# Compound Interest

Compound interest is a type of interest where the interest earned is added to the principal amount, and then the interest is calculated on the new principal amount. In other words, the interest is calculated not only on the initial principal amount but also on the accumulated interest from previous periods. This compounding effect leads to the exponential growth of money over time.

The formula for compound interest is:

A = P (1 + r/n)^(nt)

where:
A = the final amount
P = the principal amount
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years

For example, let’s say you invest Rs. 10,000 at an annual interest rate of 8%, compounded annually for 5 years. Using the formula, the calculation would be:

A = 10,000 (1 + 0.08/1)^(1×5)
A = Rs. 14,693.28

So, the final amount after 5 years with compound interest is Rs. 14,693.28, which is more than the simple interest earned on the same principal amount.

It is important to note that compound interest can work against you as well, for example, if you have a loan with compound interest, the interest accumulates over time and you end up paying more in interest than you would with simple interest.

## The formula to calculate compound interest is:

A = P (1 + r/n)^(nt)

where:

A = the final amount

P = the principal amount

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

Let’s break down the formula and understand how it works:

• Principal amount (P) – This is the initial amount of money that you invest or borrow.
• Annual interest rate (r) – This is the interest rate that is applied to the principal amount every year, expressed as a decimal. For example, an interest rate of 8% would be written as 0.08.
• Number of times interest is compounded per year (n) – This is the number of times in a year that the interest is added to the principal amount. For example, if the interest is compounded monthly, n would be 12.
• Number of years (t) – This is the length of time for which the interest is applied to the principal amount.

The formula calculates the final amount (A) by multiplying the principal amount (P) by the growth factor (1 + r/n)^(nt), where the growth factor represents the compounding effect of the interest over time.

For example, if you invest Rs. 10,000 at an annual interest rate of 8%, compounded annually for 5 years, the calculation would be:

A = 10,000 (1 + 0.08/1)^(1×5) A = Rs. 14,693.28

So, the final amount after 5 years with compound interest is Rs. 14,693.28, which is more than the simple interest earned on the same principal amount.