Answer: 4.28%

## 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).

Author: LeetQuiz .