A finance company is a business which lends money to people and charges them interest while they pay it back.
[business]
finance company in British English
or finance house
noun
an enterprise engaged in the loan of money against collateral or speculatively to manufacturers and retailers, esp one specializing in the financing of hire-purchase contracts
finance company in American English
US
a company specializing in the lending of money to consumers, the purchasing of accounts receivable, and the extension of credit to businesses