Answer:
The coupon rate of these bonds is 4%
Explanation:
The coupon rate is the interest rate written on the face of the bond and the interest payment is made on this rate.
Use the following formula to calculate the coupon rate of the bond
Price of the bond = [ C x ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]
Where
F = Face value = $1,000
Price of the bond = $938.57
r = Yield to maturity = 4.78% x 6/12 = 2.39%
n = Numbers of periods = 10 years x 12/6 = 20 periods
C = Periodic coupon payment = ?
Placing values in the formula
$938.57 = [ C x ( 1 - ( 1 + 2.39% )^-20 ) / 2.39% ] + [ $1,000 / ( 1 + 2.39% )^20 ]
$938.57 = [ C x 15.75237625 ] + $623.52
C x 15.75237625 = $938.57 - $623.52
C x 15.75237625 = $315.05
C = $315.05 / 15.75237625
C = $20 semiannually
C = $20 x 12/6 = $40 annually
Coupon rate = Coupon Payment / Face value = $40 / $1,000 = 0.04 = 4%
