Question

At what rate percent per annum will a sum of Rs. 4000 yield compound interest of Rs. 410 in 2 years?

Answer 1

Principal (P) = Rs. 4000
C.I = Rs. 410
$\therefore$ Amount (A) = Rs. 4000 + 410 = Rs. 4410
Let rate $=R\%$ p.a.
Period (n) = 2 years.
$\therefore$ Amount $=P{(1+\frac{R}{100})}^n$
$\Rightarrow \frac{A}{P}={(1+\frac{R}{100})}^2$
$\Rightarrow Rs.\frac{4410}{4000}={(1+\frac{R}{100})}^n$
$\Rightarrow \frac{441}{4000}={[1+\frac{R}{100}]}^2$
$\Rightarrow {\left(\frac{21}{20}\right)}^2={(1+\frac{R}{100})}^2$
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