Since the present worth of $ 1.06, due one year hence, at 6 per cent., is $ 1, the present worth of $ 25.44 is as many dollars as $ 1.06 is contained times in $ 25.44, or $ 24. We thus find the present worth to be $ 24, which, subtracted from the given sum, gives $ 1.44 as the discount.

RULE. ·Find the amount of $1 for the given time and rate; by which divide the given sum, and the quotient will be the PRESENT worth. The present worth subtracted from the given sum will give the DIS

COUNT.

NOTE.The discount may be found directly by making the interest of $1 for the given rate and time the numerator of a fraction, and the amount of $1 for the given rate and time the denominator, and then multiply the given sum by this fraction.

EXAMPLES FOR PRACTICE.

2. What is the present worth of $152.64, due 1 year hence?

3. What is the present worth of $ 477.71, due 4

Ans. $144.

years hence? Ans. $385.25.

4. What is the discount of $172.86, due 3 years, 4 months hence?

Ans. $28.81.

5. What is the discount of $ 800, due 3 years, 7 months, and 18 days hence? Ans. $143.186.

6. Samuel Heath has given his note for $375.75, dated Oct. 4, 1852, payable to John Smith, or order, Jan. 1, 1854; what is the real value of the note at the time given? Ans. $349.697.

7. Bought a chaise and harness of Isaac Morse for $125.75, for which I gave him my note, dated Oct. 5, 1852, to be paid in 6 months; what is the present value of the note, Jan. 1, 1853? Ans. $123.81.

213. Explain the operation for finding the present worth and discount. The reason of the operation? The rule? What other method is given?

COMMISSION, BROKERAGE, AND STOCKS.

214. Commission is the percentage paid to an agent, factor, or commission merchant, for buying or selling goods, or transacting other business.

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.

Stocks is a general name given to government bonds, and to the money capital of corporations, such as banks, insurance, railroad, manufacturing, and mining companies.

Stocks are usually divided into equal shares, the market value of which is often variable.

:

When stocks sell for their original value they are said to be at par; when for more than their original value, above par, or at a premium; when for less than their original value, below par, or at a discount.

The premium, or advance, and the discount on stocks, are generally computed at a certain per cent. on the original value of the shares.

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

Commission and brokerage are computed in the same manner. 215. To find the commission or brokerage on any sum.

Ex. 1. A commission merchant sells goods to the amount of $879; what is his commission at 3 per cent.? Ans. $26.37.

Since commission is a percentage on the given sum, the commission on $879, at 3 per cent., will be $879 × .03 = $ 26.37.

RULE. Find the percentage on the given sum cent., and the result is the commission or brokerage.

214. What is commission? Brokerage? Stock? divided? When are stocks at par? When above par? How is the premium or discount on stocks computed? and brokerage computed? -215. What is the rule?

at the given rate per (Art. 191.)

Into what are stocks

When below par? How are commission

EXAMPLES FOR PRACTICE.

2. What is the commission on the sale of a quantity of cotton goods valued at $5678, at 3 per cent. ? Ans. $170.34.

3. A commission merchant sells goods to the amount of $7896, at 2 per cent.; what is his commission?

Ans. $157.92.

4. My agent in Chicago has purchased wheat for me to the amount of $1728; what is his commission, at 1 per cent.?

Ans. $25.92. 5. My factor advises me that he has purchased, on my account, 97 bales of cloth, at $15.50 per bale; what is his commission, at 2 per cent.? Ans. $37.587.

6. My agent at New Orleans informs me that he has disposed of 500 barrels of flour at $ 6.50 per barrel, 88 barrels of apples at $2.75 per barrel, and 56cwt. of cheese at $10.60 per cwt.; what is his commission, at 3 per cent.?" Ans. $153.21.

7. A broker negotiates a bill of exchange of $2500 at per cent. commission; what is his commission? Ans. $12.50.

8. A broker in New York exchanged $46256 on the Canal Bank, Portland, at of 1 per cent.; what did he receive for his trouble? Ans. $57.82.

9. A broker in Baltimore exchanged $20500 on the State Bank of Indiana, at of 1 per cent.; what was the amount of his brokerage? Ans. $102.50.

