Most people are used to spending what they earn on housing, food, education, clothing and entertainment. Sometimes, extra expenditure have also to be met with.

Some people are wise as they manage to put aside some money for such expected and unexpected expenditures. But, most people have to borrow money for such contingencies. They promise to return it after a specified period or time. At the end of the time, we have to not only pay the money which we have borrowed but also, we have to pay some additional money for using the lender's money.

The money borrowed is called Principal. The additional money we pay back is called Interest. The total amount which is payed back to the lender at the end of the specified period is called Amount.

Therefore,
AMOUNT = PRINCIPAL + INTEREST

## What is Simple Interest?

Interest is the fee paid by a borrower to the lender in loan transactions as the consideration for keeping the money. Annually a fixed percentage of the amount involved in the transaction is calculated as Simple Interest.

Let us look at few examples to know what is simple interest.

### Examples on Simple Interest

Given below are some of the examples on Simple Interest

Example 1:

Lets take 500 dollars for an interest of 6% per annum for 3 years. Find the total amount paid by the end of three years.

Solution:

The phrase "rate of 6% per annum" means we have to pay 6 dollars for keeping 100 dollars for one year.
Interest on 100 dollars for 1 year = 6 dollars

Interest on 1 dollar for 1 year = $\frac{6}{100}$

Interest on 1 dollar for 3 years = $\frac{6 \times 3}{100}$

Interest on 500 dollars for 3 years = $\frac{500 \times 6 \times 3}{100}$

= 90 dollars

Hence, the total amount = principal + interest
= (500 + 90) dollars
= 590 dollars

Example 2:
Find the interest on 500 dollars for a period of 4 years at the rate of 8% per annum. Also, find the amount to be paid at the end of the period.

Solution:
Rate of interest = 8% per annum
It means interest on 100 dollars for 1 year = 8 dollars

Therefore,
Interest on 100 dollars for 4 years = $8 \times 4$
= 32 dollars
Hence,
Interest on 1 dollar for 4 years = $\frac{32}{100}$

So, interest on 500 dollars for 4 years = $\frac{32 \times 500}{100}$

= 160 dollars
Now,
Amount = principal + interest
= (500 + 160) dollars
= 660 dollars
Thus, interest is 160 dollars and the amount to be paid back is 660 dollars.

## Simple Interest Formula

The formula for calculating the Simple Interest is

I = P x T x R

Where,
I = Simple Interest
P = Principal or loan amount
T = Time period for loan taken as number of years
R = Rate of interest expressed as a decimal.

The amount to be repaid including the interest is therefore,
Amount = Principal + Interest

Example to Calculate Simple Interest:

Paul invested $5,000 in a savings bank account that earned 3% simple interest. Find the interest earned if the amount was kept in the bank for 4 years. Solution: In the above problem Principal P =$ 5,000.00 Time Period T = 4 years and Rate of Interest = 3% = 0.03. Plugging these values in the simple Interest formula,

I = P x T x R
= 5,000 X 4 x 0.03
= $600.00 Interest earned for the investment =$ 600.00

## Simple Interest Word Problems

Given below are some of the word problems in calculating Simple Interest.

Example 1:

Dick takes a loan of $7,000 to buy a used truck at the rate of 9 % simple Interest. Calculate the annual interest to be paid for the loan amount. Solution: From the details given in the problem P =$7,000 and R = 9% or 0.09 expressed as a decimal. As the annual Interest is to be calculated, the time period T =1. Plugging these values in the simple Interest formula,

I = P x T x R
= 7,000 x 1 x 0.09
= 630.00

Annual Interest to be paid = $630.00 Example 2: Daniel bought$ 11,000 from a bank to buy a car at 12% simple Interest. If he paid 9,320 dollars as interest while clearing the loan, find the time for which the loan was given.

Solution:

Principal = 11,000 dollars
Rate of Interest R = 12% = 0.12
Interest paid = I = 9,320 dollars.

T = $\frac{I}{PR}$

= $\frac{9320}{11000 \times 0.12}$

= 7 years.

The loan was given for 7 years.

## Find the Interest When Time and Principal is Known

Interest is said to be simple, if it is calculated on the original principal throughout the loan period(T), irrespective of the length of the period, for which it is borrowed.
To calculate Simple interest, its formula is given by,

I = $\frac{P \times R \times T}{100}$

where, P is the principal (in dollar), R is the rate per annum and T is the time (in years)

Example 1:

Find the simple interest on the sum 800 dollars for 2.5 years at 4.5% per annum.

