Question

The difference between the S.I and C.I. on a certain sum of money for 2 years at $4\%$ per annum is Rs. 20. Find the sum.

Answer 1

Difference between C.I and S.I = Rs. 20
Rate (R) $=4\%$ p.a
Period (n) = 2 years
Let principal (P) = Rs. 100
then S.I $=\frac{PRT}{100}=\frac{100\times 4\times 2}{100}=Rs.8$
and C.I $=P[{(1+\frac{R}{100})}^n-1]$
$=Rs.100[{(1+\frac{4}{100})}^2-1]$
$=Rs.100[{\left(\frac{26}{25}\right)}^2-1]=100[\frac{676}{625}-1]$
$=100\left[\frac{676-625}{625}\right]$
$=Rs.100\times \frac{51}{625}=Rs.\frac{204}{25}$
$\therefore$ Difference between C.I and S.I
$=Rs.\frac{204}{25}-\frac{8}{1}=Rs.\frac{204-200}{25}=Rs.\frac{4}{25}$
If difference is $\frac{4}{25}$, then principal = Rs. 100
If difference is Re. 1, then principal $=Rs.\frac{100\times 25}{4}\times 20=Rs.12500$
$\therefore$ Sum = Rs. 12500