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Algebra.

260. ALGEBRA APPLIED TO SOME PROBLEMS IN INTEREST.

EXAMPLE.

What principal at 6% will gain $96 in 2 yr.?

Let x = the principal. Since the interest at 6% for 2 years equals 10% of the principal

12 12 r
then
X, or

96.
100 100
Multiplying by 100 12 x = 9600

x = 800.

PROBLEMS. 1. What principal at 6% will gain $67.50 in 2 years 6 months ? *

2. What principal at 6% will gain $27.20 in 1 year 4 months?

3. What principal at 7% will gain $87.50 in 2 years 6 months ?

173

35 Let x = the principal; then

X, or x= $87.50. 100 200

4. What principal at 5% will gain $187.50 in five years ? 5. What principal at 8% will gain $64 in 1 year 3 months ?

6. What principal at 6% will gain $61.20 in 2 years 6 months 18 days?

153

153 r Let x = the principal, then

= $61.20.

1000 1000 (a) Find the sum of the six answers. * TO THE PUPIL. -Prove each answer obtained by finding the interest upon it for the given time at the given rate.

X, or

261. ALGEBRA APPLIED TO SOME PROBLEMS IN INTEREST.

EXAMPLE.

What principal at 6% will amount to $828.80 in 2 years?

Let

x = the principal.

12 x
Then x + - 828.80.

100
Multiplying by 100 100 x + 12x = 82880.
Uniting

112 x = 82880

= 740.

r =

PROBLEMS.

1. What principal at 6% will amount to $368 in 2 years 6 months ? *

2. What principal at 6% will amount to $588.30 in 1 year 10 months ?

3. What principal at 5% will amount to $393.75 in 2 years 6 months ?

121 ;

the interest; 100 the amount, $393.75.

8 4. What principal at 5% will amount to $287.50 in three years?

5. What principal at 6% will amount to $458.80 in 2 years 5 months and 12 days?

147 Let x = the principal; then

x, or

the interest, 1000 1000

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and x +

147 x

147 x

and x +

= the amount, $458.80. 1000

(a) Find the sum of the five answers.

* TO THE PUPIL. Prove each answer obtained by finding its amount for the given time at the given rate.

Geometry. 262. THE AREA OF A RECTANGLE. 1. One side of every rectangle may be regarded as its base. The side perpendicular to its base is its altitude.

2. The number of square units in the row of square units next to the base of a rectangle, taken as many times as there are linear units in its altitude, equals the number of square units in its area. In the figure given, we have 4 sq. units x 3 = 12

sq.

units. Note 1.- In the above, it is assumed that the base and altitude are measured by the same linear unit, and that the sq. unit takes its name from the linear unit.

NOTE 2.- In the actual finding of the area of rectangles for practical purposes, the work is done mainly with abstract numbers and the proper interpretation is given to the result. There can be no serious objection to the rule for finding the area of rectangles, as given in the old books, provided the pupil is able to interpret it.

RULE.— To find the area of a rectangle, multiply its base by its altitude."

PROBLEMS. 1. Find the area of the surface of a cubical block whose edge is 9 inches in length.

2. Find the area in square yards, of a rectangular piece of ground that is 36 feet by 45 feet.

3. Find the area in acres, of a rectangular piece of land that is 92 rods by 16 rods.

4. Find the area in square rods of a piece of ground that is 99 feet by 66 feet.

5. The area of a field 30 rods square is how many times as great as the area of a field 10 rods square ?

263. MISCELLANEOUS REVIEW. 1. Clarence Marshall wished to borrow some money at a bank. He was told by the president of the bank that they (the bank officials) were “discounting good 30-day paper" at 7%. Mr. Marshall's name being regarded as “good," he drew his note upon one of the forms in use at the bank, for $1000 payable in thirty days without interest. On the presentation of this note to the cashier, how much money should he receive ?

2. If Mr. Marshall's note described in problem 1 was dated April 10, 1898, (a) when must it be paid ? (b) How much money will he pay when he “takes up” the note ? (c) Does he pay for the use of the money borrowed, at the rate of exactly 7 % per annum ?

3. If a bank is discounting at 7 %, how much should be given for a note of $ 200 due in two months from the time it is discounted and bearing interest at the rate of 6% per annum from the date of discounting ?

4. Find the value at the time of settlement of the following note : Date of note,

Apr. 1, 1896.
Face of note,

$ 300.
Rate of interest, six per

cent. Payment, Aug. 1, 1896, $75. Payment, Apr. 1, 1897, $ 80.

Settled, Aug. 1, 1898. 5. What principal at 6 % will gain $6 in 1 year 4 months?

6. What principal at 6% will amount to $81 in 1 year 4 months ?

7. Find the area in square feet, of a walk 4 feet wide around a rectangular flower bed that is 40 feet long and 12 feet wide.

(P. 354.)

STOCKS AND BONDS.

264. Some kinds of business require so much capital that many persons combine to provide the necessary money. Such a combination of men organized under the laws of a State, the capital being divided into shares, is known as a corporation, or stock-company. Those who own the shares are called stock-holders. The stock-holders elect from their own number, certain men to manage the business. These managers are called directors.

265. The nominal value of a share is its face value; that is, the sum named on its face. Large corporations, usually, though not always, divide their capital into $100 shares.

If the business is prosperous, shares may sell on the market for more than their nominal value. The stock is then said to be“ above par," or “at a premium.

If the business does not prosper, the shares may sell on the market for less than their nominal value. The stock is then said to be below par,” or “at a discount.

266. If the business is profitable, a part of all of the earnings is periodically divided among the stock-holders. The sum divided is called a dividend.

Dividends are always reckoned on the nominal or par value of the stock. If a corporation declares a 2% dividend, it pays to each stockholder a sum equal to 2 % of the nominal value of the stock which he

owns.

267. The kinds of business which are usually conducted by corporations, are: The mining of coal, silver, gold, etc.; the operation of gas works, railroads, large manufacturing establishments of all kinds, creameries, etc.

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