Etymology
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Words related to interest

inter- 
word-forming element used freely in English, "between, among, during," from Latin inter (prep., adv.) "among, between, betwixt, in the midst of" (also used extensively as a prefix), from PIE *enter "between, among" (source also of Sanskrit antar, Old Persian antar "among, between," Greek entera (plural) "intestines," Old Irish eter, Old Welsh ithr "among, between," Gothic undar, Old English under "under"), a comparative of root *en "in."

A living prefix in English from 15c. and used with Germanic as well as Latinate words. Spelled entre- in French; most words borrowed into English in that form were re-spelled 16c. to conform with Latin except entertain, enterprise. In Latin, spelling shifted to intel- before -l-, hence intelligence, etc.
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*es- 

Proto-Indo-European root meaning "to be."

It forms all or part of: absence; absent; am; Bodhisattva; entity; essence; essential; essive; eu-; eucalyptus; Eucharist; Euclidean; Eudora; Eugene; eugenics; eulogy; Eunice; euphemism; euphoria; euthanasia; homoiousian; improve; interest; is; onto-; Parousia; present (adj.) "existing at the time;" present (n.2) "what is offered or given as a gift;" proud; quintessence; represent; satyagraha; sin; sooth; soothe; suttee; swastika; yes.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit asmi, Hittite eimi, Greek esti-, Latin est, Old Church Slavonic jesmi, Lithuanian esmi, Gothic imi, Old English eom, German ist.

disinterest (n.)

"impartiality," 1650s, from dis- "opposite of" + interest (n.).

self-interest (n.)

"regard to or pursuit of private interest, advantage to oneself," 1640s, from self- + interest (n.). Especially "selfishness, pursuit of egotistical interests to the exclusion of regard for others." Related: Self-interested, "characterized by self-interest" (1650s); self-interestedness.

[Self-interest] is a doctrine not very lofty, but clear and sure. It does not seek to attain great objects; but it attains those it aims for without too much effort. ... [It] does not produce great devotion; but it suggests little sacrifices each day; by itself it cannot make a man virtuous; but it forms a multitude of citizens who are regulated, temperate, moderate, farsighted, masters of themselves; and if it does not lead directly to virtue through the will, it brings them near to it insensibly through habits. [Alexis de Tocqueville, "Democracy in America"]
interested (adj.)
1660s, "characterized by concern or sympathy," past-participle adjective from interest (v.). From 1828 as "having an interest or stake (in something);" sense "motivated by self-interest" (1705) is perhaps a back-formation from disinterested. Related: Interestedness.
interesting (adj.)
1711, "that concerns, important" (archaic), present-participle adjective from interest (v.). Meaning "engaging the attention, so as to excite interest" is from 1751. Related: Interestingly. Euphemistic phrase interesting condition, etc., "pregnant" is from 1748.
uninterested (adj.)
1640s, "unbiased," from un- (1) "not" + past participle of interest (v.). It later meant "disinterested" (1660s); sense of "unconcerned, indifferent" is recorded from 1771. This is the correct word for what often is miscalled disinterested.