Question

Ramesh lends Rs. 15,000 for 2 years at a certain rate of compound interest. If after 2 years, it amounts to Rs. 16,224; find the rate of interest.

• A. 2%
• B. 4%
• C. 6%
• D. 8%

Answer 1

The correct option is B 4%

Given : P = Rs. 15000; n = 2 years and A = Rs. 16224
$\therefore 16224=15000{(1+\frac{r}{100})}^2\because A=P{(1+\frac{r}{100})}^n$
${(1+\frac{r}{100})}^2=\frac{16224}{15000}$
$=\frac{2\times 2\times 2\times 2\times 2\times 3\times 13\times 13}{2\times 2\times 2\times 3\times 5\times 5\times 5\times 5}=\frac{2\times 2\times 13\times 13}{5\times 5\times 5\times 5}={\left(\frac{26}{25}\right)}^2$
$\therefore 1+\frac{r}{100}=\frac{26}{25}$

$\Rightarrow \frac{R}{100}=\frac{26}{25}-1$

$\Rightarrow \frac{R}{100}=\frac{1}{25}$

$\Rightarrow R=\frac{100}{25}=4$%