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259. PROBLEMS IN "PARTIAL PAYMENTS.”

1. Date of note, Jan. 1, 1896.

Face of note, $800.
Rate of interest, six per cent.
Payment May 1, 1896, $125.
Payment Dec. 1, 1896, $230.
Find amount due Jan. 1, 1898.

2. Date of note, July 10, 1896.

Face of note, $500.
Rate of interest, six per cent.
Payment, Dec. 22, 1896, $200.
Payment, July 15, 1897, $200.
Find amount due Jan. 1, 1898.

3. Date of note, Jan. 1, 1897.

Face of note, $600.
Rate of interest, six per cent.
Payment Sept. 1, 1897, $100.
Find amount due Jan. 1, 1898.

NOTE.-Solve problem 3 by the Merchants' Rule and by the United States Rule. The answer obtained by the latter will be 48 cents larger than the answer obtained by the former.

Observe that the Merchants' Rule is based upon the supposition that interest is not due until the time of settlement of the note, while the U.S. Rule is based upon the supposition that interest is due whenever a payment is made. By applying the latter rule to problem 3, $24 of interest must be paid Sept. 1; by applying the former rule to the same problem the entire $100 paid Sept. 1, applies in payment of principal. The answer, then, by the U.S. Rule, ist be greater than the answer by the Merchants’ Rule, by the interest on $24 for four months, or 48 cents.

4. Change the interest in all the above problems to seven per cent, solve them by the U. S. Rule, and find the sum of the amounts due Jan. 1, 1898.

Algebra.

260. ALGEBRA APPLIED TO SOME PROBLEMS IN INTEREST.

EXAMPLE.

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

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

12 then

96. 100

100 Multiplying by 100

9600 800.

12 x

X, or

12 x =

x =

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

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 ?

17

35 Let x = the principal; then

x, or 100

$87.50. 200

X =

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 153x Let x = the principal, then

$61.20 1000 1000 (a) Find the sum of the six answers.

X, or

* To The PUPIL.-Prove each answer obtained by finding the interest upon it for the given time at the given rate.

261. ALGEBRA APPLIED TO SOME PROBLEMS IN

INTEREST.

EXAMPLE.

12 x

=

112 x =

x =

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

Let

x = the principal. Then x +

828.80.

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

82880

740.

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 Let x = the principal; then x, or š x, or = the interest;

100

8 x and x +

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 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.

x

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147 x

147 x

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?

a

a

263. MISCELLANEOUS REVIEW.

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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.

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