5. Interest of $85 for 10 mo. 15 days, at 12 per cent.? 6. What is the amount of $53 at 10 per ct. for 7 mo. ? Ans. $56'091. The time, rate per cent. and amount given, to find the principal. ¶ 85. 1. What sum of money, put at interest at 6 per cent., will amount to $61'02, in 1 year 4 months? = The amount of $1, at the given rate and time, is $1'08; hence, $61'02 $1'08 56'50, the principal required; that is, Find the amount of $1 at the given rate and time, by which divide the given amount; the quotient will be the principal required. Ans. $56'50. 2. What principal, at 8 per cent., in 1 year 6 months, will amount to $85'12? Ans. $76. 3. What principal, at 6 per cent., in 11 months 9 days, will amount to $99'311? Note. The interest of $1, for the given time, is '056; but, in these cases, when there are odd days, instead of writing the parts of a mill as a common fraction, it will be more convenient to write them as a decimal, thus, '0565; that is, extend the decimal to four places. Ans. $94. 4. Á factor receives $988 to lay out after deducting his commission of 4 per cent.; how much will remain to be laid out? It is evident, he ought not to receive commission on his own money. This question, therefore, in principle, does not differ from the preceding. Note. In questions like this, where no respect is had to time, (T 81, ex. 4, note,) add the rate to $1. Ans. $950. 5. A factor receives $1008 to lay out after deducting his commission of 5 per cent.; what does his commission amount to? Ans. $48. DISCOUNT. 6. Suppose I owe a man $397'50, to be paid in 1 year, without interest, and I wish to pay him now; how much ought I to pay him when the usual rate is 6 per cent.? I ought to pay him such a sum as, put at interest, would, in 1 year, amount to $397'50. The question, therefore, does not differ from the preceding. Ans. $375. Note. An allowance made for the payment of any sum of money before it becomes due, as in the last example, is called Discount. The sum which, put at interest, would, in the time and at the rate per cent. for which discount is to be made, amount to the given sum, or debt, is called the present worth. 7. What is the present worth of $834, payable in 1 year 7 months and 6 days, discounting at the rate of 7 per cent.? Ans. $750. 8. What is the discount on $321'63, due 4 years hence, discounting at the rate of 6 per cent. ? Ans. $62'26. 9. How much ready money must be paid for a note of $18, due 15 months hence, discounting at the rate of 6 per cent. ? Ans. $16'744. 10. Sold goods for $650, payable one half in 4 months, and the other half in 8 months; what must be discounted for present payment? Ans. $18 11. What is the present worth of $56'20, payable in 1 year 8 months, discounting at 6 per cent. ? at 4 per cent.? at 5 per cent.? - at 7 per cent. ? - at Ans. to the last, $48'869. The time, rate per cent., and interest being given, to find the principal. ¶ 86. 1. What sum of money, put at interest 16 months, will gain $10'50, at 6 per cent. ? = $1, at the given rate and time, will gain '08; hence, $10'50 $ '08 $131'25, the principal required; that is, Find the interest of $1, at the given rate and time, by which divide the given gain, or interest; the quotient will be the principal required. Ans. $131'25. 2. A man paid $4'52 interest, at the rate of 6 per cent. at the end of 1 year 4 months; what was the principal ? Ans. $56'50. 3. A man received, for interest on a certain note, at the end of 1 year, $20; what was the principal, allowing the rate to have been 6 per cent.? Ans. $333'3334. The principal, interest, and time being given, to find the rate per cent. 87. 1. If I pay $378 interest, for the use of $36 for 1 year and 6 months, what is that per cent.? The interest on $36, at one per cent. the given time, is $ '54; hence, $378 ÷ $'54 = '07, the rate required; that is,~ Find the interest on the given sum, at 1 per cent. for the given time, by which divide the given interest; the quotient will be the rate at which interest was paid. Ans. 7 per cent. 1 month, what is Ans. 6 2. If I pay $2'34 for the use of $468, the rate per cent.? per cent. 3. At $46'80 for the use of $520, 2 years, what is that per cent.? Ans. 44 per cent. The prices at which goods are bought and sold being given, to find the rate per cent. of GAIN or LOSS. T 88. 