SOLUTION: Union Local School District has a bond outstanding with a coupon rate of 3.7% paid semiannually and 16 years to maturity. The yield to maturity of the bond is 3.9%, and the bond ha
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Question 1083905: Union Local School District has a bond outstanding with a coupon rate of 3.7% paid semiannually and 16 years to maturity. The yield to maturity of the bond is 3.9%, and the bond has a par value of $5000. What is the price of the bond?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Answer: $4,881.80
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Explanation:
Refer to the PDF at the link below
https://people.ucsc.edu/~lbaum/econ80h/LS-Chap010.pdf
Specifically turn to page 6 for the formula we'll use.
An example is shown on page 7.
The formula we're using is
^{2*M}}\right] + \frac{FV}{\left(1+\text{YTM}/2\right)^{2*M}})
where
C = annual coupon payment (in dollars)
YTM = Yield To Maturity (expressed in decimal form)
M = Maturity of the bond (in years)
FV = face value of the bond (aka the par value in dollars)
In this case,
C = (coupon rate)*(Par value) = (3.7/100)*5000 = 185 dollars
YTM = (3.9/100) = 0.039
M = 16 years
FV = 5000 dollars
which are plugged into the formula to get...
^{2*16}}\right] + \frac{5000}{\left(1+\text{0.039}/2\right)^{2*16}})
^{32}}\right] + \frac{5000}{\left(1+0.0195\right)^{32}})
^{32}}\right] + \frac{5000}{\left(1.0195\right)^{32}})
So the bond price is roughly $4,881.80
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