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415. Given, the rate and the dividend or assessment, or the result of increase or decrease of stock, to find the stock.
1. A bank divides $8400 among the stockholders, being the amount of 7% dividend; required the whole amount of stock.
SOLUTION.-If $8400 is 7% of the stock, OPERATION. then .07 times the stock equals $8400; hence, $8400 the stock equals $8400 divided by .07, which =$120000, Ans. es $120000.
.07 Rule I.-Divide the dividend or assessment by the rate, to find the stock.
Rule II.—Divide the result of increase by 1 plus the rate, or the result of decrease by 1 minus the rate, to find the stock.
2. I received $880 from a 5 per cent. dividend; how much stock do I own?
Ans. $16000. 3. I receive $279 as my share of a 9% dividend; how many shares, at $50 each, do I own? Ans. 62 sbares.
4. A company divides $72000 among its stockholders, as the result of an 8% dividend; what is B's stock, provided he owns of the entire stock ?
Ans. $112500. 5. A lady receives $1260 dividend at 7%; required the amount of stock she owns and the number of shares, valued at $50 each.
Ans. 360 shares. 6. Mr. B receives $7800, payable in stock, as his share of a 12% dividend; how many shares had he at first, and how many has he now, shares at $50 ? Ans. 1456.
7. A gentleman received 7 shares and $25 in money, as his share of a 6% dividend; how many shares, valued at $50, did he then own?
Ans. 132 shares. 8. In 1864 I received a stock dividend of 25% in the Camden and Amboy Railroad, and I then had 80 shares, at $100 each ; how many shares had I at first ?
Ans. 64 shares
9. I received a stock dividend of 10% in an oil company in March, 1865, and a similar dividend of 12% in Novem. ber; I then owned 308 shares at $25 ; how many shares had I at the beginning of the year ?
Ans. 250 shares. 10. The expenses of an insurance company, capital $400,000, are 75% of the gross earnings; it reserves $10,000 and pays a dividend of 43%; what were the gross earnings ?
416. Given, the stock and dividend or assessment, or result of increase or decrease of stock, to find the rate.
1. A company whose stock is $840000, clears $56000 in a year; what rate of dividend can it declare?
SOLUTION. Since the dividend is some per cent. of the stock, the base, $840000, multiplied
56000 by the rate equals $56000; hence, the rate equals =.063, Ans.
840000 $56000 divided by $840000, which equals .063.
Rule I.—Divide the dividend or assessment by the stock, to find the rate.
Rule II.—Divide the difference between the stock and the result of increase or decrease, by the stock, to find the rata
WRITTEN EXERCISES. 2. A company whose stock is $125000, requires an assessment of $1875; what was the rate?
Ans. 11% 3. Mr. A owns 288 shares of stock, at $100, and draws a dividend of $1944 ; what was the rate ? Ans. 67%
4. The earnings of a canal company for 6 months are $70000, the stock is $2,330,000; if they declare a dividend whose rate is an integer, what is the largest rate, and what is the surplus ?
Ans. 3% ; $ 100 surplus. 5. A owns 70 shares ($100) in a railroad company whose stock is $4000000, and his dividend is $402.50; required the rate of dividend, and the whole dividend. Ans 54%.
6. After receiving a stock dividend, I had 73 shares ($50) und $10 toward another share; what was the rate of divi. dend, if I had 61 shares at first ?
7. I hold 350 shares in a Pittsburgh gas company ($50), and received two stock dividends, the first amounting to 42 sbares, and the second to 58 shares and $40; what were the rates of dividend ?
Ans. 12% and 15%.
PAR, PREMIUM, AND DISCOUNT. 417. Capital is property consisting of Money, Bonds, Stocks, Drafts, etc.
418. Drafts, Checks, and Bills of Exchange are written orders for the payment of money at some definite place.
419. Stocks is a general name applied to the scrip or bonds of a corporation, and to government bonds and public securities.
420. Scrip or Certificates of Stock are the papers issued by a corporation to its stockholders, as evidence of the number of shares belonging to each respectively.
