Question

# 13 The market price of a semi-annual pay bond is $985.26. It has 22.00 years to maturity and a yield to maturity of 7.30%. What is the coupon rate? Submit Answer format: Percentage Round to: 0 decimal places (Example: 9%, % sign required. Will accept decimal format rounded to 2 decimal places (ex: 0.09)) unanswered

Answer 1

Price of a bond is mathematically represented as: 1 1 (1+ i)" P C i (1) where P is price of bond, with periodic coupon C, n periods to maturity, periodic YTM i and face value M.

For this question,

M = $1000, P = $985.26, i = 7.30%/2 = 3.65% (semi-annually), n = 22 * 2 = 44 semi-annual periods

$985.26 = C * \frac{1-\frac{1}{(1 + 0.0365)^{44}}}{0.0365} + \frac{1000}{(1 + 0.0365)^{44}}$

985.26 = C * 21.7393 + 206.5145

C = $35.82 --> Semi-annual

Annual Coupon = $35.82 * 2 = $71.64

Coupon Rate = $71.64/$1000 = 7.16%