What will be the difference between simple and compound interest at the rate of 10% per annum on a sum of Rs. 1000 after 4 years?
A. Rs. 31
B. Rs. 32.10
C. Rs. 40.10
D. Rs. 64.10

Hint: We will first start by using the fact that simple interest on a principal P at a rate R for time T is $\dfrac{P\times R\times T}{100}$ whereas the compound interest on a principal P at a rate R for time T is $P{{\left( 1+\dfrac{R}{100} \right)}^{T}}-P$. Then we will find its difference to find the answer.

Complete step-by-step solution -
Now, we have been given a principal amount of Rs. 1000, the interest is 10% per annum for a period of 4 years.
Now, we know that the simple interest on a principal P at a rate of R for T years is $\dfrac{P\times R\times T}{100}$. So, using this we have simple interest $=\dfrac{1000\times 4\times 10}{100}=Rs.400$.
Now, we know that compound interest on a principal P at a rate R for a period of T is $P{{\left( 1+\dfrac{R}{100} \right)}^{T}}-P$.
$\begin{align}
  & =1000{{\left( 1+\dfrac{10}{100} \right)}^{4}}-1000 \\
 & =1000{{\left( 1+\dfrac{1}{10} \right)}^{4}}-1000 \\
 & =464.1 \\
\end{align}$
Hence, the difference between compound interest and simple interest is,
$\begin{align}
  & 464.1-400 \\
 & =64.1 \\
\end{align}$
Hence, the correct option is (D).

Note: It is important to note that we have used a fact that for finding SI on a principal amount P at a rate R for a period of T is $\dfrac{P\times R\times T}{100}$ and for compound interest for the same, conditions is $P{{\left( 1+\dfrac{R}{100} \right)}^{T}}-P$. Also, it is important to remember that compound interest is always greater than simple interest.