Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.

Compound Interest Equation

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

Where:

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

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

The above formula calculates the future value of the investment or interest from the investment when money is deposited initially without frequent contribution. The power of compounding investment is that the interest from end of each compounding period is added to the principal amount so that the interest is earned for the next compounding period will be more than the previous period.

If you invest money regularly, for example, contributing money monthly, your investment is determined by the following formula.

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

Where:

• A = the future value of the investment, including interest
• P = the principal investment amount (the initial deposit )
• r = the annual interest rate in decimal
• n = the number of times that interest is compounded per year
• t = the number of years the money is invested
• D = the deposit amount per compound period

This formula assumes the average annual interest rate or return rate from the investment. In reality the rate may be changed frequently. The money is deposited at the beginning of each deposit period.

In some countries the regular contribution investment is called Systematic Investment Plan (SIP). The formula is the same.