Why would you pay more than face value for a bond?
The main reason bond prices move has to do with interest rates. If a bond is issued at a given rate and then prevailing interest rates in the bond market fall, then the higher-interest bond looks better than it did previously. That in turn pushes its price higher.
The total bond premium is equal to the market value of the bond less the face value. For instance, with a 10-year bond paying 6% interest that has a $1,000 face value and currently costs $1,080 in the market, the bond premium is the $80 difference between the two figures.