8. Required the time when the following note will become legally due, and the bank discount, provided it was discounted May 16, 1856, the rate being 7 per cent. $ SOO-rW Chicago, April 16, 1856. One hundred and twenty days after date, I promise to pay to the order of Keen and Lee eight hundred and ninety -ftpa dollars, at the Marine Bank. Thomas L. Cook. Ans. August 17, 1856; discount, $ 16.103. 9. Required the legal time of maturity of the following note, and the proceeds, it having been discounted June 11, 1856. $ 1340. Philadelphia, May 1, 1856. For value received, ninety days after date, we promise to pay J. B. Lippincott 8$ Co., or order, one thousand three hundred and forty dollars, at the Girard Bank, without defalcation. Johnson & Pollock. 10. The following note was discounted, at 2 per cent, a month, July 5, 1857; how long had it to run, and what were the proceeds? $ 9000. New York, June 19, 1857. Two months after date, for value received, I promise to pay to the order of Joseph Appleton, nine thousand dollars, at the Manhattan Batik. L. T. Roberts. Ans. 48 days; proceeds, $8712.00. To find the amount for which a note must be given that the proceeds shall be a specified sum. Ex. 1. For what amount, payable in 60 days, must a note be given to a bank discounting at 6 per cent., to obtain $ 989.50? Ans. $1000. Operation. Since $ 0.9895 of pro $ 1.0 0 0 0 ceeds requires $ 1 to be Interest of $ 1 for 63 days, .0105 discounted, $ 989.50 will require as many dollars Proceeds of $ 1, $ O.'J 8 9 5 as $ 0.9895 is contained $989.50 -i- .9895 = $ 1000. in $ 98IX50, or $ 1000. Hence, Divide the given sum by the proceeds of $ 1 for the given time and rate of bank discount, including THREE days of grace, and the quotient will be the required amount. Examples. 2. What sum, payable in 90 days, if discounted at 7 per cent . bank discount, will produce $ 680? Ans. $ 692.52. 3. What must be the face of a note, which, when discounted at a bank for 120 days, shall give as its proceeds $ 540.50? Ans. $551.81. 4. For what amount must a note be given, in order that the proceeds of the note discounted, when having 6 months to run, shall be $ 1938? 5. The avails of a note, having 4 months to run, discounted at a bank, were $ 1631.60; what was the face of the note? Ans. $ 1665.74. 6. If a gentleman wishes to obtain $ 1500, for what sum must he give his note payable in 30 days, allowing it is to be discounted at 1 per cent, a month? Ans. $ 1516.68. 394. To find the rate of interest corresponding to a given rate of bank discount. Ex. 1. What rate of interest is paid when a note payable in 60 days is discounted at 6 per cent.? Ans. 6T'g^ per cent. Operation. Every ft 1 discounted for the given .06 -r- .9895 = .06TYn% time a"d rate yields as its proceeds $0.9895. Then, if $ 1 in the given time yield a certain interest at 6 per cent., ft 0.9895 in the s:ime time will yield the same interest, at as many per cent. as the given rate, .0(i, contains times .9895. Rule. — Divide the given rate per cent., expressed decimally, by (he number denoting the proceeds of $ I for the given time and rate. The quotient will be the rate of interest required. Examples. 2. What rate of interest is paid when a note payable in 30 days is discounted at 6 per cent.? Ans 6-j-ff? per cent. 3. What rate of interest is paid when a note payable in 90 days is discounted at 6 per cent.? Ans. 6T'Tf866g per cent. 4. A note payable in 4 months is discounted at 2 per cent. a month; what rate of interest is paid? 5. When a note, payable in 6 months, is discounted at 7 per cent., to what rate of interest does the bank discount correspond? 6. When a note payable in one year, without grace, is discounted, to what rate per cent. of interest does the bank discount correspond? Ans. per cent. 395i To find the rate of bank discount corresponding to a given rate of interestEx. 1. At what rate of bank discount must a note, payable in 60 days, be discounted, to produce 6 per cent, interest? Ans. 5£aM Per centOperation. Since bank discount is reckoned .06 -T- 1.0105 = -05 on an amount which equals the pro ceeds plus the interest on the proceeds for the given time and rate (Art. 389), the bank discount for every $ 1 of proceeds is equivalent to the interest on $ 1 -f- .0105 = $ 1.0105. Then, if $ 1 yield a certain interest in a given time at 6 per cent. per annum, $ 1.0105 must yield the same interest in the same time, at as many per cent, per annum as the given rate, .06, contains times 1.0105. Rule. —Divide the given rate per cent., expressed decimally, by the number denoting the amount of $ 1 for the given time and rate. The quotient will be the rate of bank discount required. Examples. 