Question

The compound interest on a certain sum for two years is $Rs.618$, whereas the simple interest on the same sum at the same rate for two years is $Rs.600$. The rate of interest per annum is:

• A. $18\%$
• B. $9\%$
• C. $6\%$
• D. $3\%$

Answer 1

The correct option is C $6\%$

Given- Compound interest on two years is $618$ Rs

$P{(1+\frac{r}{100})}^2-P=618$
$P[1+\frac{r^2}{100\times 100}+\frac{2r}{100}-1]=618$.......(1)

Simple interest on two years is $600$ Rs
$\frac{P\times r\times 2}{100}=600$
$P=\frac{600\times 100}{2\times r}$.......(2)
From (1) and (2), we get
$\therefore \frac{600\times 100}{2\times r}\times r[\frac{r}{100\times 100}+\frac{2}{100}]=618$
$\Rightarrow 300(\frac{r}{100}+2)=618$
$\Rightarrow 3r=18\%$
$\Rightarrow r=6\%$
Hence, option $C$ is the correct answer.