Question

Simple interest on a sum of money for 2 years at $6\frac{1}{2}\%$ per annum is Rs. 5200. What will be the compound interest on the sum at the same rate for the same period?

Answer 1

In first case,
S.I = Rs. 5200
Rate (R) $=6\frac{1}{2}\%=\frac{13}{2}\%$
Period (T) = 2 years
$\therefore$ Principal $=Rs.\frac{S.I\times 100}{R\times T}=\frac{5200\times 100\times 2}{13\times 2}$
$=Rs.40000$
In second case,
Principal (P) = Rs. 40,000
Rate (R) $=\frac{13}{2}\%$ p.a
Period (n) = 2 years
$\therefore$ Amount $=P{(1+\frac{R}{100})}^n$
$=Rs.40,000{(1+\frac{13}{2\times 100})}^2$
$=Rs.40000{\left(\frac{213}{200}\right)}^2$
$=Rs.40000\times \frac{213}{200}\times \frac{213}{200}=Rs.45,369$
$\therefore$ Compound interest = A - P
Rs. 45369 - Rs. 40,000 = Rs. 5369