We know that,

Modified duration = [Macaulay duration / (1 + y/n)]

We, therefore, start by calculating the Macaulay duration:

$\text{Macaulay duration} = \sum_{i=1}^{n} t_i \left[ \frac{PV(C_{t_i})}{P} \right]$

$= \frac{50}{150} \times 1 + \frac{100}{150} \times 2 = 1.6667$

Where $PV(C_{t_i})$ = present value of cash flows at time $t_i$ and $P$ is the price of the bond.

Thus,

$\text{Modified duration} = \frac{1.6667}{\left(1 + \frac{0.05}{2}\right)} = 1.62604$

Note: Choice A (1.6667) represents the Macaulay duration, not the modified duration. Choices C and D do not correspond to the correct calculation.