A Second Course in the New Mathematics

6. John Jones bought a used automobile for a note of $350 at 6% for 3 months. How much would the automobile cost him?

7. Mary Williams bought a radio for $250. She paid $100 down and gave a note for the balance for 4 months at 6%. Find the total cost of her radio.

8. Mr. Wheatraiser bought some farm machinery and gave $600 down and a note of $1500 for 6 months and 15 days at 6% for the balance. Find the total cost of his machinery.

Exact Interest is computed on the basis of 365 days to the year and the sixty-day method does not apply. The way this is done is shown in the following

Example. Find the exact interest on $1200 from Jan. 8, 1926, to March 20, 1927, at 6%.

Solution. It is one year from Jan. 8, 1926, to Jan. 8, 1927. From Jan. 8, 1927, to March 20, 1927, is 71 days.

Left in Jan. 23 days

Feb. 28 days

Mar. 20 days

71 days

The interest for 71 days will be of a year's interest.

Interest on $1200 for 1 year at

Interest on $1200 for 71 days

71 365

365X $72 Total interest

= $72.00

14.01

For whole years there is no difference between exact interest and ordinary simple interest, but for parts of a year the exact interest is less than ordinary interest because for each day there is paid only of a year's interest instead of of it.

Our United States government uses exact interest. City governments and banks, use exact interest when the interest on large amounts of money is calculated.

1. Find the exact interest on $750 for 65 days at 6%. 2. What is the exact interest on $875 for 275 days at 6%? 3. Find the exact interest on $950 for 50 days at 6%. 4. What is the exact interest on $2000 for 25 days at 6%? at 5%? at 7%?

5. Find the exact interest on $1800 from March 2, to Oct. 8 at 5%.

6. What is the difference between the exact interest on $500 for 95 days at 6% and the simple interest at 6%?

Bankers' Short-Cut. Bankers compute the exact numbers of days between two dates by the use of a table like the following:

FROM
ANY

DAY OF

TO THE SAME DAY OF

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

59 31

92 123 153 184 214

92 122 153 183

Jan. 365 31 59 120 151 181 212 243 273 304 334 Feb. 334 365 28 89 120 150 181 212 242 273 303 Mar. 306 337 365 61 92 122 153 184 214 245 275 Apr. 275 306 334 365 30 61 91 122 153 183 214 244 May 245 276 304 335 365 31 61 June 214 245 273 304 334 365 30 61 July 184 215 243 274 304 335 365 31 Aug. 153 184 212 243 273 304 334 365 31 61 Sept. 122 153 181 212 243 273 303 334 365 30 Oct. 92 113 151 182 212 243 273 304 335 365 31 61 Nov. 61 92 120 151 181 212 242 273 304 334 365 30 Dec. 31 62 90 121 151 182 212 243 274 304 332 365

62 92 123 153

The use of this table is shown by the following:

92122

61 91

Example I. What is the exact number of days between July 12 and October 12 of the same year?

Solution. Find the intersection of July Street (at left) and October Avenue (at top) and you find 92 days.

Example II. Obtain the exact number of days from April 2 to August 18 of the same year.

Solution. Intersection of April Street and August Avenue gives 122 days from April 2 to August 2. From August 2 to August 18 is 16 days. 122 16 138. Therefore the + answer is 138 days.

Example III. Find the exact number of days from November 21 to March 5 of the next year.

Solution. The table gives 120 days from November 21 to March 21. Count back from November 21 to November 5, obtaining 16 days. 120 - 16 104. Therefore the answer is 104 days. If it is a leap year add one day for February.

Mental Exercise

Using the table find the exact number of days

1. From May 25 to Nov. 25. 3. From June 30 to Sept. 20. 2. From Apr. 15 to Aug. 19. 4. From July 3 to Sept. 15.

5. From Dec. 2 to Feb. 16 of the next year.

6. From Nov. 6 to Apr. 15 of next year.

Compound Interest. — If interest is not paid when it is due, it may be added to the principal. This sum then becomes the new principal on which interest is paid. Interest so computed is called compound interest and may be compounded annually, semi-annually, or quarterly.

Example. Mr. Wood borrowed $350. from Mr. Allison at 5%. He agreed to pay interest compounded annually. Because of a poor wheat crop he was unable to pay this note until the end of three years. How much money must he pay Mr. Allison, including the compound interest?

Solution.

$350 principal for first year.

.05

17.50 interest for first year.

350.

367.50 principal for second year.

.05

18.375 interest for second year. 367.50

385.875 principal for third year.

.05

19.29375 interest for third year.

385.875

$405.16875 or $405.17 amount due at end of third year.

Savings banks pay a modified form of compound interest at a low rate, seldom more than 4%. It is usually compounded semi-annually though some banks now compound it quarterly. Interest is paid, however, only on even dollars, and on sums which have been in the bank throughout the whole interest period.

Example. George Hudnut deposited $100 in a savings. bank which paid interest at 4% compounded semi-annually. How much had he to his credit at the end of 2 years and 6 months?

Solution. (Remember that the savings bank does not pay interest on the cents left over.)