The formulas that are used to calculate Compound Interest (C.I.) are:

When the interest is compounded yearly, the formula for finding the Amount is:

$\displaystyle A = P \Big( 1+ \frac{r}{100} \Big)^{n}$

When the rates of successive years are different then:

$\displaystyle A = P\Big(1+ \frac{r_1}{100} \Big) \Big(1+ \frac{r_2}{100} \Big) \Big(1+ \frac{r_3}{100} \Big) \text{ ... and so on }$

where $\displaystyle {r_1}\%,{r_2}\%,{r_3}\%$ are the interest rates for successive years.

Also,

$\displaystyle \text{ Compound Interest = Amount - Principal }$

$\displaystyle C.I. = A - P =P \Big(1+ \frac{r}{100} \Big)^{n}-P$

$\displaystyle C.I. = P \Big[ \Big(1+ \frac{r}{100} \Big)^{n}-1 \Big]$

When the interest is compounded half yearly (which means every six months or two times a year)

$\displaystyle A = P \Big(1+ \frac{r}{2 \times 100} \Big)^{n \times 2}$

Here the rate of interest is divided by 2 and the number of years are multiplied by 2.

Similarly, if the interest is compounded quarterly, we would get the following formula.

$\displaystyle A = P \Big(1+ \frac{r}{4 \times 100} \Big)^{n \times 4}$

Here the rate of interest is divided by 4 and the number of years are multiplied by 4.

The application of this formula is pretty widespread.

This formula can be used to calculate the growth of anything. Growth of industries, population, production, number of trees, revenue, etc. For example, if production grows are r% every year, then the production output in n years would be calculated as follows:

$\displaystyle A = P \Big(1+ \frac{r}{100} \Big)^{n}$ where A is the final production, P is the initial production and n is the number of years that we are using.