Question

What will be the difference between simple and compound interest at $10\%$ per annum on a sum of $\mathrm{Rs}.1000$ after $4$ years?

Answer 1

Step 1. Calculate the simple interest.

Given that,

$\mathrm{Principal}\left(P\right)=Rs.1000,\mathrm{rate}\left(r\right)=10\%,\mathrm{Time}\left(t\right)=4\mathrm{years}$

As we know,

$$\begin{gathered} \mathrm{Simple}\mathrm{interst}=\frac{P\times r\times t}{100} \\ \Rightarrow =\frac{1000\times 10\times 4}{100} \\ \Rightarrow =\mathrm{Rs}.400 \end{gathered}$$

Step 2. Calculate the compound interest.

The compound interest is computed as,

$\mathrm{Compound}\mathrm{interest}=\mathrm{Amount}-\mathrm{Principal}$

$$\begin{gathered} \mathrm{Amount}=P{\left(1+\frac{r}{100}\right)}^t \\ \Rightarrow =1000\times {\left(1+\frac{10}{100}\right)}^4 \\ \Rightarrow =1000\times {\left(\frac{11}{10}\right)}^4 \\ \Rightarrow =\mathrm{Rs}.1,464.1 \end{gathered}$$

$$\begin{gathered} \because \mathrm{Compound}\mathrm{interest}=\mathrm{Amount}-\mathrm{Principal} \\ \therefore \mathrm{Compound}\mathrm{interest}=1464.1-1000 \\ \Rightarrow =\mathrm{Rs}.464.1 \end{gathered}$$

Step 3. Calculate the difference.

$$\begin{gathered} \mathrm{Difference}=\mathrm{Compound}\mathrm{interest}-\mathrm{Simple}\mathrm{interest} \\ =464.1-400 \\ =\mathrm{Rs}.64.1 \end{gathered}$$

Hence, the difference between simple and compound interest is $\mathrm{Rs}.64.1$.