Bond prices and maturity dates. Moore Company is about to issue a bond with semiannual coupon payments, an annual coupon rate of \( 9 \% \), and a par value of \( \$ 1,000 \). The yield to maturity. for this bond is \( 10 \% \). a. What is the price of the bond if it matures in \( 5,10,15 \), or 20 years? b. What do you notice about the price of the bond in relationship to the maturity of the bond? \( \$ 961.39 \) (Round to the nearest cent.) What is the price of the bond if it matures in 10 years? \( \$ \) (Round to the nearest cent.)

To determine the price of Moore Company's bond with a **10-year maturity**, we'll follow these steps: ### **Given:** - **Par Value (F):** \$1,000 - **Annual Coupon Rate:** 9% - **Semiannual Coupon Payment (C):** \( \frac{9\% \times \$1,000}{2} = \$45 \) - **Yield to Maturity (YTM):** 10% annually, which translates to 5% semiannually - **Number of Periods (n):** \( 10 \text{ years} \times 2 = 20 \) semiannual periods ### **Bond Pricing Formula:** The price of a bond is the present value of all future coupon payments plus the present value of the par value at maturity. The formula is: \[ \text{Price} = C \times \left[ \frac{1 - (1 + r)^{-n}}{r} \right] + \frac{F}{(1 + r)^n} \] Where: - \( C \) = Semiannual coupon payment (\$45) - \( r \) = Semiannual YTM (5% or 0.05) - \( n \) = Total number of semiannual periods (20) - \( F \) = Par value (\$1,000) ### **Calculations:** 1. **Present Value of Annuity (Coupon Payments):** \[ PV_{\text{coupons}} = 45 \times \left[ \frac{1 - (1.05)^{-20}}{0.05} \right] \] First, calculate \( (1.05)^{-20} \): \[ (1.05)^{20} \approx 2.653297705 \\ (1.05)^{-20} \approx \frac{1}{2.653297705} \approx 0.376889 \] Now, compute the annuity factor: \[ \frac{1 - 0.376889}{0.05} = \frac{0.623111}{0.05} = 12.46222 \] So, \[ PV_{\text{coupons}} = 45 \times 12.46222 \approx \$560.80 \] 2. **Present Value of Par Value:** \[ PV_{\text{par}} = \frac{1,000}{(1.05)^{20}} \approx \frac{1,000}{2.653297705} \approx \$376.89 \] 3. **Total Bond Price:** \[ \text{Price} = PV_{\text{coupons}} + PV_{\text{par}} \approx 560.80 + 376.89 = \$937.69 \] ### **Answer:** **b.** The **price of the bond that matures in 10 years** is **\$937.69**.