Question

A bond will mature in 10 years, has a YTM of 6.5%, and makes semiannual payments. If the bond price is $1104 today, what is the coupon rate?

7.93%

6.50%

8.97%

7.44%

None of the above

Answer 1

Number of periods = n = 10*2 = 20 semiannual periods

Yield I/Yr = 6.5%/2 = 0.0325

Semiannual Payment = P

Face Value FV = $1000

Present Value of Stock = $1104

Present Value = P/(1+r) + P/(1+r)² + .... P/(1+r)ⁿ + FV/(1+r)ⁿ = PP[1 - (1+r)^-n]/r + FV/(1+r)ⁿ

=> 1104 = P(1 - 1.0325^-20)/0.05 + 1000/1.0325²⁰

=>P = 39.65

Annual Payment = 39.65*2 = $79.3

=> Coupon Rate = 79.3/1000 *100% = 7.93%