Zeta Corporation has issued a $1,000 face value zero-coupon bond. Which of the following values is closest to the correct price for the bond if the appropriate discount rate is 8% and the bond matures in 8 years?
968
23
To calculate the price of a zero-coupon bond, we can use the present value formula. The formula is:
Price = Face Value / (1 + Discount Rate)^(Number of Years)
Let's plug in the given values:
Face Value = $1,000
Discount Rate = 8%
Number of Years = 8
Price = $1,000 / (1 + 0.08)^8
Calculating this value will give us the price of the bond.
To find the price of the zero-coupon bond, we can use the present value formula, which calculates the current value of future cash flows. In this case, since it is a zero-coupon bond, it only pays the face value at maturity without any periodic interest payments.
The formula to calculate the present value is:
PV = FV / (1 + r)^n
Where:
PV = Present value (price of the bond)
FV = Face value of the bond ($1,000 in this case)
r = Discount rate (8% or 0.08)
n = Number of years until maturity (8 years)
By plugging in the values, we can calculate the price of the bond:
PV = 1000 / (1 + 0.08)^8
PV = 1000 / (1.08)^8
PV ≈ 468.52
So, the closest value to the correct price for the bond is $468.52.