Grand Adventure Properties offers a 9.5 percent coupon bond with annual payments.The yield to maturity is 11.2 percent and the maturity date is 11 years from today.What is the market price of this bond if the face value is $1,000?

Question

Quizplus · Accepted Answer

The market price of a bond can be calculated using the formula for the present value of an annuity (for the coupon payments) plus the present value of a lump sum (for the face value of the bond at maturity). The formula for the present value of an annuity is: PV = PMT * [1 - (1 + r)^-n] / r, where PMT is the annual coupon payment, r is the yield to maturity (expressed as a decimal), and n is the number of periods until maturity. The formula for the present value of a lump sum is: PV = FV / (1 + r)^n, where FV is the face value of the bond.Given:- Annual coupon rate = 9.5%- Face value, FV = $1,000- Yield to maturity, r = 11.2% or 0.112- Number of years until maturity, n = 11First, calculate the annual coupon payment: PMT = 9.5% of $1,000 = $95.Next, calculate the present value of the annuity (coupon payments):PV(annuity) = $95 * [1 - (1 + 0.112)^-11] / 0.112 ≈ $695.43Then, calculate the present value of the lump sum (face value at maturity):PV(lump sum) = $1,000 / (1 + 0.112)^11 ≈ $200.00Finally, add the present values of the annuity and the lump sum to get the market price of the bond:Market price = PV(annuity) + PV(lump sum) ≈ $695.43 + $200.00 = $895.43

Grand Adventure Properties Offers a 9