What is the difference between the compound interests on Rs. 5000 for $$1\frac{1}{2}$$ years at 4% per annum compounded yearly and half-yearly?
a) Rs. 2.04
b) Rs. 3.06
c) Rs. 4.80
d) Rs. 8.30

Answer: a
Explanation:
$$\eqalign{ & {\text{C}}{\text{.I}}{\text{.}}\,{\text{when}}\,{\text{interest}}\,{\text{compounded}}\,{\text{yearly}} = Rs.\left[ {5000 \times \left( {1 + \frac{4}{{100}}} \right) \times \left( {1 + \frac{{\frac{1}{2} \times 4}}{{100}}} \right)} \right] \cr & = Rs.\left( {5000 \times \frac{{26}}{{25}} \times \frac{{51}}{{50}}} \right) \cr & = Rs.5304 \cr & {\text{C}}{\text{.I}}{\text{.}}\,{\text{when}}\,{\text{interest}}\,{\text{in}}\,{\text{compounded}}\,{\text{half – yearly}} = Rs.\,\left[ {5000 \times {{\left( {1 + \frac{2}{{100}}} \right)}^3}} \right] \cr & = Rs.\,\left( {5000 \times \frac{{51}}{{50}} \times \frac{{51}}{{50}} \times \frac{{51}}{{50}}} \right) \cr & = Rs.\,5306.04 \cr & {\text{Difference}} = Rs.\,\left( {5306.04 – 5304} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,2.04 \cr} $$