5. A speculator bought 35 shares of bank stock ($100), at 34% discount, and sold it at 11% 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 31% 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 4% discount, for 70 shares of bank stock ($50), at 5% premium, receiving the difference in cash; what amount of cash did she receive? Ans. $636.

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 a discount of 5%, receiv 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.

OPERATION.

Rule I.-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.

WRITTEN EXERCISES.

2. B sold some stocks at 34% premium and gained $210; what was their par value? Ans. $6000.

3. The premium on a draft at % 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.

5. Mr. Jones paid $5926.50 for bank stock, at 94% premium;

how many shares ($100) did he buy?

Ans. 54.

6. Sold stock bought at par, at an advance of 3%, and gained $145; how many shares ($50) did I sell ?

Ans. 87

7. Miss Hartman sold 140 shares of Columbia National

bank stock at $54 a share, premium 8%; required the par value of a share and entire premium.

Ans. $50; Prem. $560. premium, for 75 shares of

8. I gave a draft worth % turnpike stock ($50) at 3% discount; what was the face of the draft? Ans. $3610.42+.

SUPPLEMENTARY PROBLEMS.

To be omitted unless otherwise directed.

9. I sold 40 shares of stock at a premium of 44%, and received $180 advance; what was the par value of a share? Ans. $100. 10. A broker exchanged 700 shares of stock ($100), at 5% discounts, for United States bonds ($100), at 5% premium, paying $70 in money; how many did he get ? Ans. 634 bonds.

11. Mr. Fish bought a number of shares of bank stock ($50), the discount at 5% being $200; of it he sold at par and the rest at 7% advance; what was the average gain on each share?

CASE III.

Ans. $5.12.

430. Given, the par value and the real value or the premium or discount, to find the rate of premium or discount.

1. I sold a note, drawn for $860, at a premium of $51.60; what was the rate of premium?

SOLUTION. Since the premium equals the par value multiplied by the rate, $860 multiplied by the rate equals $51.60; hence, the rate equals $51.60 divided by $860, which we find is .06.

51.60

OPERATION.

=.06

860

Rule I.-Divide the premium or discount by the par value, to find the rate.

Rule II.-Divide the difference between the real value and the par value by the par value, to find the rate.

WRITTEN EXERCISES.

2. I bought a draft, drawn for $1680, at a discount of $12.60; required the rate of discount.

3. Mr. Peters bought 96 shares of railroad

for $4476; what was the rate of discount?

Ans. %.

stock ($50)

Ans. 64%.

4. If he sells these 96 shares for $4699.80, what is the rate of discount, and rate of gain? Ans. 2%; 5%.

5. When gold was at a premium, Mr. Reed gave $7500 in short time notes, at 2% discount, for $6125 in gold; what was the rate of premium on the gold? Ans. 20%.

6. A banker bought 10 shares of stock ($50) at a premium of 10%, and sold them for $600; what was the gain % on the transaction? Ans. 81% gain.

BROKERAGE.

431. Brokerage is a percentage charged by brokers for the transaction of business.

432. A Broker is a person who buys or sells money, stocks, bills of exchange, real estate, etc., for others. A stock broker is one who deals in stocks, but is generally called simply a broker.

433. The Base upon which the commission for the purchase and sale of bonds and stocks is estimated is their par value.

434. The Rate is usually %, and will be sɔ understood when no other rate is mentioned. In New York the rate is % on both bonds and stocks.

435. The Quantities considered are: 1. The Par value of the amount sold, bought, etc., 2. The Rate of Brokerage; 3. The Brokerage; 4. The Market value of $100, or of 1 share; 5. The Entire Cost, or Net Proceeds.

NOTES.-1. Stocks are quoted either at the price of one share, or at tr price of $100 of par value of the stock, whatever be the par value of a shar The former method is used in Philadelphia; the latter in New York.

2. Stocks are often named from the rate of interest they draw; thus, we have 4's, 44's, 5's, etc. The time to run or date when due sometimes gives the name; as 4's of '97.

CASE I.

436. Given, the par value, the rate and the market value, to find the brokerage, net proceeds or entire cost.

1. A broker bought for a party 15 shares Pennsylvania

R. R. ($50), rate of brokerage being %; required the

Rule I.-Multiply the par value by the rate, to find the brokerage.

Rule II-Multiply the par value by the market value minus the rate, to find the net proceeds; or by the market value plus the rate, to find the entire cost.

NOTE. It is often shorter to multiply the brokerage on one share, by the number of shares. When the par is $50, one-half the rate should be used

in applying the rule.

WRITTEN EXERCISES.

2. I bought through a broker 46 shares of bank stock ($50) at par, brokerage being 1%; required the brokerage, and the cost of the stock. Ans. $5.75.

3. A broker bought for me 76 shares of bank stock ($50) at 47; what did the stock cost me, the brokerage being per cent.? Ans. $3619.50. 4. Mr. Lyte sold through his banker 72 shares New York Central ($100), at 1027; required the brokerage, at %, and net proceeds. Ans. Proceeds, $7398.

5. My broker bought on my account 25 shares Bank of North America ($100), at 150, and sold them at 161; what was his commission and my profit? Ans. Profit, $262.50.

6. Shall I gain or lose if I buy 65 shares Northern Central ($50) at 53, and after receiving two 4% dividends sell them for 514, brokerage %, interest on money not consid ered? Ans. $97.50 gain.

CASE II.

437. Given, the rate, the brokerage, or the net proceeds, or entire cost, and the market value, to find the par value.

1. A paid a broker $150 for selling some drafts, at the rate of 24%; what amount of drafts did he sell?

SOLUTION.-At a rate of 2%, .025 times the par value of the drafts equals the brokerage, which is $150; hence the par value equals $150 divided by .025, which we find is $6000.

Rule I.-Divide the brokerage by the rate, to find the par value.

Ryle II. Divide the net proceeds by the market value minus the rate, or the entire cost by the market value plus the rate, to find the par value.

WRITTEN EXERCISES.

2. I paid a broker $12.50 at 1% for buying N. Y. Central ($100); how many shares did he buy? Ans. 100 shares.

3. I paid my broker $4712.50 for an investment in Missouri 6's (100), at 94, including brokerage at 1%; what was the par value of the bonds? Ans. $5000.

4. I sent a New York broker a draft on Fisk & Hatch for $4953, to cover an investment made by my order in IIarlem Railroad at 95 ($100), and his commission of %; how many shares shall I receive? Ans. 52 shares.

5. My broker sold $3000 Philadelphia 6's at 1014, and invested the proceeds in United Companies of New Jersey stock at 131ğ ($100); how many shares did he buy, brokerage at 4%? Ans. 22 shares; $128.75 surplus.

SUPPLEMENTARY PROBLEMS.

To be omitted unless otherwise directed.

6. Mr. Westlake bought Pennsylvania R. R. stock ($50) at 497, and sold it at 534; after paying brokerage, he found he had a profit of $237.50; how many shares did he buy? Ans. 76.

7. Wishing to meet a note for $5000, I directed my broker to sell sufficient West Phila. Pass. Railway stock ($50) to cover the uote and brokerage; if the stock was selling at 78, how many shares must he sell, and what is the surplus? Ans. 64 sh.; $24.

8. I sold 25 shares of Philadelphia National Bank ($100) at 156, and directed my broker to invest the procceds in Norristown R. R. stock ($50) at 99; what is the amount of investment, after deduct ing brokerage? Ans. 39 shares; $40.37 surplus.