1. If I purchase wheat at $1'10 per bushel, and sell it at $1'37 per bushel, what do I gain per cent. ? $275 This question does not differ essentially from those in the foregoing paragraph. Subtracting the cost from the price at sale, it is evident I gain 272 cents on a bushel, that is, of the first cost. 27525 per cent., the Answer. That is, -Make a common fraction, writing the gain or loss for the numerator, and the price at which the article was bought for the denominator; then reduce it to a decimal. 110 1610 amount of $ 550 ; 2. A merchant purchases goods to the what per cent. profit must he make to gain $ 66 ? 3. Ans. 12 per cent. What per cent. profit must he make on the same purchase to gain $38'50? -to gain $24'75? gain $275? to Note. The last gain gives for a quotient '005, which is per cent. The rate per cent., it must be recollected, (¶ 81, note,) is a decimal carried to two places, or hundredths; all decimal expressions lower than hundredths are parts of 1 per cent. 4. Bought a hogshead of rum, containing 114 gallons, at 96 cents per gallon, and sold it again at $1'0032 per gallon; what was the whole gain, and what was the gain per cent. ? $4'924, whole gain. 4 gain per cent. Ans. { 5. A merchant bought a quantity of tea for $365, which, proving to have been damaged, he sold for $332'15; what did he lose per cent. ? Ans. 9 per cent. 6. If I buy cloth at $2 per yard, and sell it for $2'50 per yard, what should I gain in laying out $100 ? Ans. $25. 7. Bought indigo at $1'20 per lb., and sold the same at 90 cents per lb.; what was lost per cent.? Ans. 25 per cent. 8. Bought 30 hogsheads of molasses, at $600; paid in duties $20'66; for freight, $40'78; for porterage, $6'05, and for insurance, $30'84: if I sell them at $26 per hogshead, how much shall I gain per cent.? Ans. 11'695 per cent. The principal, rate per cent., and interest being given, to find the time. ¶ 89. 1. The interest on a note of $36, at 7 per cent., was $378; what was the time? 1 The interest on $36, 1 year, at 7 per cent., is $2'52; hence, $378 $2'52 1'5 years, the time required; that ÷ is,—Find the interest for 1 year on the principal given, at the given rate, by which divide the given interest; the quotient will be the time required, in years and decimal parts of a year; the latter may then be reduced to months and days. Ans. 1 year 6 months. 2. If $3171 interest be paid on a note of $226'50, what was the time, the rate being 6 per cent. ? Ans. 26331 = 2 years 4 months. 3. On a note of $600, paid interest $20, at 8 per cent. ; what was the time? Ans. '416+ 5 months so nearly as to be called 5, and would be exactly 5 but for the fraction lost. 4. The interest on a note of $217'25, at 4 per cent., was $28'242; what was the time? Ans. 3 years 3 months. Note. When the rate is 6 per cent., we may divide the interest by the principal, removing the separatrix two places to the left, and the quotient will be the answer in months. To find the interest due on notes, &c. when partial payments have been made. ¶ 90. In Massachusetts the law provides, that payments shall be applied to keep down the interest, and that neither interest nor payment shall ever draw interest. Hence, if the payment at any time exceed the interest computed to the same time, that excess is taken from the principal; but if the payment be less than the interest, the principal remains unaltered. Wherefore, we have this RULE:-Compute the interest to the first time when a payment was made, which, either alone, or together with the preceding payments, if any, exceeds the interest then due; add that interest to the principal, and from the sum subtract the payment, or the sum of the payments, made within the time for which the interest was computed, and the remainder will be a new principal, with which proceed as with the first. 1. For value received, I promise to pay JAMES CONANT, or order, one hundred sixteen dollars sixty-six cents and six mills, with interest. May 1, 1822. $116,666. SAMUEL ROOD. On this note were the following endorsements: Dec. 25, 1822, received $ 16'666 The first principal on interest from May 1, 1822, $116'666 Interest to Dec. 25, 1822, time of the first pay ment, (7 months 24 days,) Payment, Dec. 25, exceeding interest then due, 4'549 Amount, $121'215 16'666 104'549 15'490 Interest from Dec. 25, 1822, to June 14, 1825, Remainder for a new principal, (29 months 19 days,) Amount carried forward, $120'039 |