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. 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 the principal. 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? Let x = the principal; then x, or 17 35 200 x = $87.50. 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? * 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. What principal at 6 % will amount to $828.80 in 2 years? 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. *TO THE PUPIL.-Prove each answer obtained by finding its amount for the given time at the given rate. 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? for $1000 payable in thirty days without interest. presentation of this note to the cashier, how muc should he receive? 2. If Mr. Marshall's note described in proble dated April 10, 1898, (a) when must it be paid? much money will he pay when he "takes up" t (c) Does he pay for the use of the money borrowe rate of exactly 7 % per annum ? 3. If a bank is discounting at 7 %, how much s given for a note of $200 due in two months from th is discounted and bearing interest at the rate of annum from the date of discounting? 4. Find the value at the time of settlement of th ing note: 5. What principal at 6 % will gain $6 in 1 year 4 6. What principal at 6% will amount to $81 in 4 months? 7. Find the area in square feet, of a walk 4 fe around a rectangular flower bed that is 40 feet long feet wide. |