jured by a fire that he was willing to lose 40 per cent on the cost. What was the value of the goods after the fire? 7. A grocer bought 7 hhds. of wine, at $154.00 a hhd. But in transportation the head of one of them was stove in, so that it was entirely lost. On this account he was willing to lose 12 per cent. on the whole. What ought he to sell the remainder at pr. gal. ? 8. A piece of cloth valued at $1,635.00, and containing 75 yds. was so much damaged by being wet, that the owner offered it at a deduction of 23 per cent. At what price pr. yd. did he offer it? 9. A merchant in selling a quantity of goods for which he paid $230.00, made a profit of 25 dollars, At what per cent did he gain? Ans. 10 pr. ct. 10. A grocer gained on 16 hhds. of molasses, each of which cost him 25 dollars, $20.00. At what rate pr. ct. did he gain? Ans. 5 pr. ct. 11. A merchant sold 15 pieces of cloth, each containing 64 yds. at 5 dollars a yd.; also, 25 bls. of flour at 11 dollars per bl.; also, 130 cwt. of lead, at 8 cents per lb. On the whole he gained 500 dolls. At what pr. ct. did he gain? 12. Sold 275 bales of cotton at 11.5 cts. pr. lb., each bale containing 362 lbs.; and 278 hhds. of brandy at $1.25 per gal.; and 15 tons of iron at 4 cts. pr. lb. On the whole there was a gain of 628 dollars. At what pr. ct. was the gain? 13. Sold merchandize which cost 1,856 dollars, at $2,784.00. At what pr. ct. was the gain? 2,784-1,856-928 dolls., amount gained. Ans. 50 pr. ct. 14. A certain amount of merchandize which cost $2,940.00 was sold at $4,116.00. At what pr. ct. was the gain? Ans. 40 pr. ct. 15. On a quantity of flour a merchant gained 575 dollars, and his gain was at 5 pr. ct. What did the flour cost him? Ans. $11,500. 16. A man gained $846.00 on 8 pieces of cloth, each containing 282 yds., gaining at the rate of 6 pr. ct. What did the cloth cost him, and what did he sell it at pr. yd. ? Ans. Cost $6.25. Sold it at $6.625. 17. A man sold 1,722 bls. of sugar, each containing 2 cwt. 2 qrs. 13 lbs. at a profit of 15 pr. ct., and his gain amounted to $6,054.552. What cost the whole, and what did he sell it for. Also, what were the buying and selling prices pr. lb. ? Ans. Cost $40,363.68. Sold for $46,418.232. Cost pr. lb. 8 cts. Sold pr. lb. at 9.2 cts. 18. On 9,856 bu. of wheat a man gained $2,464.00, gaining at the rate of 12 pr. ct. What was the whole cost, the cost pr. bu., the whole price of sale, and the price of sale pr. bu.? 19. A merchant sold 279 cwt. (100 lb,) of rice, at a profit of $69.75, gaining 10 pr. ct. What cost the whole, what was the cost pr. lb., what was the whole price of sale, and the price of sale pr. lb. ? 20. A grocer sold 7,862 boxes Malaga raisins at a profit of 15 pr. ct., and his whole profit was $3,420,00. What cost the whole, and what did he gain pr. lb., supposing each box to contain 56 lbs.? 21. A merchant sold 500 yards of cloth at $3,500.00, by which he made a gain of 163 pr. ct. What did the cloth cost, and what did he gain pr. yd.? (See COMMISSION, ex. 6.) 22. A merchant sold 17 hhds. of brandy, and 25 hhds. of wine, for $4,600.00. The wine was worth pr. gal. 3 times as much as the brandy, and on the whole he gained 15 pr. ct. What were the buy. ing and selling prices of each pr. gal. ? § LXXVI. INTEREST. As the calculation of interest is of great importance to all classes of persons, we propose to examine it somewhat minutely. MENTAL EXERCISES. 1. If a dollar gain 6 cts. interest in a year, what will 2 dollars gain in the same time? 2. If a dollar gain 6 cts. interest in a year, what will 10 dollars gain in the same time? 3. If a dollar gain 6 cts. in 1 year, how much will it gain in 2 years? in 5 years? in 9 years? 4. If a dollar gain 6 cts. in 1 year, how much will it gain in 11 years? in 7 years? in 4 years? in 10 years? 5. If a dollar gain 6 cts. in a year, what will 50 cts., that is, half a dollar, gain in the same time? 6. If a dollar gain 6 cts. in 1 year, what will it gain in 6 mo., or half a year? 7. If a dollar gain 6 cts. in a year, what will 2 dollars gain in 6 months, or half a year? what will 3? 4? 7? 8? 