To open an account.
To enter a customer's name on your ledger for the first time. (Latin, accomputare, to reckon with.)
To keep open account
is when merchants agree to honour each other's bills of exchange.
A current account
To cast accounts.
To give the results of the debits and credits entered, balancing the two, and carrying over the surplus.
A sale for the account
in the Stock Exchange means: the sale of stock not for immediate payment, but for the fortnightly settlement. Generally this is speculative, and the broker or customer pays the difference of price between the time of purchase and time of settlement.
We will give a good account of them
—i.e. we will give them a thorough good drubbing