On November $1,2021,$ Electromedical AG issued a $€500,000,3\%,5-$year bond payable. The bond has a present value at issuance of $€456,705$ and pays annual interest each October $31$st$.$ Journalize the issuance of the bond, the December $31,2021$ adjustments, and the annual interest payment in $2022.$ Answer the following questions:

a$)$ What is the reason for the difference between the face value and the present value of the bond?

b$)$ What is the nature of the account that indicates this difference?

c$)$ What is the carrying amount of the bond on December $31,2021?$

 d$)$ What is the total interest expense in $2022?$