Bond Pricing: A 20-year corporate bond has a maturity value of $25, 000 and coupons are paid at 5% at the end of each year. If an investor wants to earn a yield of 7% compounded semiannually, what should she or he pay for this bond?

To calculate the price of a bond, you need to find the present value of its future cash flows. In this case, we have a 20-year corporate bond with a maturity value of $25,000 and annual coupon payments of 5%. The yield is 7% compounded semiannually.

Step 1: Determine the semiannual coupon payment
Since the coupon payments were stated on an annual basis, we need to calculate the semiannual coupon payment. Divide the annual coupon rate by 2.

Semiannual coupon payment = (Annual coupon rate / 2) = 5% / 2 = 2.5%

Step 2: Determine the number of coupon payments
In a 20-year bond, with semiannual compounding, the number of coupon payments will be twice the number of years.

Number of coupon payments = 20 years × 2 = 40 coupon payments

Step 3: Calculate the present value of the coupon payments
To calculate the present value (PV) of the coupon payments, we need to discount each semiannual coupon payment using the semiannual yield rate and then sum them up.

PV of coupon payments = Σ (Coupon payment / (1 + Yield/2)^n) [n = 1 to 40]

Using the formula for present value of an annuity:

PV = C * (1 - (1 + r)^(-n)) / r
where C is the coupon payment, r is the yield rate per period, and n is the number of periods.

PV of coupon payments = Σ (C / (1 + r/2)^n) [n = 1 to 40]

Step 4: Calculate the present value of the maturity amount
The maturity amount is the future value of the bond at the end of its term.

PV of maturity amount = Maturity value / (1 + Yield/2)^n
where n is the number of periods.

PV of maturity amount = $25,000 / (1 + 0.07/2)^40

Step 5: Add the present value of coupon payments and the present value of the maturity amount

Bond price = PV of coupon payments + PV of maturity amount

Now, plug in the values into the formulas and calculate the bond price.