Final answer:
The current price of a zero-coupon bond with a $1,000 face value, 24 years to maturity, and a 9.45% discount rate is approximately $143.12.
Step-by-step explanation:
The current price of a zero-coupon bond can be calculated using the formula for present value of a single future cash flow. This is given by PV = FV / (1 + r)^n, where PV is the present value (current price) of the bond, FV is the face value of the bond, r is the discount rate, and n is the number of years to maturity.
For a zero-coupon bond with a face value of $1,000, a maturity of 24 years, and a current discount rate of 9.45%, we can calculate the present value (current price) of the bond as follows: PV = $1,000 / (1 + 0.0945)^24. Using this formula, we calculate the current price of the bond to be approximately $143.12.
This demonstrates how the current price of a bond is inversely related to the discount rate. As the discount rate increases, the present value of the bond decreases.