Final answer:
To calculate the current market price of a 15-year zero coupon bond with a yield to maturity of 6.85% and semiannual compounding, use the formula: PV = FV / ((1 + r)^n). The current market price is a. $321.50.
Step-by-step explanation:
To calculate the current market price of a 15-year zero coupon bond, you need to discount the bond's future cash flows to present value. In this case, the face value of the bond is $1,000 and the yield to maturity is 6.85%. Since this is a semiannual compounding bond, you need to adjust the yield to a semiannual rate by dividing it by 2. Therefore, the semiannual yield is 6.85% / 2 = 3.425%.
Next, calculate the total number of periods, which is 15 years * 2 = 30 semiannual periods. The present value of the face value can be calculated using the formula PV = FV / ((1 + r)^n), where PV is the present value, FV is the future value, r is the semiannual yield, and n is the total number of periods. In this case, PV = $1,000 / ((1 + 0.03425)^30) = $321.50.
Therefore, the current market price of the bond is $321.50.