Question

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

• A. $2$%
• B. $3$%
• C. $4$%
• D. $5$%

Answer 1

Answer: (D)

$5$%

Sum $=$ Rs. $1000$
Amount $=$ Rs. $1102.50$

Time $=2$ year

Let rate of interest be $R\%$

$\text{Amount}=P{(1+\frac{R}{100})}^2$

$\Rightarrow 1102.50=1000{(1+\frac{R}{100})}^2$

$\Rightarrow \frac{1102.50}{1000}=(1+\frac{R}{100}{)}^2$

$\Rightarrow \frac{441}{400}=(1+\frac{R}{100})$

$\Rightarrow {\left(\frac{21}{20}\right)}^2={(1+\frac{R}{100})}^2$

$\Rightarrow 1+\frac{R}{100}=\frac{21}{20}$

$\Rightarrow \frac{R}{100}=\frac{21}{20}-1$

$\Rightarrow \frac{R}{100}=\frac{1}{20}$

$\Rightarrow R=\frac{100}{20}=5\%$