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? \( \$ 937.69 \) (Round to the nearest cent.) What is the price of the bond if it matures in 15 years? \( \$ \square \) (Round to the nearest cent.)

To determine the price of Moore Company's bond with a 15-year maturity, we'll follow these steps: ### **Given:** - **Par Value (FV):** \$1,000 - **Annual Coupon Rate:** 9% - **Semiannual Coupon Payment (PMT):** \( \frac{9\% \times \$1,000}{2} = \$45 \) - **Yield to Maturity (YTM):** 10% annually, or 5% per semiannual period - **Number of Years to Maturity:** 15 years - **Total Number of Semiannual Periods (N):** \( 15 \times 2 = 30 \) periods ### **Bond Pricing Formula:** \[ \text{Price} = PMT \times \left(1 - (1 + r)^{-N}\right) / r + \frac{FV}{(1 + r)^N} \] Where: - \( PMT \) = Semiannual coupon payment (\$45) - \( r \) = Semiannual Yield (5% or 0.05) - \( N \) = Total number of periods (30) - \( FV \) = Par Value (\$1,000) ### **Calculations:** 1. **Calculate the Present Value of Coupon Payments:** \[ PV_{\text{coupons}} = 45 \times \left( \frac{1 - (1 + 0.05)^{-30}}{0.05} \right) \] \[ (1 + 0.05)^{-30} \approx 0.231377 \] \[ 1 - 0.231377 = 0.768623 \] \[ \frac{0.768623}{0.05} = 15.37246 \] \[ PV_{\text{coupons}} = 45 \times 15.37246 \approx 691.76 \] 2. **Calculate the Present Value of the Par Value:** \[ PV_{\text{par}} = \frac{1,000}{(1 + 0.05)^{30}} \approx \frac{1,000}{4.321942} \approx 231.38 \] 3. **Total Bond Price:** \[ \text{Price} = PV_{\text{coupons}} + PV_{\text{par}} \approx 691.76 + 231.38 = 923.14 \] ### **Final Answer:** **The price of the bond if it matures in 15 years is \$923.14.**