The yield to maturity of the zero coupon bond with a $338 purchase price, $1,000 face value, and 13 years until maturity is approximately 9.6%.
To calculate the yield to maturity (YTM) of a zero coupon bond, we can use the formula that sets the present value of the promised future payments equal to the current market price of the bond. The formula is as follows: PV = FV / (1 + YTM)^n, where PV is the present value (or price) of the bond, FV is the face value of the bond, YTM is the yield to maturity, and n is the number of years until maturity.
Using the information provided:
- PV = $338
- FV = $1,000
- n = 13 years
The formula can be rearranged to solve for YTM:
YTM = (FV / PV)^(1/n) - 1
Substituting the given values into the formula, we have:
YTM = ($1,000 / $338)^(1/13) - 1
Calculating the value we get:
YTM = 2.96 or approximately 9.6% when expressed as a percentage.
The yield to maturity represents the annualized rate of return on a bond if it is held until its maturity date, reflecting both the interest payments (if any) and the capital gains or losses from holding the bond.