Question

If the compound interest on a certain sum for $2\mathrm{years}$ is $Rs21$. What could be the simple interest?

Answer 1

Step 1: Find the rate of interest

Given the compound interest on a certain sum for $2\mathrm{years}$ is $Rs21$.

We know compound interest

$\mathit{A}\mathbf{=}\mathit{P}{\left(1+\frac{r}{100}\right)}^{\mathbf{t}}$

where $P$ is the principal, $t$ is the no of year the money is involved and $r$ is the rate of interest

Let the sum of money be $Rs100$

Therefore $P=Rs100$

Given the compound interest on a certain sum for $2\mathrm{years}$ is $Rs21$

So compound Interest $\left(C.I\right)=Rs21$

Therefore,

Amount $\left(A\right)=P+C.I$

$$\begin{gathered} \Rightarrow 100+21=100{\left(1+\frac{r}{100}\right)}^2 \\ \Rightarrow 1.21={\left(\frac{100+r}{100}\right)}^2 \\ \Rightarrow {\left(1.1\right)}^2={\left(\frac{100+r}{100}\right)}^2 \\ \Rightarrow 1.1=\frac{100+r}{100} \\ \Rightarrow 110=100+r \\ \Rightarrow r=10 \\ \therefore r=10\% \end{gathered}$$

Step 2: Find the Simple Interest

Simple interest $S.I=\frac{P\times r\times t}{100}$

For $2$ year the simple interest is

$$\begin{gathered} S.I=\frac{P\times r\times 2}{100} \\ =2\times 10 \\ =20 \end{gathered}$$

Hence the simple interest is $Rs20$.