421. Bonds are written or printed obligations to pay vertain sums of money at or before a specified time.
422. State Stocks or United States Stocks are bonds of a State, or of the United States, payable at some future time, with interest at a fixed rate.
423. The Par Value of capital is the value marked on its face, called the nominal value or face.
424. The Real Value or Market Value of capital is what it will sell for.
425. Capital is Above Par,or at a premium or advance, when it sells for more than its nominal value. Capital is below par, or at a discount, when it sells for less than its pominal value.
The stock of a company will generally be above par when the company is doing a lucrative business, and below par when it is doing a poor business. The stock of a town, city, etc., varies according to the confidence in its security, the fluctuations of the money market, etc.
Besides bonds, the U. S. Government issues notes, payable on demand without interest, which are a legal tender for all debts due the United States except duties. These notes, called “greenbacks," are, together with notes issued by the National Banks, the present circulating mediana, and are called currency.
If the currency becomes depreciated in value, gold becomes au object of investment, the same as stocks. The value of gold being fixed, its Auctuations in price indicate the changes in the value of the currency. Thus, when gold is said to be at a premium, currency is really at a dis
426. The Base upon which premium and discount are estimated is the par value.
427. The Quantities considered are four: 1. The Par Value ; 2. The Rate; 3. The Premium or Discount ; 4. The Real Value.
NOTE.— The problems under this subject are solved without brokerage the sales and exchanges being regarded as direct without the aid of a broker.
428. Given, the par value and the rate of premium or discount, to find the premium or discount or real value.
1. A broker bought 25 shares of stock ($50), at 5% premium; required the premium and cost, or real value.
SOLUTION.—The par value of 25 shares at $50 each is $50 x 25 =
$50 x 25= $1250, par value. $1250; and the premium at 5% is
.05 .05 times $1250, which is $62.50; and this, added to the par value,
$62.50, premium. equals $1312.50, the real value.
$1312.50, real value. Rule 1.—Multiply the par value by the rate, to find the premium or discount.
Rule II.- Multiply the par value by 1 plus the rate of premium, or by 1 minus the rate of discount, to find the real value.
2. B sold 46 shares of bank stock ($100), at 3% discount; required the discount and real value.
Ans. $4462. 3. In 1858, I sold a $20 note on an Ohio bank, at $% discount; what did I receive for it ?
Ans. $19.88. 4. When gold was at a premium of 101% a broker paid cur. rency for $560 in gold; how much currency did he pay ?
Ans. He paid $618.80.
5. A speculator bought 35 shares of bank stock ($100), at 31% discount, and sold it at 14% premium; what was his gain ?
Ans. $166.25. 6. A banker bought 48 shares ($100) of canal stock, at 6% premium, and paid for them with $5000 in drafts, at 37% discount, and the balance in cash ; how much cash did he pay?
Ans. $250.50. 7. A lady exchanged 45 shares ($100) railroad stock, at 45% discount, for 70 shares of bank stock ($50), at 5% premium, receiving the difference in cash; what amount of cash did she receive ?
CASE II. 429. Given, the rate and the premium or discount or the real value, to find the par value.
1. A man sold some securities at discount of 5%, receive ing $120 less than their face; what was their face value ?
SOLUTION.-If the discount at 5% is $120, then .05 times the par value equals $120; hence, $120.05=$2400. the par value equals $120 divided by .05, which we rind is $2400.
Rule 1.—Divide the premium or discount by the rate, to find the par value.
Rule II.—Divide the real value by 1 plus the rate of premium, or by 1 minus the rate of discount, to find the par value.
2. B sold some stocks at 31% premium and gained $210; what was their
Ans. $6000. 3. The premium on a draft at 1% was $.90; required the face of the draft and its value.
Ans. $120.90. 4. Mr. Allen paid $2587.50 for a bond, at 31% premium ; required its face and the premium. Ans. Face, $2500.
6. Mr. Jones paid $5926.50 for bank stock, at 98% premium); how many shares ($100) did he buy?
Ans. 54. 6. Sold stock bought at par, at an advance of 31 %, and gained $145; how many shares ($50) did I sell ?