Romesh borrowed a sum of Rs 245760 at 12.5% per annum, compounded annually.

Solution:

Given:

$\mathrm{P}=\mathrm{Rs} 245,760$

$\mathrm{R}=12.5 \%$ p. a.

$\mathrm{n}=2$ years

When compounded annually, we have :

$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$

$=$ Rs $245,760\left(1+\frac{12.5}{100}\right)^{2}$

$=$ Rs 311,040

When compounded semi - annually, we have :

$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{200}\right)^{2 \mathrm{n}}$

$=\mathrm{Rs} 245,760\left(1+\frac{12.5}{200}\right)^{4}$

$=\mathrm{Rs} 245,760(1.0625)^{4}$

$=\mathrm{Rs} 313,203.75$

Romesh's gain $=$ Rs $313,203.75-R s 311,040$

$=$ Rs $2,163.75$