8. If a dollar gain 6 cts. in one year, what will 2 dollars gain in 1 year and a half; that is in one year and 6 months? 9. If a dollar gain 6 cts. in a year, what will 7 dollars gain in 1 year and 6 months? what will 3? what will 4? 5? 8? 9? 10. If a dollar gain 6 cts. a year, what will it gain in 2 years and 6 months? what will 2 dollars gain in the same time? 11. What will 4 dollars gain in 4 years and 6 months, if 1 dollar gain 6 cts. a year? what will 5? 6? 7? 8 ? 9? 10? 11? 12? 12. If a dollar gain 5 cts. in a year, what will it gain in 2 years? what will 2 dollars gain in 2 years at that rate? what will 3? 13. If a dollar gain 7 cts. a year, what will it gain in 2 years? what will 3 dollars gain in 1 year? what will 3 dollars gain in 2 years? 14. If a dollar gain 8 cts. in one year, how much will 3 dollars gain in 5 years? 2 dollars in 3 years? 7 dollars in 2 years and 6 months ? INTEREST differs from the calculations of profit and loss, stock, and commission, in taking TIME into consideration. Thus on a note of two years' standing, twice as much interest must be paid, as upon a note of the same amount, of one years' standing. The same is true of insurance, but insurance is generally calculated for a number of even years; whereas, interest is estimated for months and days. A certain rate pr. ct. of interest is established by law, and this rate differs in different countries. This rate is allowed to be taken yearly, or, per annum, as it is expressed; which means, by the year. For parts of a year, as months and days, a proportion. al part of the interest per annum is allowed. The rate established by law is called LEGAL INTEREST. In NEW ENGLAND, the legal rate is 6 pr. ct.; in NEW YORK, 7 pr. ct.; and in other states various. This treatise is equally adapted to all. By saying that a rate of interest is established by law, we do not mean that this rate must always be allowed, but that no greater rate shall be required. Any less rate may be taken, which the parties shall agree upon. But if a greater rate be required than the legal rate, it is called USURY, and the person requiring it is subject to a penalty. When no mention is made of a particular rate, but the note or agreement says simply with interest, the legal interest is always understood, and may be collected by law. The sum of money on which interest is calculated is called the PRINCIPAL. The sum of the principal and interest is called the AMOUNT. YEARS. 1. What is the interest on $200.00, for one year at 6 pr. ct. pr. annum ? Ans. $12.00. At 6? 1. What is the interest on $300.00, for one year, at 4 pr. ct. pr. annum? Ans. $12.00. At 5 pr. ct. pr. an. ? Ans. $15.00. Ans. $18.00. At 7? Ans. $21.00. At 8? Ans. $24.00. Ans. $27.00. At 9 ? 3. What is the interest on $575.00 at 5 pr. ct. pr. an. ? At 6 pr. ct.? At 7? At 8? At 9 ? 4. What is the interest on $834.65 at 2 pr. ct. pr. an. ? At 3 pr. ct.? At 4? At 5? At 6? At 7? NOTE. The words per annum, or pr. an. are often omitted, but they must always be understood. When the interest is required for two years, you must double the rate before multiplying by it; when for three, make the rate three times as great, &c. For the interest of $100.00 at 6 pr. ct. for 2 years, is just as much as the interest of the same sum at 12 pr. ct. for one year; it being 12 dols. in each case. Hence, to find the interest of any sum for a number of even years, I. MULTIPLY THE GIVEN RATE IN DECIMALS, BY THE NUMBER OF YEARS, AND THE PRINCIPAL BY THAT product. Or, II. MULTIPLY THE PRINCIPAL BY THE RATE AND TIME SUCCESSIVELY. 5. What is the interest of $325.00 for 3 years at 6 pr. ct.? Ans. $58.50. 6. What is the interest of $233.00 at 5 pr. ct. for 7 years? Ans. $81.55. 7. What is the interest of $647.33 at 6 pr. ct. for 8 years? Ans. $620. NOTE. The amount may be found by adding the principal to the interest, or by adding a unit to the rate before multiplying. (§LXXIV.) 10. What is the amount of $850.00 for 5 years at 6 pr. ct.? A. $1,105. 11. What is the amount of $1,000 at 7 pr. ct. for 8 years? A. $1,560. 