Compound Interest Formula and Facts

Let Principal = P , Rate = R % per annum and Time = n years.

1. Annual Compound Interest Formula:

$$\begin{aligned} Amount = P\left( 1 + \frac{R}{100} \right)^n \\ \end{aligned}$$

2. Half Yearly Compound Interest Formula:
When interest is compounded half yearly, then

$$\begin{aligned} Amount = P\left( 1 + \frac{\frac{R}{2}}{100} \right)^{2n} \\ \end{aligned}$$

3. Quarterly Compound Interest Formula:
When interest is compounded Quarterly, then
$$\begin{aligned} Amount = P\left( 1 + \frac{\frac{R}{4}}{100} \right)^{4n} \\ \end{aligned}$$

4. When interest is compounded Annually but time is in fraction, say $$\begin{aligned}5\frac{2}{7} years \end{aligned}$$

then Amount will be,

$$\begin{aligned} Amount = P\left( 1 + \frac{R}{100} \right)^5 \times \left( 1 + \frac{\frac{2}{7}R}{100} \right) \end{aligned}$$

5. When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively.

Then Amount will be,
$$\begin{aligned} Amount = P\left( 1+\frac{R1}{100} \right) \left( 1+\frac{R2}{100} \right) \left( 1+\frac{R3}{100} \right) \end{aligned}$$

6. Present worth of Rs. x due n years hence will be:

$$\begin{aligned} \text{Present Worth} = \frac{x}{\left(1+\frac{R}{100}\right)^n} \end{aligned}$$