Question

Calculate the rate per cent per annum compound annually, if Ron lends a sum of Rs. $2000$ and will return Rs. $2205$ after $2$ years.

• A. $10\%$
• B. $4\%$
• C. $6\%$
• D. $5\%$

Answer 1

The correct option is D $5\%$

Let the required rate be $R\%$ per annum.
Here, $A=$ Rs. $2205$, $P=$ Rs. $2000$ and $n=2$ years.
Using the formula $A=P{\left(\begin{array}{c}1+\frac{R}{100}\end{array}\right)}^n$,
$\Rightarrow 2205=2000\times {\left(\begin{array}{c}1+\frac{R}{100}\end{array}\right)}^2$
$\Rightarrow {\left(\begin{array}{c}1+\frac{R}{100}\end{array}\right)}^2=\frac{2205}{2000}=\frac{441}{400}={\left(\begin{array}{c}\frac{21}{20}\end{array}\right)}^2$
$\Rightarrow \left(\begin{array}{c}1+\frac{R}{100}\end{array}\right)=\frac{21}{20}$
$\Rightarrow \frac{R}{100}=\left(\begin{array}{c}\frac{21}{20}-1\end{array}\right)=\frac{1}{20}$
$\Rightarrow R=\left(\begin{array}{c}100\times \frac{1}{20}\end{array}\right)=5$
Hence, the required rate of interest is $5\%$ per annum.