Question
The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
Answer: Option D
$$\eqalign{
& {\text{Amount}}\,{\text{of}}\,{\text{Rs}}{\text{.}}\,{\text{100}}\,{\text{for}}\,{\text{1}}\,{\text{year}}\,{\text{when}}\, \cr
& {\text{compounded}}\,{\text{half - yearly}} \cr
& = Rs.\,\left[ {100 \times {{\left( {1 + \frac{3}{{100}}} \right)}^2}} \right] \cr
& = Rs.\,106.09 \cr
& \therefore {\text{Effective}}\,{\text{rate}} = \left( {106.09 - 100} \right)\% \cr
& = 6.09\% \cr} $$
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$$\eqalign{
& {\text{Amount}}\,{\text{of}}\,{\text{Rs}}{\text{.}}\,{\text{100}}\,{\text{for}}\,{\text{1}}\,{\text{year}}\,{\text{when}}\, \cr
& {\text{compounded}}\,{\text{half - yearly}} \cr
& = Rs.\,\left[ {100 \times {{\left( {1 + \frac{3}{{100}}} \right)}^2}} \right] \cr
& = Rs.\,106.09 \cr
& \therefore {\text{Effective}}\,{\text{rate}} = \left( {106.09 - 100} \right)\% \cr
& = 6.09\% \cr} $$
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