mid-15c., "legal claim or right; a concern; a benefit, advantage, a being concerned or affected (advantageously)," from Old French interest "damage, loss, harm" (Modern French intérêt), from noun use of Latin interest "it is of importance, it makes a difference," third person singular present of interresse "to concern, make a difference, be of importance," literally "to be between," from inter "between" (see inter-) + esse "to be" (from PIE root *es- "to be"). The sense development to "profit, advantage" in French and English is not entirely clear.
The earlier Middle English word was 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 (compare German Interesse, from the same Medieval Latin source).
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." Sense of "personal or selfish consideration" is from 1620s. Meaning "business in which several people are interested" is from 1670s. Meaning "curiosity, feeling that something concerns one, appreciative or sympathetic regard" is first attested 1771. Interest group is attested from 1907; interest rate by 1868.
"cause to be interested, engage the attention of," c. 1600, earlier interesse (1560s), from the noun (see interest (n.)). Perhaps also from or influenced by interess'd, past participle of interesse.