Answer: 4.28%

To convert a semiannual yield to a quarterly yield, we need to use the following relationship: **Step 1: Understand the relationship** - Semiannual yield (SAY) = 4.3% (annual percentage rate) - This means the periodic rate per 6-month period = 4.3%/2 = 2.15% - The effective annual rate (EAR) = (1 + 0.0215)^2 - 1 = 1.04346225 - 1 = 4.346225% **Step 2: Convert to quarterly compounding** - For quarterly compounding, we need to find the quarterly rate (r_q) such that: (1 + r_q)^4 = 1 + EAR (1 + r_q)^4 = 1.04346225 - Take the fourth root: 1 + r_q = (1.04346225)^(1/4) 1 + r_q = 1.010676 r_q = 0.010676 or 1.0676% per quarter **Step 3: Convert to annual percentage rate (APR) with quarterly compounding** - Quarterly APR = r_q × 4 = 1.0676% × 4 = 4.2704% - This is approximately 4.28% **Step 4: Alternative direct formula** The direct conversion formula is: Quarterly rate = 2 × [(1 + SAY/2)^(1/2) - 1] Quarterly rate = 2 × [(1 + 0.043/2)^(1/2) - 1] Quarterly rate = 2 × [(1.0215)^(0.5) - 1] Quarterly rate = 2 × [1.010676 - 1] Quarterly rate = 2 × 0.010676 = 0.021352 Quarterly APR = 0.021352 × 2 = 0.042704 = 4.2704% Therefore, the yield-to-maturity based on quarterly compounding is closest to **4.28%** (Option B).

Author: LeetQuiz .