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 if the maturity is 20 years? \( \$ \square \) (Round to the nearest cent.)

To find the price of a zero-coupon bond, you can use the formula: \[ \text{Price} = \frac{F}{(1 + r/n)^{nt}} \] where: - \( F \) = par value of the bond (\$1,000) - \( r \) = annual yield (6% or 0.06) - \( n \) = number of compounding periods per year (2 for semiannual) - \( t \) = number of years to maturity Now, let’s calculate for the different maturities: a. **20 years**: Using the values in the formula: \[ \text{Price} = \frac{1000}{(1 + 0.06/2)^{2 \times 20}} = \frac{1000}{(1 + 0.03)^{40}} = \frac{1000}{(1.03)^{40}} \approx 208.29 \] The price of the bond with 20 years to maturity is approximately **\$208.29**. b. **35 years**: \[ \text{Price} = \frac{1000}{(1 + 0.06/2)^{2 \times 35}} = \frac{1000}{(1 + 0.03)^{70}} \approx 82.40 \] The price of the bond with 35 years to maturity is approximately **\$82.40**. c. **70 years**: \[ \text{Price} = \frac{1000}{(1 + 0.06/2)^{2 \times 70}} = \frac{1000}{(1 + 0.03)^{140}} \approx 7.56 \] The price of the bond with 70 years to maturity is approximately **\$7.56**. d. **100 years**: \[ \text{Price} = \frac{1000}{(1 + 0.06/2)^{2 \times 100}} = \frac{1000}{(1 + 0.03)^{200}} \approx 0.22 \] The price of the bond with 100 years to maturity is approximately **\$0.22**.