Just from a basic understanding of your problem, I see three tables:
tblUsers (userID, firstname, lastname, pw, etc)
tblAccounts (accountID, userID, bankName, serviceCharge, startBalance, address, etc.)
tblTransactions(transactionID, accountID, ammount, endingBalance)
Then each user can have multiple accounts, which in turn have multiple transactions. To get all the users accounts would be something like:
select * from tblAccounts where userID='quwiltw'
of course it'd be even simpler if the user could only have one account, but that isn't clear in your problem.