### Simple Interest – Definition and Calculation

When we borrow money we are expected to pay for using it – this is called interest.

There are three components to calculate simple interest: principal (the amount of money borrowed), interest rate and time. Formula for calculating simple interest:

I = Prt

Where,
I = interest
P = principal
r = interest rate (per year)
t = time (in years or fraction of a year)

CALCULATING SIMPLE INTEREST EXAMPLES

Example:
Alan borrowed \$10,000 from the bank to purchase a car. He agreed to repay the amount in 8 months, plus simple interest at an interest rate of 10% per annum (year).

If he repays the full amount of \$ 10,000 in eight months, the interest would be:

P = \$ 10,000 r = 0.10 (10% per year) t = 8/12 (this denotes fraction of a year)

Applying the above formula, interest would be
I = \$ 10,000(0.10)(8/12)
= \$ 667

If he repays the amount of \$10,000 in fifteen months, the only change is with time. Therefore, his interest would be:
I = \$ 10,000 (0.10)(15/12)
= \$ 1,250

The Bankers Rule:
In the world of finance, time is often expressed in days rather than months. Two kinds of times are used: Exact time and Approximate time.

Exact Time
It uses the precise number of days for time of the loan or investment. Assumes that each year has 360 days.
Approximate time: Assumes that each year has 360 days and each month has 30 days.

The Bankers rule
Is widely used in the United States, and uses the combination of ordinary interest and exact time.

Example: An investment of \$5,000 is made on August 31 and repaid on December 31 at an interest rate of 9%
Applying the Bankers rule, interest would be:

I = Prt
= \$5,000(0.09)(106/360)
= \$ 132.50

Determining the maturity value:
Maturity value = Interest + Principal

Formula: S = P (1 + rt)
Refer the example given under the Bankers rule. Maturity value would be,

S = \$ 5,000 [1 + 0.09(106/360)]
= \$ 5,000 (1.0265)
= \$ 5,132.50

Note: How to calculate 1.0265. First, divide 106 by 360, you will get 0.2944. Then, multiply 0.2944 by 0.09, you will get 0.0265. Add 1 to 0.0265 to get 1.0265

Finding time:
Formula: t = I/Pr
Using the same example above, time would be
t = \$ 132.50/[\$ 5,000*0.09]
= 132.50/\$ 450
= 0.2944
We have considered 360 days in a year. Therefore number of days would be,

t = 0.2944 x 360
= 106 days

Finding the interest rate:
Formula: r = I/Pt

Using the same example above, time would be
r = \$ 132.50/[\$ 5,000*(106/360)]
= 132.50/\$ 1,472.22
= 0.09 i.e. 9%

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