Question: Consider a bond with a face value of $1000. The coupon payment is made semi-annually and the yield on the bond is 12%. Would the bond sell at a premium or discount (and by how much) if:
a, the coupon rate is 8% and the remaining time to maturity is 20 years?
b, the coupon rate is 10% and the remaining time to maturity is 15 years?
Please include calculations and explanations.