Romesh borrowed a sum of Rs. 245760 at $12.5\%$ per annum compounded annually. On the same day, he lent out his money to Ramu at the same rate of interest but compounded semi-annually. Find his gain after 2 years.

In first case,
Principal (P) = Rs. 245760
Rate (R) $=12.5\%=\frac{25}{2}\%$ p.a
Period (n) = 2 years
$\therefore$ Amount $=P{(1+\frac{R}{100})}^n$
$=Rs.245760{(1+\frac{25}{2\times 100})}^2$
$=Rs.245760{\left(\frac{9}{8}\right)}^2$
$=Rs.245760\times \frac{9}{8}\times \frac{9}{8}=Rs.311040$
$\therefore$ Compound interest = A - P
= Rs. 311040 - Rs. 245760 = Rs. 65280
In second case,
Rate (R) $=\frac{25}{4}\%$ half-yearly
Period (n) = 2 years or 4 half-years
$\therefore$ Amount $=P{(1+\frac{R}{100})}^n$
$=Rs.245760{(1+\frac{25}{4\times 100})}^4$
$=Rs.245760{\left(\frac{17}{16}\right)}^4$
$=Rs.245760\times \frac{17}{16}\times \frac{17}{16}\times \frac{17}{16}\times \frac{17}{16}$
$=Rs.313203.75$
$\therefore$ C.I = A - P
= Rs. 313203.75 - Rs. 245760 = Rs. 67443.75
$\therefore$ Gain = 67443.75 - Rs. 65280
= Rs. 2163.75