Final answer:
The yield to maturity on a ten-year zero-coupon bond with a current price of $514.87 and $1,000 face value is approximately 6.91%. This is found using the formula for the present value of a zero-coupon bond and solving for the interest rate.
Step-by-step explanation:
The yield to maturity (YTM) for a bond is the total return anticipated on a bond if the bond is held until it matures. In the scenario where a zero-coupon bond with a $1,000 face value is selling for $514.87 and has ten years until maturity, one would calculate the YTM by solving for the interest rate that makes the present value of all future payments equal to the current selling price of the bond.
Calculating the Yield to Maturity
To calculate the YTM, we use the formula for the present value of a zero-coupon bond, which is:
P = F / (1 + r)n
where P is the current price of the bond, F is the face value of the bond, r is the yield to maturity (rate of return), and n is the number of years until maturity.
In this case:
P = $514.87
F = $1,000
n = 10
We need to solve for r, which represents the YTM. Rearranging the formula and using a financial calculator or algebra, we find that r is approximately 6.91%. Hence, the yield to maturity of the bond is approximately 6.91%.