Ponzi Corporation has bonds on the market with 14.5 years to maturity, a YTM of 6.1 percent, and a current price of $1,038. The bonds make semiannual payments. What must the coupon rate be on these bonds?

Coupon rate is 6.5%

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 ]

$1,038 = C x [ ( 1 - ( 1 + 6.1%/2 )^-14.5x2 ) / 6.1%/2 ] + [ $1,000 / ( 1 + 6.1%/2 )^14.5x2 ]

$1,038 = C x [ ( 1 - ( 1 + 0.0305 )^-29 ) / 0.0305 ] + [ $1,000 / ( 1 + 0.0305 )^29 ]

$1,038 = C x [ ( 1 - ( 1.0305 )^-29 ) / 0.0305 ] + [ $1,000 / ( 1..0305 )^29 ]

$1,038 = C x [ ( 1 - ( 1.0305 )^-29 ) / 0..0305 ] + [ $1,000 / ( 1.0305 )^29 ]

$1,038 = C x 19.068 + $418.42

$1,038 - $418.42 = C x 19.068

$619.58 = C x 19.068

C = $619.58 / 19.068

C = $32.49

Coupon rate = 32.49 / $1,000 = 3.25% semiannual

Coupon rate = 3.25% per semiannual x 2 = 6.5% per year

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