Question

O'Brien Ltd.'s outstanding bonds have a $1,000 par value, and they mature in 25 years. Their nominal annual, not semiannual yield to maturity is 9.25%, they pay interest semiannually, and they sell at a price of $1,025. What is the bond's nominal coupon interest rate?

Answer 1

Semiannual months = 25*2 =50

semiannual yield = 9.25/2= 4.625%               [2 semiannual months in a year]

Price =[PVA 4.625%,50 * Interest ] + [PVF 4.625%,50 *par value]

       1025 = [19.36679* I ] + [.10429*1000]

       1025 = 19.36679 SI + 104.29

        1025 -104.29 = 19.36679 SI

         SI = 920.71/19.36679

               = 47.54

Annual interest = 47.54*2 = 95.08

Annual coupon rate = 95.08/1000 = .09508 or 9.508 %   (rounded to 9.51%)