Question

At what rate percent will a sum of Rs. 1000 amount to Rs. 1102.50 in 2 years at compound interest?

Answer 1

Principal (P) = Rs. 1000
Amount (A) = Rs. 1102.50
Period (n) = 2 years
Let R be the rate of interest p.a.
$\because A=P{(1+\frac{R}{100})}^n$
$\therefore \frac{A}{P}={(1+\frac{R}{100})}^n$
$\Rightarrow Rs.\frac{1102.50}{1000}={(1+\frac{R}{100})}^2$
$\Rightarrow Rs.\frac{110250}{100\times 1000}={(1+\frac{R}{100})}^2$
$\Rightarrow Rs.\frac{441}{400}={(1+\frac{R}{100})}^2$
Comparing, we get:
$1+\frac{R}{100}=\frac{21}{20}=1+\frac{1}{20}$
$\therefore \frac{R}{100}=\frac{1}{20}\Rightarrow R=\frac{100}{20}=5$
$\therefore$ Rate $=5\%$ p.a.