Question

At what rate percent per annum will a sum of Rs. 2000 amount to Rs. 2205 in 2 years at compound interest?

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

Answer 1

Answer: (C)

$5$%

Given that, a sum of $Rs.2000$ amounts to $Rs.2205$ in $2$ years.

To find out: The rate of interest

For compound interest, we know that,

$A=P{(1+\frac{R}{100})}^T$

Here, $P=Rs.2000,A=Rs.2205$ and $T=2$years.

$\therefore 2205=2000\times {(1+\frac{R}{100})}^2$

$\Rightarrow$ $\frac{441}{400}={(1+\frac{R}{100})}^2$

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

$\Rightarrow$ $R=\frac{1}{20}\times 100=5\%$

Hence, the required rate of interest is $5\%$.