259. PROBLEMS IN "PARTIAL PAYMENTS." 1. Date of note, Jan. 1, 1896. Rate of interest, six per cent. 2. Date of note, July 10, 1896. Rate of interest, six per cent. 3. Date of note, Jan. 1, 1897. Rate of interest, six per cent. 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 must be greater than the answer by the Merchants' Rule, by the interest on $24 for four months, or 48 cents. Algebra. 260. ALGEBRA APPLIED TO SOME PROBLEMS IN INTEREST EXAMPLE. What principal at 6% will gain $96 in 2 yrs.? Since the interest at 6% for 2 years equals of the principal 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? 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? 261. ALGEBRA APPLIED TO SOME PROBLEMS IN INTEREST. EXAMPLE. What principal at 6% will amount to $828.80 in 2 years? Multiplying by 100, 100x + 12x = 82880. Uniting, PROBLEMS. 112x 82880 X = 740.* 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? 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? (a) Find the sum of the five answers. *What principal at a% will amount to b dollars in c years? 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. have 4 sq. units × 3 = 12 sq. units. In the figure given, we NOTE 1.-In the above, it is assumed that the base and altitude are measured by the same linear unit, and that the square unit takes its name from the linear unit. prac NOTE 2. In the actual finding of the area of rectangles for tical 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. 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 for the two months at the rate of 6% per annum? 4. Find the value at the time of settlement of the following note: Date of note, Face of note, $300. Rate, 6%. Apr. 1, 1896. 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. |