To find the amount of a note by compound interest, when there have been partial payments. RULE. Find the amount of the principal, and from it subtract the amount of the endorsements. EXAMPLES. 13. A., by his note, dated January 1, 1830, promises to pay B. $500 on demand. On this note are the following endorsements. July 16, 1830, received two hundred dollars. August 21, 1831, received two hundred dollars. December 1, 1832, received one hundred dollars. What was the balance Sept. 1, 1884 ? ($100.) Ans. $52.73.0. Boston, Sept. 25, 1833. For value received, I promise Peter Absalom, to pay him, or order, on demand, one hundred dollars, with interest after six months. J. P. Jay. On this note are the following endorsements. June 11, 1834, received fifty dollars. Sept. 25, 1834, received fifty dollars. What was due August 25, 1835 ? Ans. $2.24.7. SECTION XL. PRACTICE. PRACTICE is an expeditious way of performing questions in Compound Multiplication and Proportion. RULE. Assume the price at some unit higher than the given price; that is, if the price be pence, or pence and farthings, assume the price at a shilling a yard, or pound, &c. If the price be in shillings, or shillings and pence, &c., assume the price at a pound, a yard, &c.; then take the aliquot parts of a pound. 1. What will 368 yards of ribbon cost, at 6 pence a yard ? 6d.=)368s. 20) 184 Ans. 9£. 4s. We assume the price at a shilling a yard, and then say, if 368 shillings be the price, at a shilling a yard, at 6 pence it must be half as much, viz. 184 shillings. 9£. 4s. We then reduce the shillings to pounds. 2. What will 4785 yards of cotton cost, at 8 pence per yard? Ans. 159£. 10s. Od. ́ Having found the price at 6d. as before, we find it for the 2d., by saying, that 2d. is of 6d. 3. What is the interest of $368, at 15 per cent. ? 10 per cent.=)368 5.=)36.80 $55.20 Ans. $55.20. 4. What is the value of 17 acres, 3 roods, and 35 rods of land, 388 at $80 per acre? 80 17 Ans. $1437.50. By dividing the price of 1 acre by 2, we obtain the price of 2 R. and by halving this, we find the price of 1 R.; and as 20 rods is half of a rood, its value will be one half; and in the same manner 10 rods will be half the price of 20 rods, and 5 rods will be half the price of 10 r. 5. What cost 14 tons, 15 cwt. 3 qr. 21 lbs. of iron, at $120 per ton? Ans. $1775.62.5. $1775.62.5 do. 14 T. 15 cwt. 3 gr. 21 lb. = 6. What cost 387 lbs. of sugar, at 9 pence a pound? Ans. 14£. 10s. 3d. 7. What cost 498 lbs. of green tea, at 2 shillings and 6 pence per pound? Ans. 62£. 5s. Od. 8. What cost 384 yards of cloth, at 4 shillings and 9 pence a yard? 9. What cost 714 yards of broadcloth, pence per yard? Ans. 91£. 4s. Od. at 15 shillings and 6 Ans. 553£. 7s. Od. 10. What cost 16 cwt. 3 quarters, and 10 lbs. of copperas, at $2.50 per cwt.? Ans. $42.09.8. 11. What cost 27 cwt. 1 quarter, 21 lbs. of coffee, at $14 per cwt. ? Ans. $884.12. 12. What cost 7 tons, 18 cwt., 2 quarters, and 7 lbs. of hay, at $24.60 per ton? Ans. $183.88.13. 13. If 1 acre of land cost $80.50, what will 25 acres, 2 roods, and 35 rods cost? Ans. $2070.35.98. 14. If 1 acre cost $32.32, what will 51 acres, 0 R. 15 rods cost? Ans. $1651.35. 15. If 1 yard of cloth cost $5.60, what will 7 yards, 3 qrs. and 2 nails cost? Ans. $44.10. 16. What is the premium on $6780, at 124 per cent. ? Ans. $847.50. 17. What is the interest of $1728, for 5 years, 7 months, and 20 days? Ans. $584.64. 18. What will 19 tons, 19 cwt. 3 qr. 273 lbs. of copperas cost at 19£. 193. 11. per ton? Ans. 399£. 19s. 51661d. 17920 SECTION XLI. EQUATION OF PAYMENTS. WHEN several sums of money, to be paid at different times, are reduced to a mean time, for the payment of the whole, without gain or loss to the debtor or creditor, it is called Equation of Payments. EXAMPLES. 1. A owes B $19; $5 of which is to be paid in 6 months, $6 in 7 months, and $8 in 10 months. What is the equated time for the payment of the whole ? OPERATION. $5 X 6=30 $6 X 7 42 $8 X 1080 19 19)152(8 months. By analysis. $5 for 6 months is the same as $1 for 30 months; and $6 for 7 months, is the same as $1 for 42 months; and $8 for 10 months, is the same as $1 for 80 months; therefore $1, for 30+ 42 +80=152 months, is the same as $5 for 6 months, $6 for 7 months, and $8 for 10 months; but $5, $6, and $8 are $19; therefore $1 for 152 months, is the same as $19 for of 152 months, which is 8 months, as before. Hence the propriety of the following RULE.* Multiply each payment by the time, at which it is due; then divide the sum of the products by the sum of the payments, and the quotient will be the true time required. 2. A owes B $300, of which $50 is to be paid in 2 months, $100 in 5 months, and the remainder in 8 months. What is the equated time for the whole sum ? Ans. 6 months. 3. There is owing to a merchant $1000; $200 of it is to be paid in 3 months, $300 in 5 months, and the remainder in 10 months. What is the equated time for the payment of the whole sum? Ans. 7 months, 3 days. 4. A owes B $150, $50 to be paid in 4 months, and $100 in 8 months. Bowes A $250 to be paid in 10 months. It is agreed between them, that A shall make present payment of his whole debt, and that B shall pay his so much sooner as to balance the favor. I demand the time at which B must pay the $250 ? Ans. 6 months. 5. A merchant has $144 due him, to be paid in 7 months, but the debtor agrees to pay ready money, and in 4 months. What time should be allowed him to pay the remainder ? Ans. 2 years, 10 months. 6. There is due to a merchant $800, of which is to be paid in 2 months, in 3 months, and the remainder in six months; but the debtor agrees to pay down. How long may the debtor retain the other half so that neither party may sustain loss? Ans. 83 months. 7. I have purchased goods of A. B. at sundry times and on various terms of credit, as by the statement annexed. When is the medium time of payment ? Jan. 1, a bill amounting to $375.50 on 4 months' credit. 20, do. do. Feb. 4, do. do. 168.75 on 5 months' credit. 386.25 on 4 months' credit. 144.60 on 5 months' credit. 386.90 on 3 months' credit. *This is the rule usually adopted by merchants, but it is not perfectly correct; for if I owe a man $200, and $100 of which I was to pay down, and the other $100 in two years, the equated time for the payment of both sums would be one year. It is evident that for deferring the payment of the first $100 for 1 year, I ought to pay the amount of $100 for that time, which is $106; but for the other $100, which I pay a year before it is due, I ought to pay the present worth of $100, which is $94.333, whereas, by Equation of Payments, I only pay $200. Strict justice would therefore demand, that interest should be required on all sums from the time they become due, until the time of payment; and the present worth of all sums, paid before they are due. The better rule would be to find the present worth on each of the sums due, and then find in what time the sum of these present worths would amount to the payments. |