HISTORY OF A STOCK COMPANY-Continued.

(g) At the end of the third year, the profits were so small that no dividend was declared. The stock-holders became disheartened and many of them offered to sell their stock at a large discount. Z appeared in the market and bought at "50% on the dollar" all the stock of the company except that owned by X and Y. How much did this stock cost Z? (h) At the end of the fourth year, the directors, X, Y, and Z, declared a 10% dividend. How much money was divided and how much did each receive?

(i) Before the close of the fifth year, the property burned and the lot upon which it stood was sold. After the insurance money had been received, the book accounts collected, and all debts paid, there remained in the treasury of the company $4350. How much of this money should each stock-holder, X, Y, and Z, receive?

(j) Did this creamery enterprise prove a good investment for X? For Y? For Z? For A? For B? For M?

MISCELLANEOUS PROBLEMS.

1. The directors of a company whose capital is $50000 determined to distribute among the stock-holders $2500 of profits. (a) A dividend of what per cent shall be declared? (b) How much will a man receive who owns 15 100-dollar shares?

2. A company whose capital is $75000 pays a dividend of 3%. (a) How much money is divided among the stockholders?

3. Mr. Steele owns 20 shares ($100) in the C., B. & Q. R. R. He receives as his part of a certain dividend $110. What is the per cent of the dividend?

Bonds.

269. A bond is a very formal promissory note given by a government or other corporate body, as a railway or a gas company, for money borrowed. Bonds usually have attached to them small certificates called coupons. These are really little notes for the interest that will be due at different times Thus, a 10-year bond for $1000 with interest at 6% payable semi-annually may have 20 coupons attached, each calling for $30 of interest.

270. Money invested in bonds yields a specified income; but the income from money invested in stocks depends upon the profits of the company.

271. Bonds, like stocks, are sometimes sold for more than their face value. They are then said to be "above par," or "at a premium." Like stocks, too, they are sometimes "below par," or " at a discount."

1. What is the semi-annual interest on two 1000-dollar U. S. 5% bonds?

2. What sum should be named on each coupon of a 1000dollar city bond if the interest is payable annually at the rate of 7% ?

3. To raise the money to build a court-house, a certain county issued $50000 worth of 6% ten-year bonds. These sold upon the market at 2% premium. (a) How much money was received for the bonds? (b) How much did A pay, who bought three 1000-dollar bonds? (c) If the interest was payable semi-annually, how much should A receive each 6 months on this investment?

4. Has the county or city in which you live any "bonded indebtedness"? If so, how much, and what is the rate of interest?

NOTE.-Bonds are made in great variety both as to form and content; but in all, indebtedness is acknowledged, and the amount, rate of interest, and time of payment for both principal and interest, named. The above is a very short and concise form of Bond (much reduced in size) and is an exact copy of one prepared for actual use.

1. Examine the above Bond. If the time it is to run is five years, how many coupons should be attached?

2. If the Bond is dated Jan. 1, 1898, what date should be written in each coupon?

3. If the face of the Bond is $100 and the rate 5%, what sum should be written in each coupon?

272. ALGEBRA APPLIED TO SOME PROBLEMS IN INTEREST.

EXAMPLE.

At what rate per cent will $500 gain $55 in 2 yrs.?

x = the rate,

*

Let

2x

1000x

then

of 500, or

100

100

1. At what rate per cent will $450 gain $72 in 2 years? 2. At what rate per cent will $320 gain $48 in 3 years? 3. At what rate per cent will $560 gain $84 in 2 years 6 months?

4. At what rate per cent will $600 gain $75 in 2 years 6 months?

5. At what rate per cent will $600 gain $114 in 2 years 4 months 15 days?

NOTE.-Problem 5 may be solved arithmetically by finding the interest of $600 for 2 yr. 4 mo. 15 da. at 6%. Divide this interest by 6 (to find the interest at 1%) and find how many times the quotient is contained in $114.

*The arithmetical solution of this problem is as follows: The interest of $500 for 2 years at 1% is 180 of $500. 18 of $500 = $10. To gain $55 in 2 years, $500 must be loaned at as many per cent as $10 is contained times in $55. It is contained 51 times; so $500 must be loaned at 54% to gain $55 in 2 years. Observe that by this method we divide the given interest by the interest of the principal for the given time at one per cent.

Algebra.

273. ALGEBRA APPLIED TO SOME PROBLEMS IN INTEREST.

EXAMPLE.

In how long a time will $650 gain $97.50 at 6%?

1. In how long a time will $400 gain $30 at 5%?
2. In how long a time will $600 gain $96 at 6%?
3. In how long a time will $800 gain $68 at 6%?
4. In how long a time will $500 gain $56 at 6%?
5. In how long a time will $400 gain $29 at 6%?

REVIEW PROBLEMS.

6. What principal at 8% will gain $124.80 in 3 years? 7. What principal at 7% will amount to $410.40 in 2 years?

8. At what rate per cent will $900 gain $72 in 2 years? 9. In how long a time will $1000 gain $160 at 6 per cent? 10. What principal at 5% will amount to $736 in 3 years?

TO THE PUPIL.-Prove each answer by finding the interest on the given principal at the given rate for the time obtained.

*The arithmetical solution of this problem is as follows: The interest of $650 for one year at 6% is $39. As many years will be required to gain $97.50 as $39.00 is contained times in $97.50. It is contained 24 times; so in 24 years $650 will gain $97.50. Observe that by either method we divide the given interest by the interest of the principal for 1 year at the given rate.