Explanation

To convert a semiannual yield to a quarterly yield, we need to use the following relationship:

Semiannual yield (SAY) = 4.3% (given)

First, convert the semiannual yield to an effective annual rate (EAR):

$\text{EAR} = \left(1 + \frac{\text{SAY}}{2}\right)^2 - 1$

$\text{EAR} = \left(1 + \frac{0.043}{2}\right)^2 - 1$ $\text{EAR} = (1 + 0.0215)^2 - 1$ $\text{EAR} = (1.0215)^2 - 1$ $\text{EAR} = 1.04346225 - 1$ $\text{EAR} = 0.04346225 \text{ or } 4.346225\%$

Now, convert the EAR back to a quarterly yield (QY):

$\text{QY} = 4 \times \left[(1 + \text{EAR})^{1/4} - 1\right]$

$\text{QY} = 4 \times \left[(1 + 0.04346225)^{1/4} - 1\right]$ $\text{QY} = 4 \times \left[(1.04346225)^{0.25} - 1\right]$ $\text{QY} = 4 \times \left[1.010699 - 1\right]$ $\text{QY} = 4 \times 0.010699$ $\text{QY} = 0.042796 \text{ or } 4.2796\%$

This rounds to approximately 4.28%.

Alternative direct formula: $\text{QY} = 4 \times \left[\left(1 + \frac{\text{SAY}}{2}\right)^{2/4} - 1\right]$ $\text{QY} = 4 \times \left[\left(1 + \frac{0.043}{2}\right)^{0.5} - 1\right]$ $\text{QY} = 4 \times \left[(1.0215)^{0.5} - 1\right]$ $\text{QY} = 4 \times [1.010699 - 1]$ $\text{QY} = 4 \times 0.010699 = 0.042796$

Therefore, the quarterly yield is 4.28% (Option B).