Answer: 7.988%

## Explanation To calculate the 3-year spot rate, we use the concept of bootstrapping from forward rates. The spot rate is the yield that makes the present value of the bond's cash flows equal to its price. Given: - Current 1-year rate (r₁) = 6% - 1-year rate next year (f₁₂) = 8% - 1-year rate in two years (f₂₃) = 10% For a 3-year zero-coupon bond with face value $1: **Method 1: Using the relationship between spot and forward rates** (1 + z₃)³ = (1 + r₁) × (1 + f₁₂) × (1 + f₂₃) (1 + z₃)³ = (1 + 0.06) × (1 + 0.08) × (1 + 0.10) (1 + z₃)³ = 1.06 × 1.08 × 1.10 (1 + z₃)³ = 1.06 × 1.188 (1 + z₃)³ = 1.25928 z₃ = (1.25928)^(1/3) - 1 z₃ = 1.07988 - 1 z₃ = 0.07988 = 7.988% **Method 2: Present value approach** For a 3-year zero-coupon bond with face value $1: Price = $1 / [(1 + r₁) × (1 + f₁₂) × (1 + f₂₃)] Price = $1 / (1.06 × 1.08 × 1.10) = $1 / 1.25928 = $0.7941 Then solve for z₃: $0.7941 = $1 / (1 + z₃)³ (1 + z₃)³ = 1 / 0.7941 = 1.25928 z₃ = (1.25928)^(1/3) - 1 = 7.988% Therefore, the correct 3-year spot rate is **7.988%**, which corresponds to option B.

Author: LeetQuiz .