The market price of a 10-year, $1,000 bond is $1,158.91. Interest on this bond is paid semiannually and the YTM is 14%. What is the bond's annual coupon rate? (Round your answer to the nearest percent.)

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Business

Maleah Berg

24 January, 14:39

The market price of a 10-year, $1,000 bond is $1,158.91. Interest on this bond is paid semiannually and the YTM is 14%. What is the bond's annual coupon rate? (Round your answer to the nearest percent.)

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Answers (1)

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Charmer · Answer 1

17%

Explanation:

Market price of a bond is the total sum of discounted coupon payment plus par value at maturity. This is a 10-year bond with semi-annual payment so there will be 20 coupon payment in total. Let formulate the bond price as below:

Bond price = [ (Coupon rate/2) x Par] / (1 + YTM/2) + [ (Coupon rate/2) x Par] / (1 + YTM/2) ^2 + ... + [ (Coupon rate/2) x Par + Par] / (1 + YTM/2) ^20

Putting all the number together, we have

1,158.91 = [ (Coupon rate/2) x 1000] / (1 + 7%) + [ (Coupon rate/2) x 1000] / (1 + 7%) ^2 + ... + [ (Coupon rate/2) x 1000 + 1000] / (1 + 7%) ^20

Solve the equation, we have Coupon rate = 17%