Final answer:
The Yield to Maturity (YTM) for a Zero Coupon Bond with a 17-year maturity and a purchase price of $830 is calculated using the compound interest formula, resulting in a YTM of 1.2%.
Step-by-step explanation:
The student asked how to calculate the Yield to Maturity (YTM) of a Zero Coupon Bond with a face value of $1000, a purchase price of $830, and a 17-year maturity, assuming annual compounding. The YTM is the annual return you would expect to earn on the investment if you held the bond until it matured, based on its purchase price and face value.
To calculate the YTM, we use the formula for compound interest:
FV = PV * (1 + r)^n
Where:
FV = Face Value of the bond
PV = Present Value or purchase price of the bond
r = yield to maturity (rate of return)
n = number of years until maturity
We are solving for 'r' and we have:
FV = $1000
PV = $830
n = 17
By rearranging the formula:
r = (FV/PV)^(1/n) - 1
Plug in the given values:
r = ($1000 / $830)^(1/17) - 1 = 0.012 or 1.2%
Thus, the YTM the seller is offering on the bonds is 1.2%.
The YTM is a useful tool in evaluating the attractiveness of investing in bonds, especially when determining whether to purchase a bond at a discount or premium in relation to its face value.