SIMPLE INTEREST.

437. ILLUSTRATION.-A has the use of $100 of B's money end of the year he pays B for its ʊ of $ 100.

for one year, and at the
use $6, a sum equal to
Money, as $6 above,
definite period of time, is interest.

paid for the use of money for a

438. The sum for the use of which interest is paid, as $100 above, is the principal.

439. The principal, with the interest, as $100 + $6, or $106, is the amount.

Define interest, principal, amount.

440. Interest is found by taking a number of hundredths of the principal; it is therefore a PERCENTAGE, and the principal is the BASIS.

441. The number of hundredths of the principal taken to find the interest for 1 year is the rate per cent per annum, usually called the rate.

NOTE I.-Debts of all kinds draw interest from the time they become due, but not before, unless interest is specified. Interest on interest remaining unpaid, however, is not generally allowed.

NOTE II. - The rate of interest established by law is the legal rate.

NOTE III. TABLE OF LEGAL RATES OF INTEREST FROM OFFICIAL SOURCES. 1869.

NOTE IV. When no rate is mentioned, the legal rate is understood. More than the legal interest is usury.

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TO THE TEACHER. If the teacher prefers, he may allow the pupil to omit the General Method of computing Interest, and pass directly to the 6% method. (Art. 444.)

After having learned the 6% method, for additional practice the pupil may perform the following examples by that method:

442. ILL. EX. Find the interest of $309.60 for 1 y. 5 m. 18 d. at 10%.

$45.408 Interest.

Explanation. The interest of $ 309.60 for 1 y. is 10%, or of the principal, for 4 months it is of the interest for 1 year, for 1 month it is of the interest for 4 months, for 15 days it is of the interest for 1 month, and for 3 days it is of the interest for 15 days. Adding these sums we have for the interest of $309.60 for 1 y. 5 m. 18 d.,

$45.41, Ans.

From the above operation we derive the following

RULE. To compute interest for years, months, and days, at any rate per cent: -1. Find the interest for 1 year by multiplying the principal by the given rate, and for a number of years, by multiplying the interest for 1 year by the number of the years.

2. Find the interest for months by taking aliquot parts of 1 year's interest, and for days by taking aliquot parts of 1 month's interest.

NOTE I. In the answers reject mills when less than 5, and call 5 or more 1 cent.

NOTE II.

- In computing interest, 30 days are considered a month.

Find the interest of

443. EXAMPLES.

Ans. $63.60.

Ans. $30.26.

Ans. $44.27. Ans. $115.29. Ans. $5.42. Ans. $54.23.

Ans. $425.52.

Ans. $92.98. Ans. $807.03. Ans. $56.82. Ans. $625.60.

1. $720 for 1 y. 5 m. 20 d. at 6%. 2. $234 for 1 y. 7 m. 12 d. at 8%. 3. $428.75 for 1 y. 5 m. 21 d. at 7%. 4. $1265.40 for 1 y. 9 m. 26 d. at 5%. 5. $72.90 for 1 y. 10 m. 9 d. at 4%. 6. $286.20 for 2 y. 1 m. 8 d. at 9%. 7. $2500. for 2 y. 3 m. 7 d. at 71%. 8. $752.20 for 1 y. 2 m. 25 d. at 10%. 9. $3207 for 3 y. 5 m. 11 d. at 7%. 10. $287.50 for 3 y. 11 m. 13 d. at 5%. 11. $1200 for 4 y. 4 m. 4 d. at 12%. 12. $212 for 6 m. 29 d. at 1% a month. 13. $290 for 8 m. 27 d. at 1% a month. 14. $629 from Jan. 1, 1868, to Jan. 16, NOTE. - Find the time by Art. 337, Note I. 15. $422 from Jan. 1, 1869, to July 21, 1869, at 10%. 16. $2000 from April 10, 1869, to June 20, 1869, at 7%. Sum of last 2 answers, $51.83.

Ans. $14.77.

Ans. $12.91.

1870, at 7%.

Ans. $89.89.

17. If $1200 is on interest from Oct. 4, 1868, to Jan. 11, 1870, at 10%, what sum will pay the principal with the interest at the latter date? Ans. $1,352.331.

18. If $200 is loaned Oct. 1, 1869, what will pay the loan with the interest at 9%, on the 28th day of March following? Ans. $208.85.

For Dictation Exercises upon these Examples, see Key.

SIX-PER-CENT METHODS OF COMPUTING INTEREST.

FIRST METHOD.

444. ILL. EX. At 6%, what part of the principal will the interest equal for 2 months?

Explanation. Since the interest for 1 year or 12 months equals 6%, or .06 of the principal, the interest for 2 months, which is of a year, will equal of .06, or .01 of the principal.

INFERENCE. If the interest for 2 months equals .01 of the principal, the interest for any number of months will equal one half as many hundredths of the principal as there are months.

EXERCISES.

What part of the principal does the interest equal for

10 months by taking of the interest for 100 months, and for 1 month by taking of the interest for 10 months.

We then take the sum of these items, and have $266.40 for the

answer.

NOTE. In the above operation the interest for 10 months and the interest for 1 month are expressed by simply moving the decimal point in previous expressions.

EXERCISES.

Find the interest of $400 for 22 months; for 11 months; for 55 months. Ans. $44; $22; $110.

446. ILL. EX. At 6%, what part of the principal will the interest equal for 6 days?

Explanation. Since the interest for 2 months, or 60 days, equals .01 of the principal, the interest for 6 days, which is of 60 days, will equal of .01, or .001 of the principal.

INFERENCE. — If the interest for 6 days equals .001 of the principal, the interest for any number of days will equal one sixth as many thousandths of the principal as there are days.

EXERCISES.

What part of the principal does the interest equal for

447. ILL. Ex. Find the interest of $1200 for 93 days.

We then find the sum of these items to be $18.60, Ans.

From the above illustrations and exercises we derive the following

RULE. To compute interest at 6%: 1. To find the interest for 200 months, take a sum equal to the principal; for 20 months, equal to of the principal; for 2 months, equal to of the principal; and for 6 days, equal to 1 of the principal.

2. For any other periods of time, take convenient multiples or aliquot parts of the interest for the times expressed above.