What is the theory behind requiring bond issuers to charge bond discounts to interest expense when the discount is amortized?

When a bond matures the issuer has to pay the investor the full face value of the bond. The bond will also have a stated interest rate. If an investor will only accept a rate of interest which is higher than the stated interest rate, the issuer will likely sell the bond for less than the present value of the face value of the bond.

For example, If a $100,000 bond is issued with a $4,000 discount to meet the buyers desired return, the issuer will have to pay the investor the $96,000 ($100,000-$96,000) the issuer received plus the $4,000 discount upon maturity.

Since the issuer has to pay out that $4,000, upon maturity, to secure $96,000 the $4,000 discount is recognized by the issuer as interest expense (over the life of the bond).