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.

In each of the following results, we use the following denotations:

A = future value (sum recieved)
P = principal amount (initial investment)
r = annual nominal interest rate
n = number of times the interest is compounded per year
t = number of years for which the money is borrowed

Types of Compound Interest:-

1. If the interest is compounded yearly, then

(a) The amount A due after t years, when a principal P is given on compound interest at the rate R% per annum is given by
 

2. If the interest is compounded half-yearly, then
 

3. If the interest is compounded quarterly, then
 

5. When the time is given in the form of fraction, say 23/4 years, then,

6. (a) The difference between the compound interest and the simple interest on a certain sum of money for 2 years at R% per annum is given by
 

(b) The difference between the compound interest and the simple interest on a certain sum of money for 2 years at R% per annum is given by
 

7. If a certain sum becomes n times in t years at compound interest, then the same sum becomes n^m times in mt years.

8. If a certain sum becomes n times in t years, then the rate of compound interest is given by
 

9. If a certain sum of money at compound interest amounts to Rs. x in A years and to Rs. y in B years, then the rate of interest per annum is
 

10. If a loan of Rs. P at R% compound interest per annum is to be repaid in n equal yearly instalments, then the value of each instalment is given by