A 17-year, semiannual coupon bond sells for $948.63. The bond has a par value of $1,000 and a yield to maturity of 7.11 percent. What is the bond's coupon rate

Bond's Coupon rate is 3.3%

Explanation:

Bond price is the sum of present value of coupon payment and face value of the bond. If the price is available the coupon payment can be calculated by following formula

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

$948.63 = C x [ ( 1 - ( 1 + 7.11%/2 )^-17x2 ) / 7.11%/2 ] + [ $1,000 / ( 1 + 7.11%/2 )^17x2 ]

$948.63 = C x [ ( 1 - ( 1 + 0.03555 )^-34 ) / 0.03555 ] + [ $1,000 / ( 1 + 0.03555 )^34 ]

$948.63 = C x [ ( 1 - ( 1.03555 )^-34 ) / 0.03555 ] + [ $1,000 / ( 1.03555 )^34 ]

$948.63 = C x [ ( 1 - ( 1.03555 )^-34 ) / 0.03555 ] + [ $1,000 / ( 1.03555 )^34 ]

$948.63 = C x 19.55 + $304.92

$948.63 - $304.92 = C x 19.55

643.71 = C x 19.55

C = 643.71 / 19.55

C = 32.93

Coupon rate = 32.93 / $1,000 = 3.3%

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