Rakesh lent out Rs 10000 for 2 years at 20% per annum, compounded annually.

Solution:

Given:

$\mathrm{P}=\mathrm{Rs} 10,000$

$\mathrm{R}=20 \%$ p. $\mathrm{a} .$

$\mathrm{n}=2$ years

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

$=\operatorname{Rs} 10,000\left(1+\frac{20}{100}\right)^{2}$

$=\operatorname{Rs} 10,000(1.2)^{2}$

$=\operatorname{Rs} 14,400$

When the interest is compounded half-yearly, we have:

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

$=\operatorname{Rs} 10,000\left(1+\frac{20}{200}\right)^{4}$

$=\operatorname{Rs} 10,000(1.1)^{4}$

$=\operatorname{Rs} 14,641$

Difference $=$ Rs $14,641-$ Rs 14,400

$=\operatorname{Rs} 241$