Here the time is 61 days. £78 15 × 61 = 4803 ÷ 6000 = 800 ≈ 16 0 Bill....78 15 0 Discount 15 9 75 = 2 Answer 77 19 2 7. What is the present worth of a bill of 2157, drawn on the 1st of March at 6 months, and discounted the 7th of June at 5 per cent per annum? This bill will be due on the 4th of September, and from the 7th of June to this date the number of days is 89. Find the present worths of the bills described under, at the given rates per cent per annum, and for the given times, each respectively. 4th of April at 3 mo. May March 10th at 5 ds. April 11th at 6 11. 427 13 4 12. 343 12 6 13. 108 10 14. 714 16 0 7th of April at 41 ds. 15th of April at 61 ds. 1st of May at 91 ds. 10th of May at 4 mo, April 21st at 5 April 21st at 6 June 17th at 6 6 mo. Aug, 21st at 6 at 3 mo. Aug. 21st at 5 1st of June at 91 ds. July 14th at 6 7th of June at 4 mo. Aug. 21st at 6 21st at 5 19. 815 11 8 11th of June at 3 mo. July 20. 743 12 6 20th of June at 91 ds. July 21st at 6 CASE 3d.-When several bills or sums at different times of payment are to be discounted. Multiply each amount by its time, until due, add the pros ducts together, and find the discount of their sum as before. 21. Find the discount to be allowed on the following bijis, discount as interest, at 6 per cent per annum? 22. What is the present worth of the following 6 bills, discount as interest, at 6 per cent per annum; the first 170 10s. payable in 32 days, the second 145/ 4s. 8d. payable in 37 days, the third 1201 16s. 3d. payable in 45 days, the fourth 1107 13s. 4d. payable in 79 days, the fifth 1501 15s Od payable in 43 days, and the sixth 1337 12s. 6d. payable in 60 days? f To find the true present worth, or discount of any sum, payable at any time to come, the following is the rule :— As 100 with its interest for the given time, added thereto, is to the sum to be discounted, so is 100, to the present worth required. And this present worth subtracted from the debt, gives the discount. Or, as 100 with its interest added thereto, is to the given sum to be discounted, so is the interest of 1001, to the true discount; and this discount subtracted from the debt, will give the true present worth, the same as if the former rule had been employed. Examples. 23. What is the true present worth of a bill for 1481, dus at the end of 3 months, at 6 per cent. per annum? The interest of 1007 for 3 months, is 17 10s. Od. As 101 10: 148: 100 24. What is the true present worth of a bill of 787 15s. Od. due on the first of August, but paid on the 5th of June pres ceding, at 6 per cent per annum ? 1010027) 78750000 ( 77,968 707018977 19 4 Answer. 8048110 7070189 977921 909024 68897 · 60601 8296 8080 216 25. What is the true discount of a bill of 2157, drawn on the 1st of March, at 6 months, and discounted on the 7th of June, at 5 per cent per annum ? Here the number of days is 89. 89 356 days X4 70)85,44 1,2203 Correction, Interest of 100/ for given days, 1,2195 Should it be thought necessary for the Pupil to calculate discountcorrectly, the examples already given will be sufficient for the purpose, and by working those both ways, he will see the comparative advantages and disadvantages of the two methods, EQUATION OF PAYMENTS: Equation of payments, is the finding of a time to pay at once several debts due at different times to come, so that neither the holder nor receiver should suffer loss. RULE.-Multiply each payment by the time when it is due, and divide the sum of these products by the sum of the payments, the quotient is the equated time sought. Proof. If the interest of the sum of the payments for the equated time, be equal to the sum of the interest of the separate payments, the work is right,* I am aware that some have questioned the mathematical accuracy of the above rule; but for a demonstration, and other observations. thereon, I refer the reader to John Walker's Philosophy of Arithmetic, pages 63 and 64,. : Examples. 1. A merchant sells goods belonging to his correspondent, as follows to A. to the amount of 2751, payable in 3 months, to B. 2001, payable in 1 month, and to C. 2541, payable in cash at what date ought his correspondent to draw in one sum for the whole, allowing each month 30 days? 275 3 = 825 254 X 0 = 0 729) 1025(14 mo. or 32 days. 729 2. A. owes B. 251 payable in I month, 301 payable in two months; 457 to be paid in 3 months, and 157 to be paid in 4 months; what is the equated time for the payment of the whole? 3. A. purchases goods from. B. on the 15th of January, amounting to 2751; on the 1st of February, to the amount of 1251; on the 10th of March, to the amount of 3121; he is allowed 3 months credit on each purchase, but wishes to give B. a bill for the whole, at 31 days date; when should it be dated, it being a common year? 4. Received invoice of sundry goods to sell for account of A. B. which I disposed of as follows: To A. to the amount of 1501 payable in 91 days. of 1751 payable in 61 days. of 2007 payable in 124 days. . of 180 payable in cash. At what rate ought A.B. to draw on me in one bill for the whole ? 5. Suppose a debt is to be discharged thus, 4 at present, in 31 days, at 61 days, and the remainder in 91 days; what time may the whole be paid at once? 6. Suppose I have received at Limerick the following bills, all payable in that city; 100/ due in 4 months, 2007 at 3 months, 150% at 2 months, and 2507 at 1 month, and agree to pay a banker there, a reasonable commission and expense of stamp at what date ought he to give me a bill on Dublin for the whole ?? |