MISCELLANEOUS EXAMPLES. part silver. 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 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 to part for toll? Ans. 34259ts. 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 2061 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. 737. 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. 331. 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. $ 6.115. 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 Ans. $5.0933. 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. 25275 per cent. 12. A 45 day note discounted at 17 per cent. a month, without grace, yielded a bank discount of $ 36.40. What was the face of the note ? Ans. $ 1617.777. grace? 13. At what rate per cent. of bank discount should a 30 day note be discoun'ed, that interest may be received at the rate of 12 per Ans. 1139 . 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 bank till 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 64 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 $ 5, and rarely any other sum than one of these. 399. A. dividend is the interest or profit on stocks, dis. tributed to the shareholders, and is reckoned on the par or nominal value of the shares. 400. To find the market value of stocks when they are at a premium, or at a discount. Ex. 1. What is the value of 20 shares of bank stock, at 9 per cent. premium, their nominal or par value being $ 100 each ? OPERATION. $ 100 x 20 = $ 2000; $ 2000 x 1.09 = $ 2180. Since the par value of 1 share is $ 100, that of 20 shares is $ 2000; then, as $ 1 at 9 per cent. premium equals $ 1.09, $ 2000 will equal 2000 times as much, or $ 2180. RULE. Multiply the par value of the given stock by 1 increased by the rate per cent. premium, or by 1 decreased by the rate per cent. discount, expressed decimally, and the product will be the value required. Note. — The difference between the par and market value gives the per cent. of premium or discount. EXAMPLES. 2. What is the value of $ 24360 of stock, at 35 per cent. premium. Ans. $ 32886. 3. Sold 15 shares of the Camden and Amboy Railroad, the par value being $ 100 per share, at 13 per cent. advance. To what did they amount ? Ans. $ 1695. 4. What must be paid for 10 shares of the Old Colony and Fall River Railroad, at 85 per cent., the original value being $ 100 each? 5. Sold 30 shares, $ 100 each, in the Boston Bank, at 81 per cent. advance. To what did they amount, and how much was the premium ? Ans. Amount, $ 3262.50; premium, $ 262.50. 6. What must be given for 25 shares of insurance stock, par value being $ 50, at 3 per cent. discount? Ans. $ 1212.50. 7. What must be paid for 22 shares of the Iron City Manufacturing Stock, par value being $ 250, at 95 per cent., and how much is the discount? Ans. $ 5225 ; discount, $ 275. 8. What will be the cost of $ 50000 of United States gov. ernment stock, at 17 per cent, advance ? Ans. $ 58500. 9. Bought $ 19500 of State stocks at 93 per cent., and sold the same at 103 per cent. ; how much was gained by the operation ? Ans. $ 1950. OPERATION. 401. To find the par value of stocks, when they are at a premium, or at a discount. Ex. 1. Bought Ocean Insurance Company stock, at 7 per cent. premium, for $535; what is its par value? Ans. $ 500. Since $1 at 7 per cent. pre$ 535 ; 1.07 $ 500, Ans. mium equals $ 1.07, the par value of the stock must be as many dollars as 535 contains times 1.07, or $ 500. RULE. Divide the market ralue of the given stock by 1 increased by the rate per cent. premium, or by 1 decreased by the rate per cent. discount, expressed decimally, and the quotient will be the value required. EXAMPLES 2. Bought Massachusetts State stock, at 3; per cent. premium, for $ 6210; what is its par value ? Ans. $ 6000. 3. Sold 11 shares of Reading Bank, at 5 per cent. premium, for $ 1155 ; what is the par value of its shares ? Ans. $ 100. 4. Bought 41 shares of canal stock at 40 per cent. below par for $ 1230; what is the par value of its shares ? 5. Bought 19 shares of bank stock, at a premium of 8 per cent., for $ 2052; what was the amount of premium paid? 6. When government stocks are at 5 per cent. discount, how value will $ 16245 purchase, and what is amount of discount? Ans. $ 17100; discount, $ 855. 7. When railroad stock at 15 per cent. advance is selling at $57.50 per share, how many shares may be bought for $862.50, and what will be the amount of premium? Ans. 15 shares; $ 112.50 premium. 8. How many State bonds of $ 1000 each, at 12 per cent. discount, can be purchased for $ 7920, and how much may be gained by the operation, if the selling price should afterwards advance to par? Ans. 9 bonds; $ 1080 may be gained. much par 402. To find the rate of interest to which a dividend on any stock bought at a premium or discount corresponds. OPERATION. Ex. 1. Received 121 per cent. dividend on an investment in stocks at 25 per cent. above par; to what rate per cent. interest did it correspond ? Ans. 10 per cent. Since the stock was bought at 25 .125 ; 1.25 = .10, Ans. per par, every $ 1.25 of investment must represent only $1 of par value. Then, since every $ 1 of par value pays a dividend corresponding to 12; per cent. interest, every $ 1.25 of investment pays as many per cent. expressed decimally, as 1.25 is contained times in .125, or 10 per cent. RULE. — Divide the rate per cent. of dividend, expressed decimally, by 1 increased by the rate per cent. premium, or by i decreased by the rate per cent. discount, expressed decimally, and the quotient will denote the rate of interest required. Note. If it be required to find at what price a stock, paying a certain rate per cent. dividend, should be bought in order that the investment shall pay a given rate of interest, divide the rate per cent. of dividend, expressed decimally, by the given rate of interest, expressed decimally, and the quotient will be the price required of each $ 1 of the given stock. EXAMPLES. 2. Received 6 per cent. dividend on factory stock, purchased at 25 per cent. below par. What rate per cent. interest did the investment pay? Ans. 8 per cent. 3. When railroad stock paying 11 per cent. dividend is worth $110 per share, or $10 per share above par, to what rate of interest would the income from an investment in its shares correspond? Ans. 10 per cent. 4. How much advance must be paid for stocks paying 12 per cent. dividends, in order that the investment shall pay exactly 8 per cent. interest ? Ans. 50 per cent. 5. Which is the better investment, the buying of 9 per cent. stocks at 25 per cent. advance, or 6 per cent. stocks at 25 per cent. discount? 6. At what per cent. discount must government 5 per cent. stock be bought that the investment may yield 7 per cent. ? Ans. 284 per cent. 7. How much more income yearly may be derived from $ 20000 invested in 5 per cent. stock bought at 20 per cent. discount, than by letting the same sum at 6 per cent. interest? Ans. $ 50. |