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If Alice is trying to pay $10 to Bob and they both have accounts at the
same bank, it is relatively straightforward. Alice instructs her bank to
make the payment, and they bank then adjusts their records by
subtracting $10 from Alice’s account and adding $10 Bob’s account. In
banking jargon some banks call this a ‘book transfer’ as it is just a transfer
from one account to another and no money moves into, or out of, the
bank.
If you imagine a bank as managing a giant spreadsheet with a list of
account holders in the first column and a list of balances in another
column, the bank subtracts ten from Alice’s row and adds ten to Bob’s
row. I refer to this book transfer as a ‘-10/+10’ transaction. Because this
accounting entry has been entirely internal to the bank, we can say that
the transaction ‘settles across the bank’s books’ or is ‘cleared by the bank’.

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It is important to understand that the money in customer accounts is a
liability of the banks: when you log into your online banking and see
$100 in your account, this means the bank owes you $100 and should
either pay you that money on demand (via a cashier or cash machine), or
they need to pay someone else (a coffee shop, a supermarket, or your
friend) when you instruct and authorise them to do so.
So while from your point of view the money in your account is an asset,
from the bank’s point of view, the money in your account is an
outstanding liability. So the transaction on the bank’s balance sheet
(where assets and liabilities are recorded) looks more like this:

Although we don’t touch the asset side of the balance sheet for transfers
between customers of the same bank, we will need it later.

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