There was a great deal of business done by keeping accounts in 18th c. Britain and the colonies.

You would go into a shop, with the help of a clerk or storekeeper select your purchases. Those amounts would be entered into a day book, along with all the purchases of other customers done that day. Later, the merchant would transfer yours to the page in her ledger that had your account. Periodically, you'd be expected to settle your account- especially if the amount owing got to be rather large. The merchant dunning a customer for an overdue bill is a familiar figure in Hogarth's paintings, and there's also one that shows the next step. In The Arrest, a merchant has given up dunning, and has gone to a magistrate who has then handed over the task to a tipstaff, or bailiff. As soon as he touches the debtor with his staff ( which has a rolled up authorization for the arrest inside it) the tipstaff and his men can haul the unfortunate Rake off to a debtor's prison, where he'll stay until some relative comes to pay his debt. But, in this case, the Rake's being rescued ( temporarily, it turns out) by an angelic Sarah Young, who still loves him and presents a bag of money.

Demanding cash was unusual for a merchant in the mid 18th c., though apparently there was an increase in the number of businesses in England doing it later in the century. Some of it was convenience - a lot of people like farmers had seasonal earnings, not weekly paychecks. There was also a shortage of currency, especially small-value coins, to the extent that some merchants in England began making their own, a type of currency now known as Conder Tokens, for the man who first collected and wrote about them. It also could simplify things to carry accounts: in a rural setting, farmers would commonly have credits for goods they brought into a shop ( apples, honey, wool) as well as debits for supplies they needed, and money didn't always need to be handed back and forth. In western Massachusetts in 1784, there was such a shortage of currency that farmer and merchants were mostly carrying accounts and writing and trading notes, or IOU's, rather than try to find hard money. When the state government attempted to collect taxes in hard money, there was even a revolt: Shays' Rebellion.

But to buy on credit, of course the customer had to establish trust, have an account. Sometimes that could be easy- sometimes not.

Berry, H. (2002). Polite Consumption: Shopping in Eighteenth-Century England. Transactions of the Royal Historical Society, 12, 375–394. http://www.jstor.org/stable/3679353