Under what conditions of bond issuance do a discount on bonds payable arise? Under what conditions of bond issuance does a premium on bonds payable arise?

Bonds payable are those bonds issued by the company to raise funds, creating a liability. It is borrowings for the company. It is issued at par (face value) or at a premium (more than face value) or a discount (less than face value)

The current market rate is higher than the interest rate being paid by the issuer, so the investors pay less for the bond in order to derive a higher effective rate of interest on their investment.

Stated Interest rate < Market Interest rate

Premium on bonds payable is the excess amount by which bonds are issued over their face value. This is classified as a liability in the books of the issuer and is amortized to interest expense over the remaining life of the bonds.

Stated Interest rate > Market Interest rate