Amit borrowed Rs 16000 at $17 \frac{1}{2} \%$ per annum simple interest. On the same day, he lent it to Ashu at the same rate but compounded annually. What does he gain at the end of 2 years?
Amount to be paid by Amit:
$\mathrm{SI}=\frac{\mathrm{PRT}}{100}$
$=\frac{16000 \times 17.5 \times 2}{100}$
$=\operatorname{Rs} 5,600$
Amount gained by Amit:
$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$
$=\operatorname{Rs} 16,000\left(1+\frac{17.5}{100}\right)^{2}$
$=\operatorname{Rs} 16,000(1.175)^{2}$
$=\operatorname{Rs} 22,090$
We know that:
$\mathrm{CI}=\mathrm{A}-\mathrm{P}$
$=\operatorname{Rs} 22,090-\operatorname{Rs} 16,000$
$=\operatorname{Rs} 6090$
Amit's gain in the whole transaction $=$ Rs $6,090-$ Rs 5,600
$=\operatorname{Rs} 490$