Question

. Suppose a bond that has semiannual coupons is selling for $10,500. It has 7 years left until maturity. Its par value is $10,000 and its YTM is 7%. What is this bond’s annual coupon rate?

Answer 1

7.92% annually

Step-by-step 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 ]

$10,500 = C x [ ( 1 - ( 1 + 7%/2 )^-7x2 ) / 7%/2 ] + [ $10,000 / ( 1 + 7%/2 )^7x2 ]

$10,500 = C x 10.92 + $6,177.82

$10,500 - $6,177.82 = C x 10.92

$4,322.18 = C x10.92

C = $43,22.18 / 10.92

C = $395.8

Coupon rate = 395.80 / $10,000 = 3..96% semiannually = 3.96% x 2 = 7.92% annually