Premium on bonds payable is the excess amount by which bonds are issued over their face value. This is classified as a liability, and is amortized to interest expense over the remaining life of the bonds. The net effect of this amortization is to reduce the amount of interest expense associated with the bonds.
A premium occurs when the market interest rate is less than the stated interest rate on a bond. In this case, investors are willing to pay extra for the bond, which creates a premium. They will pay more in order to create an effective interest rate that matches the market rate.
For example, a bond with a stated interest rate of 8% is sold. At the time, the market rate is lower than 8%, so investors pay $1,100 for the bond, rather than its $1,000 face value. The excess $100 is classified as a premium on bonds payable, and is amortized to expense over the remaining 10 year life span of the bond. At that time, the recorded amount of the bond has declined to its $1,000 face value, which is the amount the issuer will pay back to investors.