12. What is the amount of $1,275.63 for 9 years at 5 pr. ct.? 13. What is the amount of $9,653.61 for 10 years, at 6 pr. ct.? 14. What is the amount of $11,943.11 for 11 years, at 8 pr. ct. ? § LXXVII. MONTHS. It will be observed that when the time is a number of even years, it is as easy to calculate interest at one rate as at another; since the rule is the same for all. Whatever be the rate pr. cent., then, if the time be even years, let the pupil proceed as in the last section. But when there are months and days, 6 pr. ct. is the easiest rate. In the following examples then, 6 per. ct. may be understood, unless another rate be expressed. Particular rules will, afterwards, be given, for calculating interest at different rates. MENTAL EXERCISES. 1. If the rate for a year (12 months) be 6 pr. ct., what ought it to be for half a year, that is for six months? 2. If the rate for 6 months be 3 pr. ct., what ought it to be for 2 months ? 3. If the rate for two months be 1 pr. ct., what ought it to be for 4 months? What for 8 months? What for 10 months? 4. If the rate for 2 months be pr. ct. what ought it to be for 1 month? For 3 months? For 5 months? For 7 months? For 9 months? For 11 months? Here the pupil will observe, that the rate per ct. is always just half the number of months. The same is true if we go above a year, thus, 5. Ifthe rate for 2 months be 1 pr. ct., what is that for 14 months? For 16 months? For 18 months? For 20 months? 6. If the rate for 1 month be pr. ct., what is that for 13 months? For 15 months? For 17 months? For 19 months? Hence, when interest is at 6 pr. ct. pr. an... THE RATE FOR ANY NUMBER OF MONTHS, IS HALF THE NUMBER OF MONTHS. Let the following be written. 1. What is the interest on $98.75 for 2 months? Half of 2 months is 1 month. 1 pr. ct. then, is the rate. 98.75X.01 $0.9875 Ans. A. $0.83325. 2. What is the interest on $29.25, for 4 months? Half of 4 is 2. Therefore the rate is 2 pr. ct. Ans. $0.585. 3. Find the interest on $33.33 for 5 months. NOTE. In practice, neglect the decimals of a mill if under .5 or a mill; if equal to or over, add another mill instead of them. Or, rather, men in business usually neglect the mills, if under half a cent, if equal to or over, they add another cent instead of them. This is only to be done in the final result. If done before multiplying, it will make too great an error. In the examples, thus far given, however, the decimals have been retained, in order to insure perfect accuracy in the operations. 4. What is the interest on 72.05 for 3 months? Half of 3 is 1. Therefore the rate is 1 pr. ct.-.015. A. $1.08075. 5. What is the interest on $294.63 for 6 months? A. $8.8389. 6. Find the interest on $765.23 for 7 months. A. $25.78305. 7. Find the interest on $895.64 for 8 months. A. $35,8256. 8. Find the interest on $934.31 for 9 months. 9. Find the interest on $1.853.63 for 10 months. 10. Find the interest on $3.293 for 11 months. 11. Find the interest on $7.86345 for 11 months. NOTE. The pupil may, in the examples which follow, multiply by the rules given in § LXIII., Multiplication of decimals, retaining decimals only to three places, or mills. The nearest mill is usually given in the answer. 12. What is the interest of $243.23 for 14 months? A. $17.026 13. What is the interest of $147.96 for 6 months? A. $4.439 14. Find the interest on $15.125 for 11 months. A. $0.832 15. Find the interest on $28.14 for 5 months. A. $0.703 16. Find the interest on $284.85 for 3 months. A. $4.273 17. Find the interest on $396.27 for 7 months. 18. Find the interest on $19.395 for 9 months. 19. Find the interest on $1,288.91 for 10 months. 20. Find the interest on $2,956.84 for 11 months. The 21. What is the interest on $37.00 for 2 years and 4 months? In this example, we may either reduce the whole time to months, and find the rate by taking half, as usual; or we may find the rates for the years and months separately, and add them together. latter mode is best, when the number of years is great. Rate for 2 years =2×.06=.12; for 4 months =.02 .12+.02= .14, rate for the whole time. Ans. $5.18. 22. Find the interest on $834.31 for 3 years and 8 months. Ans. 183.5482. 23. Find the interest on $976.24 for 5 years and 7 months. |