Final answer:
The current market price of a five-year zero-coupon bond with a face value of $1,000 and an 8% yield to maturity, using annual compounding, is calculated to be approximately $681. This is done by calculating the present value of the bond's future face value.
Step-by-step explanation:
The subject of this question is determining the current market price of zero-coupon bonds when considering the yield to maturity. Shana Norris is looking at a five-year zero-coupon bond with a face value of $1,000 and a yield to maturity of 8 percent. To calculate the present value of this bond, we use the formula for present value, which is:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value (face value of the bond)
r = yield to maturity (as a decimal)
n = number of years until maturity
Plugging in the given values we get:
PV = $1,000 / (1 + 0.08)^5
Calculating this, the present value comes out to be:
PV = $1,000 / (1.469328)
PV = $680.58
Therefore, the closest option to the current market price of these bonds is $681, which corresponds to option D.