Question

Find the sum on which the difference between the simple interest and compounded interest at a rate of $8%$ per annum compounded annually would be Rs. $64$ in $2$ years.

Answer 1

Hint: For the first year there will be no difference between the simple interest and the compound interest. After the first year we have to find the difference and that should be equal to the given difference.

Complete step-by-step answer:
Let Rs. X be the sum.
Simple Interest$=\dfrac{P\times R\times T}{100}$
$=\dfrac{X\times 8\times 2}{100}=0.16X$
Now, we need to calculate compound interest for the 2 years.
Compound interest for the first year :
$P=X,R=8%$
$Interest(I)=\dfrac{X\times 8\times 1}{100}=0.08X$
Compound interest for the second year :
$P=X+0.08X=1.08X$
$Interest(I)=\dfrac{1.08X\times 8\times 1}{100}=0.0864X$
The difference between the simple interest and compound interest at the rate $8%$ compounded annually should be Rs. $64$ in $2$ years.
$\begin{align}
  & 0.08X-0.0864X=64 \\
 & 0.0064X=64 \\
 & X=10000 \\
\end{align}$

Hence the principle amount $X=10000$

Note: Another method to do this question is to use the direct formula for the compound interest. In the question where the time period is bigger than it is recommended to use the direct formula. One more thing to note here is that the simple interest and compound interests are the same for the first year only if the compound interest is compounded annually. If the compound interests compounded half yearly then the simple interest for the first six months will be equal to the compound interest. So, we need to keep these points in our mind.