Question

a 30 year bond matures in 7 years sells for $1,125 pays interest semiannually a face value of $1,000 and has a yield to maturity of 10.5%. What is the bond's current yield?

Answer 1

Rate = 10.5% / 2 = 5.25%

Number of periods = 7 * 2 = 14

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

1,125 = Coupon * [1 - 1 / (1 + 0.0525)¹⁴] / 0.0525 + 1000 / (1 + 0.0525)¹⁴

1,125 = Coupon * [1 - 0.488529] / 0.0525 + 488.529211

1,125 = Coupon * 9.742305 + 488.529211

65.3306 = Coupon

Annual coupon = 65.3306 * 2 = 130.6612

Current yield = (Annual coupon / price) * 100

Current yield = (130.6612 / 1,125) * 100

Current yield = 11.61%