If the interest due on savings is added to the principal at given
intervals, then the interest is said to be compounded (or converted)
into principal and thereafter also earns interest. Consequently, the
principal increases periodically and the interest compounded into the
principal increases periodically throughout the term of the transaction.

The sum due at the end of the transaction is called the compound
amount and is denoted by A.

The difference between the compound amount and the original principal
is called the compound interest and is denoted by CI.

Consider an investment of $P at the percentage r per
annum.

First year of investment

Second year of investment

We, often write the formula for the accumulation of principal at
compound interest as:

This formula is also applied in problems dealing with population
growth. If there is a decrease instead of an increase, then r is negative.

Example 22

Calculate the compound interest on $6000 if it is invested for 3 years
at 7.5% per annum.