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