A person would buy a bond at a premium (pay more than its maturity value) because the bond's stated interest rate (and therefore its interest payments) are greater than those expected by the current bond market. It is also possible that a bond investor will have no choice. For example, if you wish to purchase a bond maturing in 8 years with a specific bond rating, there might be only one bond available. If its stated interest rate is greater than the market interest rate on the day that you are purchasing, you either buy the bond at a premium or you don't buy a bond.
The bond premium is the present value of both the future interest payments and the maturity amount minus the bond's undiscounted maturity amount. In short, the bond market is very efficient. If a bond's actual interest payments will be greater than the interest payments expected by the market, the bond will sell for more than the bond's maturity amount. If the bond's interest payments will be lower than the interest payments expected by the market, the bond will sell for less than the bond's maturity amount. The difference (premium or discount) is computed by discounting all of the future cash amounts.
Paying a small premium is not unusual. Remember that the premium is directly related to the higher interest amounts you will be receiving. If the bond purchase will result in a large premium, you should investigate whether the bond is callable and its call price. The call price may limit the amount of premium that you are willing to pay.