A compound interest is interest which calculated not only from initial principal, but also in addition of previous interest.
For example:
My principal is $10,000 the annual interest rate is 1% and invest it with period of 2 years, the calculation is:
First year:
Second year:
Therefore the final amount is $10,201 and total earnings is $201
The above calculation can be generalize by:
where:
A is final amount
P is principal (initial investment)
r is annual nominal interest rate
t is number of years
n is number of compounding periods per year (e.g. it is 12 for monthly compounding)
For compound continuously, the equation is:
where:
A is final amount
P is principal (initial investment)
r is annual nominal interest rate
t is number of years
e is e constant or Euler's number which is roughly equals to 2.718281828459
Source: Wikipedia