Question

On what sum of money will the difference between the compound interest and simple interest for $2$ years be equal to Rs. $25$ if the rate of interest charged for both is $5\%$ p.a?

Answer 1

Let the principal be Rs. $P$
Given : $R=5\%,T=24$ years
C.I. for $2$ years $=P{(1+\frac{5}{100})}^2-P$
S.I. for $2$ years $=\frac{P\times 5\times 2}{100}=\frac{P}{10}$
$\because$ Difference between C.I. and S.P. $=$ Rs. $25$
$P{(1+\frac{5}{100})}^2-P-\frac{P}{10}=25$
$\frac{441P}{400}-\frac{11P}{10}=25$
$\frac{441P-440P}{400}=25$
$P=10,000$
Hence, the principle should be Rs. $10,000$