'rent' (the word behind 'rents') originates from Old French, specifically the word 'rente', where it referred to a return or yield (a payment).

'rent' came into Middle English from Old French 'rente' (from Medieval Latin 'renta'); the sense 'payment for the use of land or property' developed from these noun forms. Separately, the noun 'rent' meaning 'a tear' is historically connected to the past participle of Old English/Old Norse verbs related to 'rend' and entered English by a different route.

Initially, forms like 'rente' mainly meant 'a return, yield or income'; over time this evolved into the modern primary meaning 'a payment for the use of property.' The 'tear' sense originally reflected the past-participle form of 'rend' and has remained as a separate, older meaning.