Question

AB Builders, Inc., has 25-year bonds outstanding with a par value of $2,000 and a quoted price of 97.511. The bonds pay interest semiannually and have a yield to maturity of 6.83 percent. What is the coupon rate?

A) 5.96%

B) 6.62%

C) 6.29%

D) 9.93%

E) 13.24%

Answer 1

Number of periods = 25 * 2 = 50

Price = 97.511% of 2,000 = $1,950.22

Rate = 6.83% / 2 = 3.415%

Price = Coupon * [1 - 1 / (1 + r)n] / r + FV / (1 + r)n

1,950.22 = Coupon * [1 - 1 / (1 + 0.03415)50] / 0.03415 + 2000 / (1 + 0.03415)50

1,950.22 = Coupon * [1 - 0.186562] / 0.03415 + 373.123997

1,950.22 = Coupon * 23.819561 + 373.123997

Coupon = $66.2101

Annual coupon = 66.2101 * 2 = 132.4202

Coupon rate = (Annual coupon / face value) * 100

Coupon rate = (132.4202 / 2000) * 100

Coupon rate = 6.62%