I would have two tables. Account_Balances (account_ID, account_Balance, timestamp) && Transaction_Records (payer, payee, amount, timestamp)
Then I would have three records... two updates and one insert all wrapped in a transaction to maintain the acid transaction.
"update Account_Balances set account_Balance=account_Balance-{$amount} where account_ID='{$transferee}';";
"update Account_Balances set account_Balance=account_Balance+{$amount} where account_ID='{$receiver}';";
"insert into Transaction_Records (payer, payee, amount) values ('{$transferee}','{$receiver}',{$amount});";
This assumes both accounts are at the same bank, of course. And this design is super simple meant to address your base question... I'm sure with more time and energy I could brainstorm a whole bank, but I don't have the time or the energy...