will issue a new 10 year AA rated corporate bond with a coupon rate of 7.00%. The bond pays interest semi-annually and has a face value of $ 1,000. If existing AA corporate bonds with 10 years to maturity have a yield to maturity of 5.00%, what will be the discount or premium of JAN Corp.'s bond relative to its face value.

The bond is sold at a premium of $1155.89 - $1000 = $155.89

Explanation:

N = 10 years * 2 semiannual = 20 payments of interest

coupon interest = 7% / 2 = 0.035

market interest = 5% / 2 = 0.025

interest = 1000*0.035 = $35 per semiannual

Pv interest for interest = [1-1 / (1+0.025) ^20]0.025 = 15.89 * $35 = $545.62

Pv for capital = 1000 / (1+0.025) ^20 = $610

value of the Bond = 610.27 + 545.62 = 1155.89

The market rate is less than the coupon rate meaning the bond is traded at a premium

Pv factor for many years = [1-1 / (1+r) ^n]/r