CHAPTER IX

INTEREST

LESSON 27

This is probably the most common business problem. Everyone must figure interest at some time. Some businesses are of such a nature that their very existence is dependent upon interest returns. The principles you will learn in this chapter will be of inestimable value to you all the rest of your life.

Definitions.

money.

Interest is money paid for the use of

The amount borrowed is called the principal.

The per cent charged for one year's use of the principal is called the rate.

The period for which the money is borrowed is called the time.

The amount paid for the use of the principal is called the interest.

Thus, if $240 is paid for the use of $4000 for 1 year at 6%, $4000 is the principal, 6% or .06 is the rate, 1 year is the time, and $240 is the interest.

Kinds. There are three kinds of interest; namely, simple interest, periodic or annual interest, and compound interest.

Definition.

cipal only.

SIMPLE INTEREST

Simple interest is interest upon the prin

Kinds. There are three kinds of simple interest; namely, ordinary interest, bankers' interest, and exact interest.

Definition.

ORDINARY INTEREST

Ordinary interest is interest computed on

a basis of 360 days to a year.

Finding the time. The time for which to compute ordinary interest is found by subtracting dates, using 30 days for each month.

When used. Ordinary interest is used in all cases unless there is an established custom, or a contract, which requires bankers' or exact interest. In dealing with banks, it is the custom to use bankers' interest, and in figuring interest on government bonds, it is customary to use exact interest.

Methods. There are many methods of computing ordinary interest, all of which are founded on the custom of charging a certain per cent of the principal for one year's use of the principal.

When the time is in years, we may multiply the principal by the rate to find the interest for one year, and then multiply the interest for one year by the number of years to find the interest for the given time. Or, more briefly, multiplying the principal, rate, and years together gives the interest. Stated as a formula, we have:

Principal

Rate of interest X Years

=

Interest.

PROBLEM. Find the interest on $385 at 6% for 3 years.

To find the interest on any principal at any rate for any number of years, multiply the principal by the rate to find the interest for one year, and multiply this result by the number of years.

18% of the principal would be earned in 3 years. 18% of $385 is $69.30, the interest for 3 years. Hence:

To find the interest on any principal at any rate for any number of years, multiply the rate by the number of years, then multiply the principal by this result.

When the time is in months, we may multiply the principal by the rate to find the interest for one year. Dividing the interest for one year by 12 gives the interest for one month. Multiplying the interest for one month by the number of months gives the interest for the given time. Or, more briefly stated, multiplying the principal, rate, and number

of months together, and dividing by 12 gives the interest. As a formula, we have:

Principal

Rate of interest X Number of months

12

= Interest.

PROBLEM. Find the interest on $248 at 6% for 7 months.

FIRST SOLUTION

22

124 $248

X .06

X

7

$8.68

EXPLANATION

The interest for 1 year is 6% of $248, or $248.06. The interest for 7 months is of the interest for 1 year, or of ($248X.06), or $248X.06X, or ($248X.06X7)÷12, as shown in the solution at the left. Cancelling common factors, and multiplying, we obtain $8.68 as the interest for 7 months. This method is known as the cancellation method. Hence:

To find the interest on any principal at any rate for any number of months, multiply the principal by the rate by the number of months, and divide by 12, using cancellation when possible.

we obtain $8.68, the interest for 7 months. This method is known as the aliquot part method. Hence:

To find the interest on any principal at any rate for any number of months, first multiply the principal by the rate to find the interest for one year, then take aliquot parts of one year's interest for the given number of months.

When the time is in days, we may multiply the principal by the rate to find the interest for one year. Dividing the interest for one year by 360, we get the interest for one day. Multiplying the interest for one day by the number of days gives the interest for the given time. Or, briefly, multiplying the principal, rate, and days together, and dividing by 360 gives the interest. Stated as a formula, we have:

Principal

Rate of interest × Number of days = Interest.

360

PROBLEM. Find the interest on $1140 at 6% for 17 days.

multiplying, we get $3.23, the interest for 17 days.

Hence:

To find the interest on any principal at any rate for any number of days, multiply the principal, rate, and number of days together, and divide by 360, shortening by cancellation.