means of aliquot parts, or otherwise: the sum of all will be the whole price required. Exam. 5. Required the price of 79 yards 3 qrs. of cloth, at £1 28. 11d. per yard? 79 yds. 3 qrs. at £1 2s. 11d. per yd. £91 7s. 74d. Ans. yard. In resolving this example, the price of 79 yards is first found, (or rather the parts of which it is made up are found ;) and then for half a yard the half of £1 2s. 11d. is taken, and for a quarter of a yard the half of that is taken then the sum of all those parts is £91 7s. 71d. the result required. Exam. 5. What $5.62 per acre? : cost 135 acres, 3 roods, 20 poles, at 135 acrs. 3 r. 20 p. at $5.62 per acre. $135 the price of 135 acrs. at $1 per acr. 5 Ans. $764-2911 the price of 135 acres, 3 roods, 20 poles, at $5.621 per acre. Ex. 16. What cost 2363 yards of carpeting, at $1-311 per yard? Ans. $310.731. 17. What cost 165 cwt. 3 qrs. 14 lbs. of pork, short weight, at $5.432 per cwt. 18. What is the cost of a farm, rood, 30 poles, at $6.80 per acre? 19. What cost 105 tons, 17 cwt. 3 at $9.60 per cwt.? Ans. $901.94.3. containing 256 acres, 1 Ans. $1743-77.5. qrs. 20 lbs. of sugar, Ans. $20332.11.3+. 239. RULE V.-In many calculations, instead of multiplying the quantity by the price, it is better to multiply the price by the quantity. This is often the case, when compound multiplication can conveniently be employed. Exam. 6. Required the price of 12 cwt. 2 qrs. 8 lbs. of hops, at £6 16s. 6d. per cwt.? 12 cwt. 2 qrs. 8 lbs. at £6 16 6 Ex. 20. Required the price of 18 cwt. 3 qrs. 24 lbs. of hops, at $16.87 per cwt. 21. The quantity of wool was 4337 cwt. 3 qrs. 8 lbs. 71⁄2d. per cwt. Ans. $319.92.7+. exported from Ireland in 1806, What was the value at £3 198. Ans. £17269 18s. 10d. 22. What is the freight of 39 tons, 17 cwt. 3 qrs. of ashes, at £1 17s. 6d. sterling money per ton, which is the usual freight at present from New-York to Liverpool? Ans. £74 15s. 9ld. 240. RULE I.-To find the interest of a given sum for any number of days: multiply the principal, the days, and twice the rate, continually together; and divide the product by 73000. Exam. 7. What is the interest of $372.50, from February 12, till December 17, 1827, at 42 per cent. per annum? Here, $372.50×308, (the number of days from February 12, till December 17,) $114730.00; this multiplied by 9, (the double of the rate,) =1032570.00; and $1032570.00 73000-$14.142, the answer.* * The reason of the rule will be evident from the operation in compound proportion, if instead of $100 and the rate per cent. their doubles be employed. Thus, we should have in this example, As $100: $9 365 days: 308 days :: $372.50 : $14.14); and in working this, we should, by the rule for compound proportion, multiply together the principal, the days, and twice the rate, and divide the product by 365X200, or 73000. 241. When the rate is 5 per cent., divide the product of the principal and days by 7300; for other rates than 5 per cent., increase or diminish the product of the principal and days, by the method of aliquot parts, and then proceed by the rule.* Exam. 8. Required the interest of $250 for 63 days, at 6 per cent. per annum. Here, $250×63=$15750, to which add one-fifth of itself, and the sum will be $18900; then, $18900÷7300=$2.59, nearly, the interest required. 242. RULE II. To find the discount of a given sum for 60 days, at 6 per cent., as practised in the banks of NewYork: divide the given sum by 100, and the quotient will be the discount required. For any other number of days than 60, increase or diminish the given sum, by the method of aliquot parts, and then proceed by the rule. Exam. 9. What is the discount on a note of $575, that has 60 days to run, at 6 per cent. per annum? Here, $575-100-$5.75, the discount.† Ex. 23. What is the discount on a note of $675, for 63 days, at 6 per cent. per annum ? Ans. $7.08.7 24. What is the discount on a note for $1150.75, for 90 days, at 6 per cent. per annum? Ans. $17.26.11. The following is another false rule, that is generally used in computing discount on notes. 243. RULE III.—To find the bank discount on notes that have 33, 63, or any number of days to run, inclu *The reason of this rule is obvious from the last, since the double of 5 is 10, and 73000-10-7300. †The reason of this rule is obvious from the operation in compound proportion, and from this false principle, the year being reckoned only 360 days: thus, As $100: $6 45 days: 80 days} :: $575: $5.75; Or, as $100 $1 :: $575: $5.75. If it had 63 days to run, add the one-twentieth of $5.75 to itself, and the sum, $6.034, will be the discount for 63 days; this is obvious, since 3 days is the one-twentieth of 60 days. ding 3 days of grace: multiply the amount of the note by the number of days it has to run, and divide that product by 6000; the quotient will be the discount required. Exam. 10. What is the discount on a note of $500, for 33 days, at 6 per cent. per annum ? Here, $500×33=$16500; then, $16500÷6000=$2.75, the discount required.* Ex. 25. What is the discount of $9760, for 63 days, at 6 Ans. $102.48. per cent. per annum ? 26. What is the discount of $870.75, for 93 days, at 6 Ans. $13.49.65. per cent. per annum? 244. RULE IV.-To find the interest of a given sum for any number of days. Multiply the principal, the days, the rate, and 274, continually together; reject from the resulting product four figures to the right, and the remainder will be the interest in mills. If the principal contain dollars and cents, six figures must be rejected from the product. Exam. 11. Find the interest of $619 for 126 days, at 5 per cent. per annum. Here, 619×126×5×274=106851780; then, rejecting four figures to the right, we have 10685 mills, or $10.681, the interest required.† Ex. 27. Find the interest of $754.87 for 147 days, at 6 Ans. $18.24.3, nearly. per cent. per annum. *The reason of this rule depends upon the same principle as the last: that is, As $100 $6 360 days: 33 days :: $500 : $2.75; Or, as 6000: 33:: $500: $2.75, since 360×100÷66000. The reason of this rule is evident from compound proportion and decimals. Thus, in this example, we should have, As $100: $5 365 days: 126 days: $619 : $10.684; Here, instead of dividing the continual product of 619, 126, and 5, according to the rule of compound proportion, we multiply it by .0000274, which is found by dividing 1 by 36500; or, which is the same thing, by multiplying the product by 274, and rejecting four figures, the remainder will be mills. When the time and principal are not very great, this rule will be found extremely near the truth; in large amounts, it may be corrected by deducting one cent for every $100 in the answer. |