The English terms credit and debit seem to come from the Latin verbs credere and debere. However, it is not clear to me what forms of these verbs are behind these English words. It could be that they used to be the third person singular forms credit and debet and the second one was changed by analogy. Or perhaps they are abbreviated from creditor and debitor, both of which make sense in Latin. Do we know what exact Latin forms of these verbs are behind these two financial terms?
From French débit and crédit, which are from Latin debitum and creditum respectively.
Concerning the latter the OED writes:
Etymology: < (i) Middle French credit (French crédit ) belief, faith, trust (a1450), reputation, influence, esteem (c1470 or earlier), money lent or borrowed with an agreement as to repayment (1481), trust or confidence in a customer's ability and intention to pay at some future time (1508 in a credit on credit), confidence that someone or something inspires (1539), and its etymon (ii) Italian credito financial transaction in which payment is deferred (1353), position of a creditor, right of a creditor (a1375), belief, fact of being believed (14th cent.), reputation for solvency and probity in financial dealings, ability to obtain money, etc., on this basis (a1400), reputation, esteem (a1498), money placed at a person's disposal in the books of a bank (mid 16th cent.) < classical Latin crēditum loan or debt, in also post-classical Latin article of faith (14th cent. in a British source), use as noun of neuter past participle of crēdere to trust, to believe (see credit v.).