Question

A sum compounded annually becomes $\frac{49}{16}$ times itself in 2 years. The rate of interest per annum is _____.

• A. 25%
• B. 50%
• C. 75%
• D. 60%

Answer 1

The correct option is C

75%

Let the sum be P.
Amount after two years = ₹$\left(\frac{49}{16}P\right)$
Let r% be rate per annum.
Hence after two years, we have,
$\left(\frac{49}{16}P\right)=P(1+\frac{r}{100}{)}^2$
$\left(\frac{49}{16}\right)=(1+\frac{r}{100}{)}^2$
Taking Square root on both sides, we get,
$\frac{7}{4}=1+\frac{r}{100}$
$\Rightarrow \frac{7}{4}-1=\frac{r}{100}$
$\Rightarrow \frac{r}{100}=\frac{3}{4}$
$\Rightarrow r=75\%$