 # Simple Interest Formula

While learning about the theory of simple interest, we will also study how to calculate simple interest. Running through the formula for simple interest you will get to know more about it. Likewise, when we raise a sum of money from any financial institution (bank, NBFC’s, post offices, agency) or other source (moneylender), we need to pay them back the money after a specified time period along with an interest amount in lieu of utilizing the money borrowed. The additional money we are required to pay in addition to the money borrowed is the simple interest.

### Solving Simple Interest Problems

In Simple interest, the interest is computed on the same sum of money in each time period, and, hence, the interest to be paid or received in each time period is the same. i.e., if the interest on a sum borrowed for a specified period is calculated uniformly, then it is called simple interest.

## Simple Interest Notations

 Terms Symbols Principal P Rate of interest % per annum R Time Period T Simple interest I Amount A

### Formula to Find Simple Interest

A standard formula to find simple interest in math is as below;-

S.I = (P × R × T)/100

Note that: Formula for calculating amount is A = P + I

Interest calculated on the original principal throughout the holding period

Simple Interest = $\frac{Principal \; \times \; Time \; \times \; Rate \; of \; interest}{100}$ = $\frac{PTR}{100}$

### Components for Calculating Simple Interest

Simple Interest is calculated based on the money borrowed and the time period availed to use that facility until the return. That said,

• The sum borrowed from the lender for a given time is called the principal

• Additional money payable is called the simple interest

•  Interest is the extra money that the borrower pays for using the lender’s money

• It is represented as rate percent per annum (p.a.) i.e., 12% per month means, the interest on Rs.20000 for 1 year is Rs2400

• Frame of time for which money is borrowed is called the time period

• The total sum of money paid back after the specified time is called the amount

### Key to Calculate Simple Interest Using Time Period

While computing the time period in order to calculate simple interest we need to take into account the following:

• We do not count the day on which the money is borrowed but we count the day for which the money is returned.

• When the sum is borrowed in terms of years, we always convert the number of days into a year and thus divide the number of days by 365, whether it is a leap year or a standard year.

Now that we already know what simple interest is and how we can calculate it using the simple interest formula in maths, let’s get going with some practice exercises.

### Example 1:

Mark borrowed a sum of Rs 20,000 from a private money lender Tony, at a rate of interest 15% per annum for 3 years. Calculate the simple interest on this sum and the amount to be paid at the end of 3 years.

### Solution1:

On Rs 200, interest charged for 1 year will beRs.30

15/100×20000 = Rs.3000

So, on Rs 20,000, interest charged for 3 years will be = 3000×3=Rs.9000

Thus, Amount to be paid at the end of 3 years = Principal + Interest

That is

20,000 + 9,000 = 29000

Hence,

A= 29000 (Total sum that Mark is liable to pay Rs.29000 to Tony at the end of 3years)

And S.I for 3years = Rs.9000 (interest amount of 3years)

### Example 2:

Alex took a car loan of Rs. 50000 from a private bank on 28 February 2020 at the rate of 8% p.a. and paid back the same on 16th July 2020. Find the total amount paid by Alex?

Solution2:

P = \$50,000

R = 8 % p.a.

T = 139/365

Given that,

Time = February + March + April + May + June + July

= 1day + 31 days + 30 days + 31 days + 30 days + 16 days

= 139 days

Now that, S.I. = (P × R × T)/100

= (50000 × 8 × 139)/(100 × 365)

= Rs.1523.30

Therefore, the amount paid by Alex = Rs (50,000 + 1523.30) = Rs.51,523.30

Note: February 2020 is a leap year, thus 29days and since we do not count the day on which money is borrowed, hence 1 day in Feb will be counted).

### Example 3:

At what percent will Rs. 2500 amount to Rs. 6000 in 5 years? Calculate the rate of interest.

Solution3:

P = Rs.2500

R = ?

T= 5 years

A = Rs.6000

S.I. = A - P

=Rs (6000-2500)

= Rs3500

Using the formula for simple interest:

S.I. = (P × R × T)/100

3500 = (2500 × R × 5)/100

Therefore, R = (3500 × 100)/ (5 × 2500) = 28%