Question

A bond with 7 years left to maturity is trading for $1004. It pays coupons semiannually. Its YTM is currently 3.3%. The coupon rate for this bond must be ________%. Do not round any intermediate work. Round your *final* answer to 2 decimal places (example: .1234567 = 12.35). Do not enter the % sign. Margin of error for correct responses: +/- .03%.

Answer 1

Number of periods = n = 7*2 = 14 semiannual periods

Yield I/Y= 3.3%/2 = 0.033/2

Semiannual Coupon Payment = P

Face Value FV = $1000

Present Value = PV = 1004

Hence, PV = P/(1+r) + P/(1+r)² + .... + P/(1+r)ⁿ + FV/(1+r)ⁿ

= P[1 - (1+r)^-n]/r + FV/(1+r)ⁿ

=> 1004 = P(1 - (1+0.033/2)^-14)/(0.033/2) + 1000/(1+0.033/2)¹⁴

=> 12.410P = 208.762

=> P = 16.82

Hence, Coupon rate for bond = Annual Coupon/Face Value *100% = 2*P/1000 * 100% = 3.36%