Final answer:
The price of a zero-coupon bond with a yield of 9% maturing in 6 years with a $1,000 face value is approximately $596.27, calculated using the present value formula accounting for the time value of money.
Step-by-step explanation:
To calculate the price of a zero-coupon bond with a yield of 9% that is maturing in 6 years, given a face value of $1,000, you would use the present value formula. This formula is:
PV = FV / (1 + r)^n
Where PV is the present value (or price), FV is the face value, r is the yield or interest rate as a decimal, and n is the number of years until maturity.
For this specific bond:
PV = $1,000 / (1 + 0.09)^6
PV = $1,000 / (1.67710)
PV = $596.27 approximately
The price of the zero-coupon bond would therefore be about $596.27. It's important to note that bonds can be priced below their face value depending on the interest rates and time until maturity. In this case, because the yield is 9%, the bond sells for less than its face value to compensate the investor for the time value of money.