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).