2. At what rate must a note, payable in 30 days, be discounted, to produce 6 per cent, interest? Ans. 5ig^| per cent. 3. At what rate must a note, running 60 days, be discounted, to yield 2 per cent. a month interest? Ans. 23fl/t per cent. 4. At what rate must a note, running 90 days, be discounted, to produce 6 per cent, interest? 5. At what rate must a note, running 120 days, be discounted, to produce 8 per cent, interest? 6. At what rate must a note, running 6 months, be discounted, to produce 7 per cent. interest? 7. At what rate must a note, payable 1 year hence, without grace, be discounted, to produce 6 per cent. interest? 8. What rate of bank discount on a note, payable 8 years and 4 months hence, without grace, corresponds to 5 per cent interest? Ans. 3-^ per cent. MISCELLANEOUS EXAMPLES. 1. The gold coinage of the United States contains 9 parts of pure gold to 1 part of alloy, and the alloy is 1 part copper to 1 part silver. What per cent, of the whole is each metal? Ans. Gold 90 per cent.; silver 5 per cent.; copper 5 per cent. 2. How much grain must be sent to the miller that a bushel of meal may be returned, the miller taking -fa part for toll? Ans. 34T25qts. 3. If a gentleman, possessing $ 25000, has a net yearly income of 4 per cent, of that sum, how much may he spend each year in order that his expenses shall just equal his income? 4. The half-dollar of coinage previous to 1853 contains 206£ grains of standard silver, and that of present coinage contains 192 grains; what per cent, more of standard silver does the one contain than the other? Ans. 7§J. 5. My horse is worth 50 per cent, more than my buggy; how many per cent. is the buggy worth less than the horse? Ans. 33$. 6. How many years longer will it take $ 10 to become $ 20 at 5 per cent, than at 6 per cent, simple interest? Ans. 3$ years. 7. What is the present worth of $ 500 due 4 years hence, at 5 per cent, compound interest? Ans. $411,351. 8. Bought cloth at $ 5.00 per yard. What must be "the asking price," in order to fall on it 10 per cent., and still make 10 per cent, on the purchase? Ans. $ 6.11^. 9. A merchant sold a cargo of hemp for $ 7860, for which he received a note payable in 6 months. How much money will he receive for the note at a bank? Ans. $7620.27. 10. What is the difference between the true discount and that taken by banks on $1500 due one year hence without grace? Ans. $5.09§§. 11. When a note payable in 60 days is discounted at the rate of 2 per cent. a month, what rate of interest is bank discount equal to? Ans. 25r27^- per cent. 12. A 45 day note discounted at ly per cent. a month, without grace, yielded a bank discount of $36.40. What was the face of the note? Ans. $ 1617.77 J. 13. At what rate per cent. of bank discount should a 30 day note be discounted, that interest may be received at the rate of 12 per cent.? Ans. ll§§f 14. How much more can a bank make in 693 days with $ 50000 by discounting notes on 60 days' time, than by discounting those on 30 days, the rate of discount being 6 per cent., and the profits in both cases to be retained in the banktill the end of the time? 15. A merchant bought 450 quintals of fish at $3.50 cash, and sold them immediately for $ 4.00 on 6 months' credit, for which he received a note. If he should get this note discounted at a bank, what will he gain on the fish? Ans. $ 170.10. 16. A bank by discounting a note at 6 per cent. receives for its money a discount equivalent to 0£ per cent, interest. How long must the note have been discounted before it was due? Ans. lyr. 3mo. 12d. STOCKS. 396. Stocks is a general name given to government bonds, and to money capital invested in corporations. The capital of banks, and of insurance, railroad, manufacturing, mining, and like companies, is usually divided into equal shares, the market value of which is often variable. 397. Stocks are said to be at par when they sell for their original value; above par, or at a premium, when for more than their original value; below par, or at a discount, when for less than their original value. 398. The premium and discount on stocks are generally computed at a certain per cent, on the original or nominal value of the shares. Note. — The original value of a share of bank, insurance, railroad, or like stock, is usually $ 100, but sometimes $ 50, and rarely any other sum than one of these. 399. A dividend is the interest or profit on stocks, dis |