Answer:
293.05
Step-by-step: Can be calculated using the formula:
Price = Face Value / (1 + (YTM / n))^(n * m)
where:
- Face Value is the amount paid at maturity ($1000 in this case)
- YTM is the yield to maturity (8% in this case)
- n is the number of compounding periods per year (2 for semiannual compounding)
- m is the number of years to maturity (20 in this case)
Plugging in the values, we get:
Price = $1000 / (1 + (0.08 / 2))^(2 * 20)
Simplifying the expression inside the parentheses:
Price = $1000 / (1.04)^(40)
Calculating (1.04)^(40):
Price = $1000 / 3.4149
Therefore, the price of the 20-year, zero coupon bond is approximately $293.05.
Correct me if i'm wrong :>