# Simple Interest

Simple interest is calculated on the principal, or amount of a loan.

The simple interest rate is a ratio and is typically expressed as a percentage. It plays an important role in determining the amount of interest on a loan or investment.

Principal (P): The original sum of money loaned/deposited. It is also known as capital.

Interest (I): The amount of money that you pay to borrow money or the amount of money that you earn on a deposit.

Terms (n): The duration for which the money is borrowed/deposited.

Rate of Interest (R): The percent of interest that you pay for money borrowed, or earn for money deposited

The formula for calculating simple interest is:

Simple Interest

= Principal x Interest Rate x Term of the loan

= P x i x n

Amount Due at the end of the time period, A = P (original amount) + SI

A = P+ (p X i X n) / 100

Demonstration:

What is the SI on Rs. 7500/- at the rate of 12% per annum for 8 years?

Using the Basic Formula:

Simple Interest (SI) = (p X i X n)/100

P – Principal amount, T- Number of years, R – Rate of Interest

Given P = 7500, T = 8 Years, R = 12%

Simple Interest (S.I.) = (7500X12X8)/100

Simple Interest (S.I.) = 7200

Compound Interest

Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus be regarded as “interest on interest.”

Let's say you borrow 2,000 rupees over a 3 year period, pay 10% annual interest on your debt and are not making regular repayments. In this case, the amount you will have to repay will look like this:

Year 1: 2,000 x 10% = \$200.
Year 2: 2,200 x 10% = \$220.
Year 3: \$2,420 x 10% = \$242.

The total repayment figure after 3 years is Rs.2,662 (the Rs.662 interest is the sum of each year's interest).

It should be noted that if you make regular repayments on your loan, the total compound interest will be lower because the remaining principal on the loan will be decreasing at each compound interval.

The formula for annual compound interest, including principal sum, is:

A = P (1 + r/n) (nt)

Where:

A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

Note that this formula gives you the future value of an investment or loan, which is compound interest plus the principal. Should you wish to calculate the compound interest only, you need this:

Total compounded interest = P (1 + r/n) (nt) - P

Example:

If an amount of Rs.5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly, the value of the investment after 10 years can be calculated as follows..

P = 5000. r = 5/100 = 0.05 (decimal). n = 12. t = 10.

If we plug those figures into the formula, we get:

A = 5000 (1 + 0.05 / 12) ^ (12(10)) = 8235.05.

So, the investment balance after 10 years is Rs.8,235.05.