A discount bond is simply a bond that is selling below its par value.  It would be quoted at a price that is less than 100 percent of par, like 99.05.  A premium bond is a bond selling above its par value.  Its price will be quoted as over 100 percent of par value, like 101.15.  A bond becomes a discount bond when market interest rates rise above the bond’s coupon rate. A bond becomes a premium bond when market interest rates fall below the bond’s coupon rate.