216. When the given sum includes both the brokerage or commission and the sum to be invested.

Ex. 1. A merchant in Cincinnati sends $1500 to a commission merchant in Boston, with instructions to lay it out in goods, after deducting his commission of 2 per cent.; what is his commission? Ans. $36.586.

Since the agent is entitled to 2 per cent. of the amount he lays out, it is evident he requires $1.02 to purchase goods to the amount of $1. Hence, he can expend for goods as many dollars as $1.02 is contained times in $1500, or $1463.414; which, being subtracted from $1500, the amount sent him, leaves as his commission $36.586.

216. How do you find the commission or brokerage when the given sum includes both the brokerage or commission and the sum to be invested?

RULE.

· Divide the given sum by 1 increased by the per cent. of commission, and the quotient will be THE SUM TO BE INVESTED.

Subtract the sum to be invested from the given sum, and the remainder will be THE COMMISSION.

EXAMPLES FOR PRACTICE.

2. A town agent has $2000 to invest in bank stock, after deducting his commission of 14 per cent.; what will be his commission, and what the sum invested?

Ans. $29.557 commission; $1970.443 sum invested.

3. A shoe-dealer sends $5256 to his agent in Boston, which he wishes him to lay out for shoes, reserving his commission of 3 per cent.; what is his commission? Ans. $153.088.

4. A broker expends $3865.94 for merchandise, after deducting his commission of 4 per cent.; what was his commission, and what sum did he expend?

Ans. $148.69 commission; $ 3717.25 sum expended.

5. I have sent to my agent at Buffalo, N. Y., $10000, to be expended in flour, after deducting his commission of 3 per cent.; what will be his commission, and the value of the flour purchased? Ans. $314.76+ com.; $9685.23+ val. of flour.

217. To find the value of stocks, when at an advance or at a discount.

Ex. 1. What is the value of $2150 railroad stock, at 7 per cent. advance? Ans. $2300.50.

OPERATION.

$2150 × .07 = $150.50; $ 2150 + $ 150.50

= $2300.50.

RULE. — Find the percentage on the given sum, and add or subtract, according as the stock is at an advance or at a discount. (Art. 191.)

EXAMPLES FOR PRACTICE.

2. What must be given for 10 shares in the Boston and Maine Railroad, at 15 per cent. advance, the shares being $100 each? Ans. $1150.

3. What must be given for 75 shares in the Lowell Railroad, at 25 per cent. advance, the original shares being $100 each? Ans. $9375.

216. What is the rule?-217. at an advance or at a discount?

How do you find the value of stocks, when
What is the rule?

4. What is the purchase of $8979 bank stock, at 12 per cent. advance? Ans. $10056.48.

5. What is the purchase of $1789 bank stock, at 9 per cent. below par? Ans. $1627.99.

6. A stockholder in the Illinois Central Railroad sells his right of purchase on 5 shares of $100 each at 12 per cent. advance; what is the premium? Ans. $60.

7. What is the value of 20 shares canal stock, at 12 per cent, discount, the original shares being $100 each. Ans. $1750.

8. What is the value of 15 shares in the Livingston County Bank, at 8 per cent. advance, the original shares being $100 each? Ans. $1623.75.

9. Bought 87 shares in a certain corporation, at 12 per cent. below par, and sold the same at 19 per cent. above par; what sum did I gain, the original shares being $175 each? Ans. $4795.874.

BANKING.

218. A Bank is a joint stock company, established for the purpose of receiving deposits, loaning money, dealing in exchange, or issuing bank-notes or bills, as a circulating medium, redeemable in specie at its place of business.

The Capital of a bank is the money paid in by its stockholders, as the basis of business.

Banking is the general business commonly transacted at banks.

NOTE. The persons chosen by the stockholders to manage the affairs of the bank are called its board of directors, who select one of their own number as president, and some person as cashier.

The president and cashier sign the bills issued, which also are, in some instances, countersigned by some State officer.

The cashier superintends the bank accounts; and another person, called the teller, usually receives and pays out money.

A check is an order drawn on the cashier of the bank for money.

218. What is a bank? The capital of a bank? Banking? Who choose the directors? Who choose the president and cashier? Who sign the bills issued? Who superintends the accounts? Who receives and pays out the money? What is a check?