An eight-year corporate bond has a 7 percent coupon rate. What should be the bond's price if the required return is 6 percent and the bond pays interest semiannually?

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To find the bond's price when the coupon is paid semiannually, we use the formula for the present value of an annuity to calculate the present value of the coupon payments, and the present value formula for a single sum to calculate the present value of the bond's face value. The bond's price is the sum of these two present values. Given a 7% annual coupon rate on a $1,000 face value bond, semiannual payments are $35 ($1,000 * 7% / 2). The required semiannual return is 3% (6% annual return / 2). The number of periods is 16 (8 years * 2). The bond's price is calculated as follows:$$ \text{Present Value of Coupons} = 35 \times \left( \frac{1 - (1 + 0.03)^{-16}}{0.03} \right) $$$$ \text{Present Value of Face Value} = \frac{1000}{(1 + 0.03)^{16}} $$Adding these two components gives the bond's price, which is approximately $1,062.81.

An Eight-Year Corporate Bond Has a 7 Percent Coupon Rate