Union Local School District has bonds outstanding with a coupon rate of 3.2 perc

Question

Union Local School District has bonds outstanding with a coupon rate of 3.2 percent paid semiannually and 14 years to maturity. The yield to maturity on these bonds is 3.8 percent and the bonds have a par value of $5,000.

What is the price of the bonds? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Union Local School District has bonds outstanding with a coupon rate of 3.2 percent paid semiannually and 14 years to maturity. The yield to maturity on these bonds is 3.8 percent and the bonds have a par value of $5,000.

Explanation / Answer

Given that C = 3.2%/2*5000 = $80, n = 14*2 = 28, YTM = 3.8%/2 = 1.9% and FV = $5,000

The price of the bond, P is

P = C (PVIFA @ YTM, n) + FV (PVIF @ YTM, n)

P = 80 (PVIFA @ 1.9%, 28) + 5000 (PVIF @ 1.9%, 28)

P = 80 [(1.019^28-1)/ (0.019*1.019^28)] + 5000 (1/1.019^28)

P = 80 (21.5596) + 5000 (0.5904)

P = $4,676.61

Hence, the price of the bonds is $4,676.61

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