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Homework answers / question archive / A coupon bond with a par value of $1,000 and a 10-year maturity pays semi-annual coupons of $22
A coupon bond with a par value of $1,000 and a 10-year maturity pays semi-annual coupons of $22. a. Suppose the current interest rate for this bond is 4% per year compounded semi-annually. What is the fair price of the bond? b. Is the bond selling above or below par value?
No of periods = 10 years * 2 = 20 semi-annual periods
Bond Price = 
Coupon / (1 + YTM / 2)period + Par value / (1 + YTM / 2)period
Bond Price = $22 / (1 + 4% / 2)1 + $22 / (1 + 4% / 2)2 + ...+ $22 / (1 + 4% / 2)20 + $1000 / (1 + 4% / 2)20
Using PVIFA = ((1 - (1 + Interest rate)- no of periods) / interest rate) to value coupons
Bond Price = $22 * (1 - (1 + 4% / 2)-20) / (4% / 2) + $1000 / (1 + 4% / 2)4
Bond Price = $1032.70
The bond is selling above par value since the calculated fair Bond price is above the par value of $1000.
