Answer: 99.60.

## Explanation To calculate the price of a 3-year 0.2% annual coupon bond using forward rates, we need to discount each cash flow using the appropriate forward rates. **Given:** - Forward rates: - f(0,1) = 0.1% = 0.001 (for year 1) - f(1,1) = 0.3% = 0.003 (for year 2) - f(2,1) = 0.6% = 0.006 (for year 3) - Coupon rate: 0.2% = 0.002 - Par value: 100 **Cash flows:** - Year 1: Coupon = 100 × 0.002 = 0.2 - Year 2: Coupon = 100 × 0.002 = 0.2 - Year 3: Coupon + Principal = 0.2 + 100 = 100.2 **Discount factors calculation:** 1. **Year 1 discount factor:** DF₁ = 1 / (1 + f(0,1)) = 1 / (1 + 0.001) = 1 / 1.001 = 0.999000999 2. **Year 2 discount factor:** DF₂ = 1 / [(1 + f(0,1)) × (1 + f(1,1))] = 1 / (1.001 × 1.003) = 1 / (1.001 × 1.003) = 1 / 1.004003 = 0.99601396 3. **Year 3 discount factor:** DF₃ = 1 / [(1 + f(0,1)) × (1 + f(1,1)) × (1 + f(2,1))] = 1 / (1.001 × 1.003 × 1.006) = 1 / (1.001 × 1.003 × 1.006) = 1 / 1.010018018 = 0.990079 **Present value of cash flows:** - PV₁ = 0.2 × DF₁ = 0.2 × 0.999000999 = 0.1998002 - PV₂ = 0.2 × DF₂ = 0.2 × 0.99601396 = 0.199202792 - PV₃ = 100.2 × DF₃ = 100.2 × 0.990079 = 99.2059158 **Total price:** Price = PV₁ + PV₂ + PV₃ = 0.1998002 + 0.199202792 + 99.2059158 = 99.604918792 ≈ 99.60 **Verification with spot rates:** We can also calculate spot rates from forward rates: - s₁ = f(0,1) = 0.1% - s₂ = [(1 + f(0,1)) × (1 + f(1,1))]^(1/2) - 1 = (1.001 × 1.003)^(1/2) - 1 = 1.004003^(0.5) - 1 = 0.0020005 = 0.20005% - s₃ = [(1 + f(0,1)) × (1 + f(1,1)) × (1 + f(2,1))]^(1/3) - 1 = (1.001 × 1.003 × 1.006)^(1/3) - 1 = 1.010018018^(1/3) - 1 = 0.003333 = 0.3333% Using spot rates: Price = 0.2/(1.001) + 0.2/(1.0020005)² + 100.2/(1.003333)³ = 0.1998 + 0.1992 + 99.2059 = 99.6049 ≈ 99.60 Therefore, the price is closest to **99.60**, which corresponds to option **C**.

Author: LeetQuiz .