Question

The difference between the compound interest and simple interest on a certain sum at $15\%$ per annum for 3 years is$Rs.283.50$. Find the sum.

Answer 1

Let sum $\left(P\right)=Rs.100$
Rate (R) $=15\%$ p.a
Period $\left(n\right)=3$ years
$\therefore$ Simple interest $=\frac{PRT}{100}$

$=\frac{100\times 15\times 3}{100}$
$=Rs.45$
and when interest is compounded annually then
$C.I=P[{(1+\frac{R}{100})}^n-1]$
$=Rs.100[{(1+\frac{15}{100})}^3-1]$
$=Rs.100[{\left(\frac{23}{20}\right)}^3-1]$
$=Rs.100[\frac{23}{20}\times \frac{23}{20}\times \frac{23}{20}-1]$
$=Rs.100\times [\frac{12167}{8000}-1]$
$=Rs.100\times \frac{12167-8000}{8000}$

$=Rs.\frac{4167}{80}$
Difference in C.I and S.I.
$=Rs.(\frac{4167}{80}-\frac{45}{1})$

$=Rs.\frac{4167-3600}{80}$
$=Rs.\frac{567}{80}$
If difference is $Rs.\frac{567}{80}$, then principal = Rs. 100
If difference is $Re.1$, then principal $=Rs.\frac{100\times 80}{567}$
and if difference is $Rs.283.50$, then
Principal $=Rs.\frac{100\times 80}{567}\times 283.50$
$=Rs.\frac{100\times 80\times 28350}{567\times 100}=Rs.4000$
Sum $=Rs.4000$