At what percent of compound interest per annum. a sum of money will double in 14 years?

Correct option is B

​$$\text{Let the principal amount be } P \text{ and the rate of interest be } r\%. \\[5pt]\text{Using the compound interest formula:} \\A = P\left(1 + \frac{r}{100}\right)^{14} \\[10pt]\text{Since the amount doubles in 14 years:} \\2P = P\left(1 + \frac{r}{100}\right)^{14} \\[10pt]\text{Divide both sides by } P: \\2 = \left(1 + \frac{r}{100}\right)^{14} \\[10pt]\text{Take the 14th root of both sides:} \\1 + \frac{r}{100} = 2^{1/14} \\[10pt]\text{Now, calculate } 2^{1/14} \approx 1.05 \\[5pt]\Rightarrow \frac{r}{100} = 0.05 \\[5pt]\Rightarrow r = 5$$

Correct answer is (b) 5%.