Question

Union Local School District has bonds outstanding with a coupon rate of 2.8 percent paid semiannually and 25 years to maturity. The yield to maturity on these bonds is 2.4 percent and the bonds have a par value of $5,000. What is the price of the bonds?

Answer 1

To find the price of the bonds, we can use the present value formula which is as follows:

Price of bond = (C / 2) * [1 - (1 + r)^(-n * 2)] / r + FV / (1 + r)^n*2

Where:
C = coupon payment
r = yield to maturity
n = number of years to maturity
FV = face value or par value

Substituting the given values into this formula, we get:

Coupon Payment (C) $140 (($5000 x 2.8%) / 2))
Yield to Maturity(r) 0.024
Years(Maturity)n 25
Face Value(FV) $5,000

Now substituting these given variables in above equation :
Price of bond= ($140/annum)*[1-((1+0.024)^(-50))]/(0.024)+$5,000/(1+0.024)^50

This gives us a price of approximately $4,623 for these bonds.

Therefore, Union Local School District Bond's selling price is around $4,623 with a coupon rate of 2.8%, yield to maturity at 2.4% and having remaining time towards its final payoff after twenty-five years from today's date..