\( 1 \leftarrow \) Zero-coupon bond. Addison Company will issue a zero-coupon bond this coming month. The bond's projected yield is \( 6 \% \). If the par value is \( \$ 1,000 \), what is the bond's price using a semiannual convention if a. the maturity is 20 years? b. the maturity is 35 years? c. the maturity is 70 years? d. the maturity is 100 years? a. What is the price of the bond using a semiannual convention it the maturity is 20 years? \( \$ \square \) (Round to the nearest cent.)

To determine the price of Addison Company's zero-coupon bond using a semiannual convention with a maturity of 20 years, we can follow these steps: ### Given: - **Par Value (\( FV \))**: \$1,000 - **Annual Yield (\( r \))**: 6% - **Maturity (\( t \))**: 20 years - **Compounding Frequency**: Semiannual ### Steps: 1. **Determine the Semiannual Yield and Number of Periods**: - **Semiannual Yield (\( r_{\text{semi}} \))**: \( \frac{6\%}{2} = 3\% \) or 0.03 - **Total Number of Periods (\( n \))**: \( 20 \text{ years} \times 2 = 40 \) periods 2. **Present Value Formula for a Zero-Coupon Bond**: \[ PV = \frac{FV}{(1 + r_{\text{semi}})^n} \] 3. **Plug in the Values**: \[ PV = \frac{1000}{(1 + 0.03)^{40}} \] 4. **Calculate \( (1 + 0.03)^{40} \)**: - Using the formula for compound interest: \[ (1.03)^{40} \approx 3.26204 \] 5. **Compute the Present Value**: \[ PV = \frac{1000}{3.26204} \approx 306.28 \] ### **Answer:** a. The price of the bond is **\$306.28**.