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? \( \$ 923.14 \) (Round to the nearest cent.) What is the price of the bond if it matures in 20 years? \( \$ \square \) (Round to the nearest cent.)

To determine the price of Moore Company's bond if it matures in 20 years, we'll use the **present value (PV) formula for bonds**. Here's a step-by-step breakdown: ### **Given:** - **Annual Coupon Rate:** 9% - **Semiannual Coupon Rate:** 4.5% (since coupons are paid semiannually) - **Par Value (F):** \$1,000 - **Yield to Maturity (YTM):** 10% annually or 5% semiannually - **Maturity:** 20 years - **Number of Periods (n):** 20 years × 2 = 40 periods - **Coupon Payment (C):** \$45 every six months (4.5% of \$1,000) ### **Bond Pricing Formula:** \[ PV = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) + \frac{F}{(1 + r)^n} \] Where: - \( C \) = Semiannual coupon payment - \( r \) = Semiannual yield (YTM/2) - \( n \) = Total number of periods - \( F \) = Par value of the bond ### **Calculations:** 1. **Calculate the Present Value of the Coupons:** \[ PV_{\text{coupons}} = 45 \times \left( \frac{1 - (1 + 0.05)^{-40}}{0.05} \right) \] - First, calculate \( (1 + 0.05)^{-40} \): \[ (1.05)^{-40} \approx 0.1410 \] - Then: \[ 1 - 0.1410 = 0.8590 \] \[ \frac{0.8590}{0.05} = 17.18 \] \[ 45 \times 17.18 = 773.10 \] 2. **Calculate the Present Value of the Par Value:** \[ PV_{\text{par}} = \frac{1000}{(1.05)^{40}} \approx 1000 \times 0.1410 = 141.00 \] 3. **Total Present Value (Price of the Bond):** \[ PV = 773.10 + 141.00 = 914.10 \] ### **Conclusion:** The price of the bond maturing in **20 years** is **\$914.10**. Answer: The bond priced with a 20‑year maturity is $ 914.10 when rounded to the nearest cent.