11. I received $4850 and a consignment of 2000 barrels of flour from Badeau & Co., which I sold at $7.50 a barrel, and invested the net proceeds and cash in cotton; how much did I invest in cotton, my commission being 3% for selling and 1% for buying, and the expenses for storage and freight $350? Ans. $18768.47.

CASE III.

539. Given, the base and the commission or the net proceeds or the entire cost, to find the rate.

OPERATION.

1. A commission merchant collected $8650, and his commission was $302.75; what was the rate of commission? SOLUTION. The commission, $302.75, equals the base, $8650, multiplied by the rate; hence, the rate equals $302.75 divided by $8650, which we find is .03, or 31%.

302.75

8650

= .03

=

Rule I. Divide the commission by the base, to find the rate.

Rule II.-Divide the difference between the base and the net proceeds or the entire cost, by the base, to find the rate. 2. A factor in Iowa sold some land for me, and after retaining his commission, $90, remitted me $1910; what rate of commission did he charge? Ans. 4%.

3. A commission merchant sells 5980 pounds of tea, at $1.12 a pound, and remits the net proceeds, $6559.311; what is his rate of commission? Ans. 21%.

4. I sold a consignment of goods through an agent for $5745; my commission was $201.07, and I paid the agent $86.17; what was the rate of commission of each?

Ans. Mine, 3%; agent's, 11%. 5. My agent bought 40 horses at $150 each, paid $25 for their keeping, and $80 for transportation; he drew on me for $6315; what was his commission? Ans. 31%.

6. A commission merchant in Philadelphia having received a consignment from Chicago of 1850 bushels of wheat, sells it at $1.25 a bushel; having deducted $35 for freight, and $25 for storage, and his commission, he remits to Chicago $2171.564; what was his rate of commission?

Ans. 31%.

STOCKS AND DIVIDENDS.

540. A Company is an association of individuals for the transaction of business. It may or may not be incorporated.

541. A Corporation is a company regulated in its operation by a general law or a special charter.

542. The Stock of a company is the capital invested in the business. The owners of stock are called Stockholders. 543. A Share is one of the equal parts into which the stock is divided. A share is usually $50 or $100.

544. 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.

545. Stocks is a general name applied to the scrip or bonds of a corporation, and to government bonds and public securities.

546. Bonds are written or printed obligations to pay certain sums of money at or before a specified time.

547. 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.

548. An Installment is a sum required of stockholders as a payment on their subscription.

549. A Dividend is a sum paid to stockholders out of the gains of the company.

550. An Assessment is a sum required of stockholders to meet the expenditures or losses of the company.

551. The Base upon which dividends and assessments are estimated is the original or par value of the stock. 552. The Quantities considered are as follows: 1. The Stock; 2. The Rate; 3. The Dividend or Assessment.

The capital stock of any corporation is limited by the charter. In general, only a certain percentage is paid at the time of subscription, the remainder being reserved for future expenses.

When the capital is all paid up, if more money is needed, it may be obtained by loans, secured by mortgage upon property of the company.

The bonds issued for these loans entitle the holder to a certain fixed interest, while the stockholders participate in the profits of the company in proportion to the stock they hold. The increase of the stock of a company by the issue of new shares is termed "watering" the stock.

CASE I.

553. Given, the stock and the rate of dividend or assessment, to find the dividend or assessment.

1. A man owns 65 shares of bank stock at $50 a share; the bank declares a dividend of 7%;

SOLUTION.-If one share of stock is worth $50, 65 shares are worth 65 times $50, or $3250, and 7% of $3250 is .07 times $3250, or $227.50.

what does he receive?

OPERATION.

65 × 503250 $3250 X .07 $227.50

=

Rule.-Multiply the par value of the stock by the rate, to find the dividend or assessment.

NOTE. It is often convenient to find the result by multiplying the dividend or assessment on one share by the number of shares.

2. A man owns 98 shares of Pennsylvania R. R. stock at $50 each; if the company declares a semi-annual dividend of 5%, what is his dividend? Ans. $245.

