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 × 20 = $2000; $ 2000 × 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. what did they amount?

Ans. $1695.

To

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 82 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.

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.

OPERATION.

$535 1.07 = $500, Ans.

lars as 535 contains times 1.07, or

Since $1 at 7 per cent. premium equals $ 1.07, the par value of the stock must be as many dol$ 500.

RULE. Divide the market 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 quotient will be the value required.

EXAMPLES.

2. Bought Massachusetts State stock, at 31⁄2 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 much par 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.

402.

To find the rate of interest to which a dividend on any stock bought at a premium or discount corresponds.

Ex. 1.

Received 12 per cent. dividend on an investment

in stocks at 25 per cent. above par; to what rate per cent. inAns. 10 per cent.

terest did it correspond?

OPERATION.

.125 1.25 =

Since the stock was bought at 25

.10, Ans. per cent. above 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 1 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.

BROKERAGE AND COMMISSION.

403. BROKERAGE is the percentage paid to a dealer in money and stocks, called a broker, for making exchanges of money, negotiating different kinds of bills of credit, or transacting other like business.

404. COMMISSION is the percentage paid an agent, factor, or commission merchant for buying or selling goods, making collections, or transacting other business.

405. When the person transacting the commission business lives in a foreign country, he is frequently called a correspondent or consignee.

The goods shipped or forwarded to a consignee to be sold on commission are termed a consignment, and the person sending or consigning the same is called the consignor.

406. The rate per cent. of brokerage or commission is not regulated by law, but varies in different places, and with the nature of the business transacted.

Brokerage and commission are computed in the same man

ner.

407. To find the brokerage or commission on any given

sum.

Ex. 1. Paid a broker, for exchanging $ 896 uncurrent bills for par funds, 2 per cent. brokerage. How much was the brokerage? Ans. $17.92. Since brokerage is a percentage on the given sum, the brokerage on.$ 896 at 2 per cent. will be $ 896 X .02 = = $17.92.

RULE. — Find the percentage on the given sum at the given rate per cent., and the result will be the brokerage or commission.

NOTE. When the brokerage or commission, and the sum on which it is reckoned, are given, the rate per cent. may be found as in Art. 348.

EXAMPLES.

2. My agent in New Orleans has purchased cotton, on my account, to the amount of $18768. What is his commission at 12 per cent.?

Ans. $328.44.

3. I have engaged a broker to purchase for me 12 shares in the New York Central Railroad, at $112.25 per share; what is his commission at per cent.? Ans. $3.363.

4. My agents, Hilton and Marcy of Cincinnati, advise me that they have purchased on my account a cargo of pork, consisting of 700 barrels, at $ 12.25 per barrel; what is their commission at 1 per cent.? Ans. $150.064.

5. What rate per cent. of brokerage does a broker charge who takes $50 for investing $ 10000?

6. What is the commission on the sale of 173cwt. of sugar, at $8.95 per cwt., at 17 per cent.? Ans. $29.03.

7. My factor at Mobile advises me that he has purchased on my account 37 bales of cotton, at $ 107.75 per bale; what is his commission at 3 per cent.? Ans. $14.952.

8. A consignee in London writes that he has purchased for his employer goods to the amount of 395£. 15s. 5d.; what is his commission at 21 per cent.? Ans. 8£. 18s. 1,65 d. 9. Paid G. Willis $5.46 for exchanging $364 of depreciated currency; what was the rate of brokerage?

Ans. 1 per cent.

408. or commission, and the sum to be invested.

When the given amount includes both the brokerage

Ex. 1. A gentleman intrusts $20050 to a broker in New York City, with instruction, after deducting his brokerage of 4 per cent., to invest the balance in government bonds. What will be the sum invested, and how much will be the brokerage?

OPERATION.

$20050 ÷ $1.0025
$20050 $20000 =

$20000, Investment.
$50, Brokerage.

Since the broker is entitled to per cent. of the sum he invests, it is evident he requires $1.0025 in order to invest $1. Hence, the investment he can make will be as many dollars as $ 20050 contains times 1.0025, or $20000; which, being subtracted from the amount forwarded him, leaves as his brokerage $50.

RULE. Divide the given amount by 1 increased by the rate per cent. of brokerage or commission, expressed decimally, and the quotient will be the investment.

Subtract the investment from the given amount, and the remainder will be the brokerage or commission.