Answer : Option D

Explanation :

Let principal, P be Rs.100
Amount after 1 year on Rs.100 at 6% per annum when interest is compounded half-yearly
$MF#%=\text{P}\left(1 + \dfrac{\text{(R/2)}}{100}\right)^\text{2T} = 100\left(1 + \dfrac{(6/2)}{100}\right)^{2 \times 1}\\\\= 100\left(1 + \dfrac{3}{100}\right)^2= 100\left(\dfrac{103}{100}\right)^2= \dfrac{100 \times 103 \times 103}{100 \times 100}= \dfrac{103 \times 103}{100} = 106.09$MF#%
This means, if interest is compounded half-yearly at 6%, Rs.100 becomes Rs.106.09 after 1 year
Now, we need to find out the rate of interest on which Rs.100 becomes Rs.106.09 after 1 year
when the interest is compounded annually
$MF#%\begin{align}&\text{P}\left(1 + \dfrac{\text{R}}{100}\right)^\text{T} = 106.09\\\\ &100\left(1 + \dfrac{\text{R}}{100}\right)^1 = 106.09\\\\ &100\left(1 + \dfrac{\text{R}}{100}\right) = 106.09\\\\ &100 + \text{R} = 106.09\\\\ &\text{R} = 106.09 - 100 = 6.09\%\end{align}$MF#%
i.e, effective annual rate of interest is 6.09%