Question

A person lent out the certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and 2 years is 16 : 49. The rate of interest per annum is:

• A. 9%
• B. $8\frac{1}{7}\%$
• C. $13\frac{1}{3}\%$
• D. 7%
• E. $6\frac{1}{4}\%$

Answer 1

The correct option is E $6\frac{1}{4}\%$

For 2 years, difference in CI and SI $=\frac{P{r}^2}{{100}^2}$
For 3 years difference is $\frac{P{r}^2(r+300)}{{100}^3}$
$\frac{\frac{P{r}^2}{{100}^2}}{\frac{P{r}^2(r+300)}{{100}^3}}=\frac{16}{49}So,\frac{100}{r+300}=\frac{16}{49}Bysolvingtheaboveequation,r=6\frac{1}{4}$.