interest (n.)
mid-15c., "legal claim or right; concern; benefit, advantage;" earlier interesse (late 14c.), from Anglo-French interesse "what one has a legal concern in," from Medieval Latin interesse "compensation for loss," noun use of Latin interresse "to concern, make a difference, be of importance," literally "to be between," from inter- "between" (see inter-) + esse "to be" (see essence).

Compare German Interesse, from the same Medieval Latin source. Form in English influenced 15c. by French interest "damage," from Latin interest "it is of importance, it makes a difference," third person singular present of interresse. Financial sense of "money paid for the use of money lent" (1520s) earlier was distinguished from usury (illegal under Church law) by being in reference to "compensation due from a defaulting debtor." Meaning "curiosity" is first attested 1771. Interest group is attested from 1907; interest rate by 1868.
interest (v.)
"to cause to be interested," c.1600, earlier interesse (1560s), from the noun (see interest (n.)). Perhaps also from or influenced by interess'd, past participle of interesse.