Final answer:
The market value of a one-year zero-coupon bond with a face value of $1000 and a discount rate of 2% is approximately $980.39.
Step-by-step explanation:
The market value of a zero-coupon bond can be calculated using the formula for the present value of a single future cash flow, which is the face value of the bond. To find the present market value of the bond, we need to discount the face value of the bond by the discount rate, which in this case, is also the risk-free rate.
The calculation is as follows:
- Face value of the bond = $1000
- One-year discount rate = 2%
- Market value of the bond = Face value / (1 + discount rate)
Inserting the values into the formula gives us:
Market value of the bond = $1000 / (1 + 0.02)
Market value of the bond = $1000 / 1.02
Market value of the bond = $980.39
Therefore, the market value of a one-year zero-coupon bond with a face value of $1000 sold in a market where the one-year discount rate is 2% is approximately $980.39.