3. A telegraph Co., whose stock consists of 5780 shares at $25 each, declares a quarterly dividend of 21%; what sum was divided among the stockholders? Ans. $3612.50.

4. The Lancaster Gas Co., with a capital of $65,000, declares a dividend of 8%, and has a surplus of $800; how much has it earned to do this? Ans. $6000.

5. The net earnings of the Manor Turnpike Company are $9000, and the stock $157,000; the company declared a 5% dividend; what was the surplus? Ans. $1150.

6. A owns 72 shares, at $100 each, in a mutual insurance company, which on account of losses, requires an assessment of 3%; how much does A pay?

Ans. $240.

7. B has 135 shares of Farmers' Bank stock ($50); the bank declares a dividend of 8%; how many shares of stock could he buy with his dividend? Ans. 10; $40 surplus.

8. Mr. Wilson owns 80 shares of N. Y. Central R. R. stock ($100); if the company declares a dividend of 5%, payable in stock, how many shares will he then own? Ans. 84.

9. If a company "water" its stock by issuing 20% of

new stock, and their original capital was $5,000,000, what would be the amount of a dividend of 8% before the watering, and what afterwards? Ans. $400,000; $480,000.

10. The capital stock of a Western railroad is $1,750,000, and its debt is $675,000; its gross earnings for the year 1873 were $565,000, and expenses $384,500; after deducting interest on the debt at 6%, what dividend would a stockholder receive on 20 shares at $100 each? Ans. $160.

CASE II.

554. 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 $4875 among its stockholders, being a 5% dividend; required the whole amount of stock.

SOLUTION.—If $4875 is 5% of the stock, then .05 times the stock equals $4875, the dividend, hence the stock equals $4875, the dividend, divided by .05, the rate, which is $97500.

OPERATION.

4875

=97500.

.05

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. A company divides $15,000 among its stockholders, as the result of a 71% dividend; what is A's stock, provided he owns of the entire stock? Ans. $20,000.

3. A man pays an assessment of $275, at 51%, on his insurance stock; how many shares does he own, the shares being valued at $50 each? Ans. 100.

4. A gas company whose annual expenses are $2980, and gross carnings $5780, pays a dividend of 5% semi-annually; required the value of the stock. Ans. $28,000.

5. Mr. B received $240 payable in stock, as his share of an 8% dividend; how many shares had he at first, and how many has he now, shares at $50? Ans. 60; 64, and $40.

6. Henry received a 6% stock dividend, and then had 93 shares, $50 each, and $14 of another share; how many shares had he at first? Ans. 88.

7. Mr. D received 12 shares and $7.50 in money as his share of a 7% dividend; how many shares, at $50 each, did he then own? Ans. 174 shares.

8. I received two dividends in the stock of the Pittsburgh Gas Company, one at 8%, another at 10%, and I then had 297 shares ($100); how many shares had I at first? Ans. 250.

9. I received a stock dividend of 5% in a Nevada mining company, in April, and a similar dividend of 10% in December; I then owned 231 shares at $50; how many shares had I at first? Ans. 200.

CASE III.

555. Given, the stock and the dividend or assessment, or the result of increase or decrease of stock, to find the rate.

1. My dividend on $6500 worth of bank stock was $975; what was the rate of dividend?

OPERATION.

975 6500 .15

SOLUTION. Since the dividend is some per cent. of the stock, the base, $6500, multiplied by the rate, equals $975; hence the rate equals the dividend, $975, divided by the stock, $6500, which equals .15, or 15%. 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 rate.

2. A owns 85 shares of railroad stock, at $100 a share, and receives a dividend of $680; what was the rate of dividend? Ans. 8%.

3. An oil company, whose stock is $100,000, clears $7850; required the largest integral rate of dividend that they can declare, and the surplus. Ans. 7%; surplus, $850. 4. After receiving a stock dividend, I had 93 shares ($100) and $28 toward another share; what was the rate of the dividend, if I had 88 shares at first? Ans. 6%.

5. I have 250 shares in a Chicago Gas Company ($100); I received two stock dividends, the first amounting to $2000 and the second to $2700; what were the rates of the dividends? Ans. 8% and 10%.