293. The method of finding the interest on any principal, for any rate and time, is represented by the

FORMULA: I= PX RX T, and read,

INTEREST equals the product of the PRINCIPAL, the RATE PER ANNUM, and the TIME, expressed in years.

Of the various methods in use for computing interest, the most simple, brief, and practical are presented in this work.

Since 6% is the legal rate in the majority of the States, the “six per cent. method" is presented as likely to be largely used.

The method by Cancellation, uniform in its applications to any rate and time, is brief and simple, hence, practical, and needs only to be understood to be preferred to all others.

294. 1. Find the interest and the amount of $97.50, at

2. Find the int of $267.60, for 1 yr. 4 mo. 18 da., at 5%.

RULE.-1. Multiply the principal by the rate, to find the interest for 1 year.

2. Divide the interest for 1 yr. by 12, to find the interest for 1 month.

3. Multiply the interest for 1 mo. by the time in months and tenths of a month, to find the required interest.

The above is a very simple and practical rule, and much used.

In like manner, find the interest and the amount,

3. Of $137.25 for 1 yr. 6 mo. 10 da. at 6%.

At 7%.

At 4%.

At 8%.

At 71%

At 71%.

4. Of $510.50 for 3 yr. 7 mo. 15 da. at 5%. 5. Of $1297.60 for 2 yr. 11 mo. 18 da. at 7%. 6. Of $36.40 for 1 yr. 7 mo. at 6%. 7. Of $750.50 for 3 yr. 1 mo. at 5%. At 8%. At 9%. 8. Required the amount of $408.60 from Aug. 20 to Dec. 18, 1886, at 10%.

9. What is the interest on a note for $515.62, dated March 1, 1883, and payable July 16, 1885, at 7%?

10. What is the value of a note of $65.75, due with interest for 3 yr. 2 mo., at 61%?

11. If a person borrow $375 at 5%, what will be due the lender at the end of 2 yr. 6 mo.?

12. A man sold his house and lot for $12500; the terms were, $4000 in cash on delivery, $3500 in 9 mo., $2600 in 1 yr. 6 mo., and the balance in 2 yr. 4 mo., with 6% interest. What was the whole amount paid?

SIX PER CENT. METHOD.

295. The interest of $1 at 6%,

For 12 mo., or 1 year, is 6 cents, or .06 of the principal.

66 " .01

" .005

66

2

66 "

66

661 66

66

66

Hence, the following

PRINCIPLES.-I. The interest on any sum at 6%, is SIX times as many hundredths of the principal, as there are YEARS in the given time; or,

II. ONE HALF as many hundredths of the principal, as there are MONTHS in the given time; or,

III. ONE SIXTH as many thousandths of the principal, as there are DAYS in the given time.

Thus, the interest on any sum, at 6% for 3 yr., is 6 times .03, or .18 of the principal; for 9 mo. it is of .09, or .043, or .045 of the principal; for 19 da. it is of .019, or .003 of the principal. Hence, for 3 yr. 9 mo. 19 da. it is .18+.045+.003 .2281 of the principal.

=

To find the interest at any other rate per cent., divide the interest at 6% b. 6, and multiply the quotient by the given rate.

296. 1. Find the int. of $427.20, at 6%, for 2 yr. 5 mo. 27 da.

14. $450 for 63 da.; 33 da.; 93 da.; 120 da.; 47 da.

Find by either of the preceding methods the int. of

297. This uniform method of computing interest for any time and rate by Cancellation, so simple and easily understood, is especially commended to the attention of the learner.

All cases of simple interest that can arise are covered by the following

FORMULAS:

1. When the time is expressed in years.

Principal rate × time = interest (293).

2. When the time is expressed in months.

Principal rate × time

12

= interest.

3. When the time is expressed in days.

Principal rate × time

360

= interest.

WRITTEN EXERCISES.

298. 1. Find the int. of $337 for 2 yr. 8 mo. at 6%; also, of $320 for 3 mo. 15 da. at 41%; of $76.50 for 2 yr. 2 mo. at 5%.

It will be observed that the principle and the solution of the above examples are essentially the same as before presented; namely, that the interest is the product of the principal by the rate and time (293).

The rate may be expressed decimally, but it is more convenient to express it as a fraction-100, expressed or understood, being the denominator.

When the principal contains cents, removing the decimal point multiplies by 100; if mills, by 1000. Hence, if the principal contains cents or mills, place 100 or 1000 on the left, as the case may be, and remove the decimal point.

In the above examples, the time, 2 yr. 8 mo., may be expressed as 23 or & yr., or as 32 mo. (3 yr.); 3 mo. 15 da. as 3 mo., or mo., or 105 da. (18 yr.); and the rate, 4%, as %. All mixed numbers should be changed to improper fractions.

RULE.-1. Draw a vertical line, and on the right, first write the principal in dollars, next the rate per year, and last the time in years, placing numerators on the right and denominators on the left.

2. Cancel equal factors, if any, on opposite sides of the line ; and the product of the remaining factors on the right, divided by the factor, or product of the factors on the left, will give the required interest.

For "Exact Int." and "Annual Int.," see 438 and 439, Addenda. The advantage of this method is, that the operation is always correctly indicated, and in most examples the work is shortened by cancellation.