Question

The difference between the compound interest on a certain sum at the rate of $5\%$ per annum for $2$ years compounded annually and simple interest for the same $2$ years is Rs. $1000$. What is the principal sum?

Answer 1

Compound interest $=$ Amount $-$ Principal
For two years, CI $=P{(1+\frac{R}{100})}^{2\times 1}-P$
CI $=P{(1+\frac{5}{100})}^2-P$
CI $=P(1.05{)}^2-P$
CI $=1.1025P-P=0.1025P$
Simple interest on $P$ at $5\%$ for $2$ years $=$ $\frac{PRT}{100}$
We know, SI $=$ $\frac{P\times 5\times 2}{100}=\frac{P}{10}$
Given that difference between compound interest and simple interest $=1000$.
Therefore, $0.1025P-\frac{P}{10}=1000$
$\Rightarrow 1.025P-P=10000$
$\Rightarrow 0.025P=10000$
$\Rightarrow P=$ Rs. $400000$