Question

The difference between the compound interest and simple interest on a certain sum for 2 years at $7.5\%$ per annum is Rs. 360. Find the sum.

Answer 1

Let sum (P) = Rs. 100
Rate (R) $=7.5\%=\frac{15}{2}\%$ p.a
Period (n) = 2 years
$\therefore$ C.I. = A - P $=P{(1+\frac{R}{100})}^n-P$
$=P[{(1+\frac{R}{100})}^n-1]$
$=100[{(1+\frac{15}{2\times 100})}^2-1]$
$=Rs.100[{\left(\frac{43}{40}\right)}^2-1]=Rs.100[\frac{1849}{1600}-1]$
$=Rs.100\left(\frac{1849-1600}{1600}\right)=Rs.100\times \frac{249}{1600}$
$=Rs.\frac{249}{16}$
and S.I $=\frac{PRT}{100}=\frac{100\times 15\times 2}{100\times 2}=Rs.15$
$\therefore$ Difference in C.I and S.I $=Rs.\frac{249}{16}-15$
$=Rs.\frac{249-240}{16}=Rs.\frac{9}{16}$
If difference is $\frac{9}{16}$, then sum = Rs. 100
if difference is Re. 1, then sum $=Rs.\frac{100\times 16}{9}$
and if difference is Rs. 360, then sum
$=Rs.\frac{100\times 16\times 360}{9}=Rs.64000$