Final answer:
The present value of a bond is calculated by summing the present value of its future coupon payments and its face value using the present value of an annuity and a lump sum formulas, with adjustments based on the market interest rate versus the coupon rate.
Step-by-step explanation:
The student is asking how to calculate the present value of a 17-year bond with a coupon rate of 8% and a face value of $1,000 given that the market interest rate for similar bonds is 6%. To find the present value, we sum the present value of all future coupon payments and the present value of the face value paid at the bond's maturity.
For the coupon payments, the present value of an annuity formula is used: PV = PMT [(1 - (1 + r)^-n) / r], where PMT is the annual coupon payment ($1,000 x 0.08 = $80), r is the market interest rate (0.06), and n is the total number of payments (17). The present value of the face value is calculated using the present value of a lump sum formula: PV = FV / (1 + r)^n, where FV is the face value of the bond.
Calculating the present value of the annuity (coupon payments) plus the present value of the face value (maturity amount) and then adding them together gives the present value of the bond, which will differ depending on the market interest rate. If the market rate is below the coupon rate, the bond sells at a premium; if it's above, the bond sells at a discount.