Final answer:
Using the formula for present value and the given yield to maturity of 10%, the price of a 15-year, $1,000 face value, zero coupon bond would be approximately $239.
Step-by-step explanation:
The question asks for the price of a 15-year, $1,000 face value, zero coupon bond, given a yield to maturity (YTM) of 10%. To find the present value of the bond, which is the price we would pay today, we use the formula for present value of a single future cash flow, which is:
PV = FV / (1 + r)^n
where:
- PV is the present value of the bond (what we're solving for)
- FV is the future value of the bond ($1,000)
- r is the annual yield to maturity (0.10)
- n is the number of years until maturity (15)
Using the above formula, we calculate:
PV = $1,000 / (1 + 0.10)^15
PV = $1,000 / (1.10)^15
PV = $1,000 / 4.177248
PV = $239.39 (rounded to two decimal places)
Thus, the price of the bond today is approximately $239.