Question

Find the compound interest on $\mathrm{Rs}.20000$ at $10\%$ per annum for $3$ years.

Answer 1

Step 1: Calculate the amount after the given period

Given,

Principal amount, $P=\mathrm{Rs}.20,000$

Time period, $T=3$ years

Rate of interest, $R=10\%$

The formula for the amount after compounding interest for given period is given as:

$A=P{(1+R)}^T$

Where $A$ is the final amount, $P$ is the initial amount, $R$ is the rate of interest in decimal and $T$ is the time period. Thus,

$\begin{array}{rcl}A& =& 20000{\left(1+\frac{10}{100}\right)}^3\\ & =& 20000{\left(1+0.1\right)}^3\\ & =& \mathrm{Rs}.26620\end{array}$

So, the total amount after $3$ years is $\mathrm{Rs}.26620$.

Step 2: Subtract the initial amount

Compound interest for $3$ years$=$Amount after $3$ years $-$ Initial amount

$$\begin{gathered} =26620-20000 \\ =\mathrm{Rs}.6,620 \end{gathered}$$

Hence, the compound interest on $\mathrm{Rs}.20000$ at $10\%$ per annum for $3$ years is $\mathrm{Rs}.6,620$.