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}