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.
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 $2,163.75$