When the banks lends me money my demand deposits end up in his liabilities and my loan is on his assets. Lets say I paid that money to somebody who has an account at another bank. Lets ignore how the two banks settle that and just focus on that the bank has no liabilities to me and still has my loan on his assets. My employer pays me a salary via a bank transfer in my bank. No changes to my banks net liabilities - they just swapped owners. Now I make the loan payment. Does the bank just simply destroy my demand deposits? What happens to his asset side when I make that payment? What happens eventually to the loan on the banks assets when I finish paying my loan?
If you make a payment of \$X, then:
- loan balance (bank asset) goes down by \$X, and
- deposit balance (bank liability) goes down by \$X.
I.e., the bank balance sheet shrinks (as do money aggregates that include bank deposits).
The bank may have held a loan loss provision against the loan, and so the loan may have been carried on the balance sheet at less than \$X. For example, a bank might think there is an expected loss rate on this loan of 2%, so the bank would have a provision of .02*\$X. The loan would be carried on the balance sheet at a value of .98X, not X. The creation of this provision generates a loss, causing a corresponding reduction of equity. (Note: how this is accounted for probably depends on the jurisdiction.) Note that there are no transactions associated with this loss, so it is a non-cash loss.
Since you paid off the loan in full, the provisioned loss did not materialise, and so it would be reversed. The value of the loan would be written up to \$X before cancellation. This would generate a non-cash profit, as equity would rise by the amount of the reversal of the loss provision.
In the comments, it was asked how banks make money on loans. They make money off the interest payments, which are supposed to be higher than the interest costs of the bank.