Let's break down and solve the problem step-by-step: **Problem Recap:** - Face value of the bond (\( F \)): $1,000 - Coupon rate: 7.3% (annual payments) - Yield to maturity (YTM): 5.6% - Time to maturity (\( n \)): 10 years **Step 1: Calculate the Annual Coupon Payment (\( C \))** \( C = \text{Coupon Rate} \times \text{Face Value} \) \( C = 0.073 \times \$1,000 = \$73 \) **Step 2: Write the Bond Price Formula** The price of a bond is the present value of all future coupon payments and the face value, discounted at the yield to maturity: \[ \text{Price} = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n} \] Where: - \( C \) = annual coupon payment = $73 - \( F \) = face value = $1,000 - \( r \) = YTM = 5.6% = 0.056 - \( n \) = 10 **Step 3: Calculate the Present Value of Coupon Payments (Annuity)** \[ PV_{\text{coupons}} = C \times \left[\frac{1 - (1 + r)^{-n}}{r}\right] \] \[ PV_{\text{coupons}} = 73 \times \left[\frac{1 - (1 + 0.056)^{-10}}{0.056}\right] \] First, calculate \( (1 + 0.056)^{-10} \): \[ (1.056)^{-10} \approx 0.5678 \] So, \[ PV_{\text{coupons}} = 73 \times \left[\frac{1 - 0.5678}{0.056}\right] = 73 \times \left[\frac{0.4322}{0.056}\right] = 73 \times 7.717857 \approx 563.40 \] **Step 4: Calculate the Present Value of the Face Value** \[ PV_{\text{face}} = \frac{F}{(1 + r)^n} = \frac{1000}{(1.056)^{10}} \] \[ (1.056)^{10} \approx 1.725 \] So, \[ PV_{\text{face}} = \frac{1000}{1.725} \approx 579.71 \] **Step 5: Add Both Present Values** \[ \text{Bond Price} = PV_{\text{coupons}} + PV_{\text{face}} = 563.40 + 579.71 = 1143.11 \] --- ### **Final Answer (to the nearest cent):** \[ \boxed{1,\!143.11} \] --- **Explanation:** The bond price is higher than the face value because the coupon rate is higher than the yield to maturity. This means investors are willing to pay a premium for the above-market coupon payments.