(a) 5%
Let the sum of money invested be Rs x and interest rate per annum = r%
Then, x\(\big(1+\frac{r}{100}\big)^3\) = Rs 2400 .....(i)
and x\(\big(1+\frac{r}{100}\big)^4\) = Rs 2520 ........(ii)
Dividing equation (ii) by (i), we get
\(\big(1+\frac{r}{100}\big)\) = \(\frac{2520}{2400}\) \(\Rightarrow\) \(\frac{r}{100}\) = \(\frac{2520-2400}{2400}\) = \(\frac{120}{2400}\)
\(\Rightarrow\) r = \(\frac{1}{20}\)x 100 = 5% p.a