What will be the compound interest accrued on an amount of Rs.10000 @ 20 p.c.p.a in 2 years if the interest is compounded half-yearly?
a) Rs. 4600
b) Rs. 4641
c) Rs. 4400
d) Rs. 4680

Answer: b
Explanation:
$$\eqalign{ & {\text{P = Rs}}.10000, \cr & {\text{R}} = 20\% \,p.a. \cr & \,\,\,\,\,\,\, = 10\% \,{\text{per}}\,{\text{half year}} \cr & T = 2\,{\text{years}} = 4\,{\text{half}}\,{\text{years}} \cr & {\text{Amount}} \cr & {\text{ = Rs}}.\left[ {10000 \times {{\left( {1 + \frac{{10}}{{100}}} \right)}^4}} \right] \cr & = {\text{Rs}}.\left( {10000 \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} \times \frac{{11}}{{10}}} \right) \cr & = {\text{Rs}}.14641 \cr & \therefore {\text{C}}{\text{.I}}{\text{. = Rs}}.\left( {14641 – 10000} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\,4641 \cr} $$