Final answer:
The yield to maturity (YTM) of a zero-coupon bond that has a face value of $100, is currently trading for $68.21, and matures in 8 years, is 4.73%. The YTM represents the annual return an investor would receive if the bond is held until maturity.
Step-by-step explanation:
To calculate the yield to maturity (YTM) of a zero-coupon bond, we use the formula that relates the current price of the bond, its face value, and the time left until it matures. The formula can be given as:
YTM = (Face Value / Current Price)^(1/n) - 1
Where:
- Face Value is what the bond will be worth at maturity, which is typically $1,000, but in this question, it is $100 for simplification.
- Current Price is what you pay for the bond today, which is $68.21 according to the student's question.
- n is the number of years until the bond matures, which is 8 years in this case.
Let's insert the values into the formula:
YTM = ($100 / $68.21)^(1/8) - 1
YTM = (1.4661)^(0.125) - 1
YTM = 1.0473 - 1
YTM = 0.0473 or 4.73%
The bond's yield to maturity is therefore 4.73%. This represents the annual return that an investor would receive if they held the bond until maturity, assuming there are no defaults.