Definition of Bond Premium
Bond premium or premium on bonds occurs when the bond's actual interest payments are greater than the interest payments expected by the market. The amount of the bond premium = (actual future interest payments + actual maturity amount) discounted by the market interest rate at the time of the bond sale.
Example of a Bond Premium
A person would buy a bond at a premium (pay more than its maturity value) because the bond's stated interest rate (and therefore the bond's interest payments) will be greater than those expected by the current bond market.
It is also possible that a bond investor will have no choice. For example, if the investor wants to purchase a bond with a high rating that matures in 8 years, perhaps only one bond will be available. If its stated interest rate is greater than the market interest rate on the day of the transaction, the investor either buys the bond at a premium or doesn't buy a bond.
You will find another example of bond premium at https://www.accountingcoach.com/blog/what-is-premium-on-bonds-payable