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