Question

A sum compounded annually becomes $\frac{64}{25}$ times itself in 2 years. Determine the rate of interest per annum

• A. 75%
• B. 60%
• C. 50%
• D. 67.5%

Answer 1

The correct option is B 60%

Let the sum be P
Amount after two years = ₹$\left(\frac{64}{25}P\right)$
Let r% be rate per annum
Hence, after two years , we have
$\left(\frac{64}{25}P\right)$ = P$(1+\frac{r}{100}{)}^2$
$\left(\frac{64}{25}\right)$ = $(1+\frac{r}{100}{)}^2$
Taking Square root on both sides , we get
$\left(\frac{8}{5}\right)$ = $1+\frac{r}{100}$
r = 60%