Finance
late Middle English: from Old French, from finer ‘make an end, settle a debt’, from fin ‘end’ (see fine2). The original sense was ‘payment of a debt, compensation, or ransom’; later ‘taxation, revenue’. Current senses date from the 18th century, and reflect sense development in French.
wiktionary
From Middle English finaunce, from Anglo-Norman, Middle French finance, from finer(“to pay ransom”) (whence also English fine(“to pay a penalty”)), from fin(“end”), from Latin fīnis. [1] [2]
Original English sense c. 1400 was “ending”. Sense of “ending/satisfying a debt” came from French influence: in sense of “ransom” mid 15th century, in sense of “taxation” late 15th century. In sense of “manage money” first recorded 1770. [1]
etymonline
finance (n.)
c. 1400, "an end, settlement, retribution," from Old French finance "end, ending; pardon, remission; payment, expense; settlement of a debt" (13c.), noun of action from finer "to end, settle a dispute or debt," from fin (see fine (n.)). Compare Medieval Latin finis "a payment in settlement, fine or tax."
The notion is of "ending" (by satisfying) something that is due (compare Greek telos "end;" plural tele "services due, dues exacted by the state, financial means"). The French senses gradually were brought into English: "ransom" (mid-15c.), "taxation" (late 15c.); the sense of "management of money, science of monetary business" first recorded in English 1770.
finance (v.)
late 15c., "to ransom" (obsolete), from finance (n.). Sense of "to manage money" is recorded from 1827; that of "to furnish with money" is from 1866. Related: Financed; financing.