Question

The difference between compound interest and simple interest on a certain sum for 2 years at $7\frac{1}{2}$% per anum is Rs. 360. Find the sum. Verify your answer.

Answer 1

Given : $n=2$ years, $R=7\frac{1}{2}=\frac{15}{2}$

$S.I.-C.I.=360$ ....... $\left(i\right)$

S.I. $=\frac{P\times n\times R}{100}$

$=\frac{P\times 2\times \frac{15}{2}}{100}=\frac{15P}{100}$

Amount $\left(A\right)=P{(1+\frac{R}{100})}^n$

$=P{(1+\frac{15}{2\times 100})}^2$

$=P{(1+\frac{3}{40})}^2$

C.I. $=A-P$

$=P{(1+\frac{3}{40})}^2-P$

$=P(1+\frac{9}{1600}+\frac{2\times 3}{40}-1)$

$=P(\frac{9}{1600}+\frac{6}{40})$

$C.I.=P\left(\frac{249}{1600}\right)$ ........ $\left(ii\right)$

It is given that,

$|S.I.-C.I.|=360$

$⟹|\frac{15P}{100}-P\left(\frac{249}{1600}\right)|=360$

$⟹\frac{9P}{1600}=360$

$⟹P=64000$

Hence, the sum is Rs. $64,000$.

Verification :-

S.I. $=\frac{P\times n\times R}{100}=\frac{64000\times 2\times 15}{2\times 100}=9600$

C.I. $=P[{(1+\frac{R}{100})}^n-1]$

$=64000[{(1+\frac{15}{2\times 100})}^2-1]$

$=9960$

$|S.I.-C.I.|=|9600-9960|=360$.