Question

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.)

Answer 1

17%

Step-by-step 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%