Answer: USD 104.18

## Explanation This question involves bond replication using the law of one price. We need to find the price of an 8% coupon bond using the given zero-coupon bond and 10% coupon bond. **Given:** - 1-year zero-coupon bond: USD 96.12 - 1-year 10% coupon bond (semi-annual): USD 106.20 - Face value: USD 100 (assumed) **Step 1: Create a replicating portfolio** Let's create a portfolio that replicates the 8% coupon bond using the other two bonds: - 8% coupon bond pays: 4% × 100 = USD 4 at 6 months, and 4% × 100 + 100 = USD 104 at 1 year We need to find weights w₁ and w₂ such that: w₁ × (cash flows of zero-coupon) + w₂ × (cash flows of 10% coupon) = cash flows of 8% coupon **Step 2: Set up equations** Zero-coupon bond: Pays USD 100 at maturity (1 year) 10% coupon bond: Pays 5% × 100 = USD 5 at 6 months, and 5% × 100 + 100 = USD 105 at 1 year At 6 months: w₁ × 0 + w₂ × 5 = 4 At 1 year: w₁ × 100 + w₂ × 105 = 104 **Step 3: Solve the system** From first equation: w₂ = 4/5 = 0.8 Substitute into second equation: w₁ × 100 + 0.8 × 105 = 104 w₁ × 100 + 84 = 104 w₁ × 100 = 20 w₁ = 0.2 **Step 4: Calculate price** Price of 8% coupon bond = w₁ × Price(zero) + w₂ × Price(10% coupon) = 0.2 × 96.12 + 0.8 × 106.20 = 19.224 + 84.96 = 104.184 ≈ USD 104.18 Therefore, the correct price is USD 104.18, which corresponds to option D.

Author: LeetQuiz Editorial Team