 6 per cent. and 7300 for 5 per cent. (the days in which any sum will double at those rates) and the quotient is the interest. For months, multiply the principal by them, and divide by 200 for 6 per cent. or 240 for 5 per cent. (the months in which any sum will double at those rates) and the quotient is the answer. Hence, when interest is to be calculated on cash accounts, or accounts current, where partial payments are made, or partial debts contracted; multiply the several balances into the days they are at interest, which should be done at every transaction, and the sum of these products divided by 6083 and 7300 will give the interest at 6 and 5 per cent. For any other rate, make the proper addition or deduction, or find a divisor as before directed. When partial payments are made at short periods, subtract the several payments from the original sum in their order, placing their dates in the margin. 16. Suppose a bill of $359 was due January 1, 1807; that $75 was paid February 3d, $50 March 5th, $80 April 9th, and June 7th, $145: What interest is due at 5, 6 and 7 per cent.? After the dates are placed in the margin, the number of days in each of those periods is to be computed and marked against its respective sum lastly, divide the sum of the products by 6083, &c. Interest on accounts current is calculated nearly in the same manner. 17. Compute the interest at 6 per cent. on the following account to August 10th. Dr. 1807. Jan. 1, To Cash, Mr. A. Jones, his account current, with B. Carr, Cr. Feb. 10, To do. May 15, To do. Here the sums on either side are introduced according to the order of their dates; those on the Dr. side are added to the former balance, and those on the Cr. side subtracted. Before we calculate the days, we try if the last sum $250 be equal to the balance of the account, which proves the additions and subtractions. And before multiplying we try if the sum of the column of days be equal to the number of days from January 1 to August 10. When payments are made at considerably distant periods, it is usual to calculate the interest to the date of each payment, and add it to the principal, and then subtract the payment from the amount. 18. A note was given for $540 the 18th August, 1304, and there was paid the 19th of March, 1805, $50, and the 19th of December, 1805, $25; and the 23d of September, 1806, $25; and the 18th of August, 1807, $110: Required the interest, and balance due on the 11th of November, 1807, at 6 per cent.? A note given 18th August, 1804, for Interest to 19th March, 1805, 218 days, $19-352 Paid 19th March, 1805, $540 19.352 559-352 50 19. A owes B the following sums, with interest at 6 per cent. per annum: $60 for 7 months, $150 for 9 months, $75.50 for 3 months, $365-25 for 8 months, and 510-20 for 5 months: Required the amount? 20. A note for $1000 is given January 1, 1803, with interest at 6 per cent per annum; February 19, 1803, $100 are paid; June 7, 1803, $150; April 14, 1804, $37-50; July 11, 1804, $75; Sept. 29, 1804, $250; Dec. 17, 1805, $39; March 4, 1806, $175: Ang. 7, 1806, $105; Oct. 30, 1806, $50; May 12, 1807, $40, and Nov. 17, 1807, 2: How much is due, January 1, 1803? |