Solution:

Given, principal (P) = 800 dollars
Time (T) = 2.5 years
Rate (R%) = 4.5% per annum

So, Simple interest = $\frac{P \times R \times T}{100}$
= $\frac{800 \times 4.5 \times 2.5}{100}$
= 90 dollars

Example 2:

Find the simple interest on 7300 dollars from 11 May 1987 to 11 September 1987 at 5% per annum.

Solution:

Out of the starting and the closing date, it is common practice to leave one of the dates and to count the other. So, let us leave out 11th May and count the 11th September. Thus, the number of days is,
May = 20days
June = 30 days
July = 31 days
August = 31 days
September = 11 days

Hence, the interest is to be paid for 20 + 30 + 31 + 31 + 11 = 123
Thus, Principal (P) = 7300 dollars
Time (T) = $\frac{123}{365}$ years

Rate (R%) = 5%
Hence,

Simple Interest = $\frac{P \times R \times T}{100}$
= $7300 \times $$\frac{123}{365} x \frac{5}{100} = 123 dollars ## Find the Time When Interest and Principal is Known To calculate Simple interest, we use the formula, Simple Interest = \frac{P \times R \times T}{100} where, P is the principal (in dollar), R is the rate per annum and T is the time (in years) Now, in order to calculate time when interest and principal is given we get, I = \frac{P \times R \times T}{100} Multiply by 100 on both sides, 100 \times I = 100 \times$$\frac{ P \times R \times T}{100}$
$100 \times I$ = $P \times R \times T$
Divide by P on both sides,

$\frac{100 \times I}{P}$ = $\frac{P \times R \times T}{P}$
$\frac{100 \times I}{P}$ = $R \times T$
Divide by R on both sides,

$\frac{100 \times I}{P \times R}$ = $T$

$T$ = $\frac{100 \times I}{P \times R}$

Here, we take time (T) in years. If you want to find the interest in months, then you can't directly substitute the months in T but have to convert the months into years.

The following table shows how the time given in months can be converted in terms of years:
 Months Years 1 $\frac{1}{12}$ 2 $\frac{2}{12}$ = $\frac{1}{6}$ 3 $\frac{3}{12}$ = $\frac{1}{4}$ 4 $\frac{4}{12}$ = $\frac{1}{3}$ 5 $\frac{5}{12}$ 6 $\frac{6}{12}$ = $\frac{1}{2}$ 7 $\frac{7}{12}$ 8 $\frac{8}{12}$ = $\frac{2}{3}$ 9 $\frac{9}{12}$ = $\frac{3}{4}$ 10 $\frac{10}{12}$ = $\frac{5}{6}$ 11 $\frac{11}{12}$ 12 $\frac{12}{12}$ = 1

Example 1:

How much time will the simple interest on a certain sum be 0.125 times the principal at 10% per annum.

Solution:

Suppose Principal, P = 1 dollar
Interest, I = 0.125 dollars
Rate, R = 10% per annum

I = $\frac{P \times R \times T}{100}$
Time, T = $\frac{100 \times I}{P \times R}$

= $\frac{100 \times 0.125}{1 \times 10}$

= 1.25 years

Example 2:

What sum of money lent out at 6.25% per annum simple interest produces 37.50 dollars as interest in 8 months?

Solution:

Interest, I = 37.50 dollars
Time, T = 8 months = $\frac{8}{12}$ years = $\frac{2}{3}$ years

Rate, R = 6.25% per annum
Since, I = $\frac{P \times R \times T}{100}$

So, P = $\frac{100 \times I}{R \times T}$

= $\frac{100 \times 31.50}{6.25 \times (2/3)}$

= 900 dollars

Example 3:

Find the interest on 1200 dollars at 6% per annum for 146 days.

Solution:

The interest is 6% per annum.
It means 6% for 365 days.
Therefore, rate of interest per day = $\frac{6}{365}$

Rate of interest for 146 days = $\frac{146 \times 6}{365}$

= $\frac{146 \times 6}{365 \times 100}$

Hence, Interest = $1200 \times$$\frac{146 \times 6}{365 \times 100}$

= 28.8 dollars

## Simple Interest Vs Compound Interest

Simple interest is an interest that is only earned on the orginal principal that is borrowed or loaned. A simple interest is calculated by using the formula:
I = p i n

Where,
I = simple interest .
p = principal borrowed or loaned
i = interest rate per time period
n = number of time periods

Compound interest is an interest that is earned on both the principal and the interest. When interest is compounded, the interest is earned each time period on the original principal and on the interest which is accumulated from the preceding time periods.

We shall illustrate the difference between simple and compound interest and show how effective interest compounding can be on an investment after a few years.