A bond with 23 years to maturity is selling for $991 and has a yield to maturity of 8.12%. If this bond pays its coupon payments semi-annually and par value is $1,000, what is the bond's annual coupon rate?
A) 7.45%
B) 8.03%
C) 9.39%
D) 10.82%

Question

Quizplus · Accepted Answer

First, we need to calculate the semi-annual coupon payments:
Coupon payment = (Coupon rate x Par value) / 2 = (Coupon rate x $1,000) / 2
Next, we can use the bond price, yield to maturity, and the semi-annual coupon payments to solve for the coupon rate using the bond pricing formula:
$991 = [($C / 2) / (1 + 0.0812 / 2)^46] + [$1,000 / (1 + 0.0812 / 2)^46]
Solving for $C, we get:
$C = $40.15
Therefore, the coupon rate is:
Coupon rate = ($C / Par value) x 2 = ($40.15 / $1,000) x 2 x 100% = 8.03% (rounded to 2 decimal places)

A Bond with 23 Years to Maturity Is Selling for $991