I know PayPal "Buy-in-4" has no interest or late fees in its terms. So in that regard, it really is a 0-interest loan, paid in 4 installments. I haven't looked into Klarna, but there's an NPR Planet Money podcast about these types of schemes. The profits are made up by the fact that demand increases compared to credit cards (many are ineligible for credit cards, or don't use them for whichever reason), and that the merchant is charged a higher rate by the BNPL company.