Money deposited with a bank becomes a liability of the bank, because the bank has an obligation to pay the depositor the money deposited; usually on demand. The money deposited is an asset for the depositor; but this asset will not be recorded by the bank because it is not the bank's asset. If the depositor maintains accounting records separate and apart from the bank account maintained by the bank, only then will the asset be recorded. A debit increases an asset; and a credit decreases an asset. A debit decreases a liability; and credit increases a liability.
When a bank receives a deposit it credits a liability account called "deposits" and credits the depositor's bank account for the same amount (the bank's "deposits" account is the sum of all of the amounts credited to all of its customer's individual bank accounts). A deposit received by a bank is credited because the bank's liability to its customer, the depositor, increases. When a bank informs its depositor that it has debited the depositor's bank account, it means that the depositor's bank account has been decreased by the amount debited.
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