late Middle English (originally as interess): from Anglo-Norman French interesse, from Latin interesse 'differ, be important', from inter- 'between' + esse 'be'. The -t was added partly by association with Old French interest 'damage, loss', apparently from Latin interest 'it is important'. The original sense was 'the possession of a share in or a right to something'; hence sense 4 of the noun. sense 1 of the noun and the verb arose in the 18th century sense 2 of the noun was influenced by medieval Latin interesse 'compensation for a debtor's defaulting'
Spell interest and the related word interesting with -er- in the middle.