Question

What is the Coupon Rate of a bond that makes semi-annual coupon payments and has a current price of $967.70, a par value of $1000, a YTM of 8.2%, and has 13.5 years until maturity?

Answer 1

Current Price = $967.70

Par value = $1000

r = semi annual YTM = 8.2%/2 = 4.1%

n = 13.5*2 = 27 semi annual years

Let C = semi annual coupon

Current Price = [C * [1 - (1+r)^-n] / r] + [Par Value / (1+r)^n]

$967.70 = [C * [1 - (1+4.1%)^-27] / 4.1%] + [$1,000 / (1+4.1%)^27]

$967.70 = [C * 0.662067234 / 0.041] + [$1,000 / 2.95916851]

$967.70 = [C * 16.1479813 ] + $337.932766

[C * 16.1479813] = $629.767234

C = $38.99975

Coupon rate = 2 * C / Par Value

= 2* $38.99975 / $1,000

= $77.9995 / $1,000

= 0.0779995

= 7.8%

Therefore, Coupon rate is 7.8%