The story
Originally referring merely to the registry of transactions (deposits, withdrawals) for a fund held by a bank, the sense came to encompass the fund being held.
Etymology from Wiktionary, CC BY-SA 4.0.
bank account
Today it means: A fund, held by a bank in a contractual arrangement between the bank and the owner of the fund, a customer of the bank, into which they can deposit and from which they can withdraw money. Full definition →