Final answer:
The price of a Treasury STRIP with a 2.9% yield-to-maturity, $1,000 par value, and 14 years until maturity is $637.22, calculated using the present value formula adapted for semi-annual compounding.
Step-by-step explanation:
Bond's price calculation for a zero-coupon US Treasury bond, commonly known as a Treasury STRIP, involves finding the present value of the bond's par value discounted at the yield to maturity with the number of periods until maturity taken into account. In this case, with a yield-to-maturity of 2.9%, a par value of $1,000, and 14 years to maturity, we recognize that compounding occurs semi-annually.
To calculate the present value, we use the formula:
PV = Par Value / (1 + r/n)^(nt)
Where:
- PV is the present value or the price of the bond today
- Par Value is the face value of the bond, which is $1,000
- r is the annual yield to maturity (0.029)
- n is the number of compounding periods per year (2)
- t is the number of years to maturity (14)
Plugging in the values we get:
PV = $1,000 / (1 + 0.029/2)^(2*14)
PV = $1,000 / (1 + 0.0145)^(28)
PV = $1,000 / (1.0145)^(28)
PV = $1,000 / 1.569507
PV = $637.22
Therefore, the bond's price today, rounded to the nearest penny, is $637.22.