Etymology
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federal (adj.)

1640s, as a theological term (in reference to "covenants" between God and man), from French fédéral, an adjective formed from Latin foedus (genitive foederis) "covenant, league, treaty, alliance" (from PIE *bhoid-es-, suffixed form of root *bheidh- "to trust, confide, persuade").

Secular meaning "pertaining to a covenant or treaty" (1650s) led to political sense of "formed by agreement among independent states" (1707), from use of the word in federal union "union based on a treaty" (popularized during formation of U.S.A. 1776-1787) and like phrases. Also from this period in U.S. history comes the sense "favoring the central government" (1788) and the especial use of the word (as opposed to confederate) to mean a state in which the federal authority is independent of the component parts within its legitimate sphere of action. Used from 1861 in reference to the Northern forces in the American Civil War.

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loan (n.)
late 12c., "that which is lent or owning, a thing furnished on promise of future return," also "a gift or reward from a superior, a gift of God," from Old Norse lan "loan," from Proto-Germanic *laikhwniz (source also of Old Frisian len "thing lent," Middle Dutch lene, Dutch leen "loan, fief," Old High German lehan, German Lehn "fief, feudal tenure"), originally "to let have, to leave (to someone)," from PIE *loikw-nes-, suffixed form of root *leikw- "to leave."

The Norse word also is cognate with Old English læn "gift," which according to OED did not survive into Middle English, but its derived verb lænan is the source of lend (v.). From early 15c. as "a contribution to public finances" (ostensibly voluntary but often coerced; sometimes repaid, sometimes not). As a verb, loan is attested from 1540s, perhaps earlier, and formerly was current, but it has now been supplanted in England by lend, though it survives in American English. Slang loan shark first attested 1900 (see shark (n.)).
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mortgage (v.)

"to grant (immovable property) as security for money lent or contracted to be paid," late 15c., morgagen, from mortgage (n.). Related: Mortgaged; mortgaging.

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home (v.)
1765, "to go home," from home (n.). Meaning "be guided to a destination by radio signals, etc." (of missiles, aircraft, etc.) is from 1920; it had been used earlier in reference to pigeons (1862). Related: Homed; homing. Old English had hamian "to establish in a home."
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corporation (n.)

mid-15c., corporacioun, "persons united in a body for some purpose," from such use in Anglo-Latin, from Late Latin corporationem (nominative corporatio) "assumption of a body" (used of the incarnation of Christ), noun of action from past-participle stem of Latin corporare "embody, make or fashion into a body," from corpus (genitive corporis) "body, dead body, animal body," also "a whole composed of united parts, a structure, system,community, corporation, political body, a guild" (from PIE root *kwrep- "body, form, appearance").

Meaning "legally authorized entity, artificial person created by law from a group or succession of persons" (such as municipal governments and modern business companies) is from 1610s.

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mortgage (n.)
Origin and meaning of mortgage

late 14c., morgage, "a conveyance of property on condition as security for a loan or agreement," from Old French morgage (13c.), mort gaige, literally "dead pledge" (replaced in modern French by hypothèque), from mort "dead" (see mortal (adj.)) + gage "pledge" (see wage (n.)).

So called because the deal dies either when the debt is paid or when payment fails. Old French mort is from Vulgar Latin *mortus "dead," from Latin mortuus, past participle of mori "to die" (from PIE root *mer- "to rub away, harm," also "to die" and forming words referring to death and to beings subject to death). The -t- was restored in Modern English based on Latin.

And it seemeth, that the cause why it is called mortgage is, for that it is doubtful whether the feoffor will pay at the day limited such sum or not: and if he doth not pay, then the land which is put in pledge upon condition for the payment of the money, is taken from him for ever, and so dead to him upon condition, &c. And if he doth pay the money, then the pledge is dead as to the tenant, &c. [Coke upon Littleton, 1664]
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home (n.)

Old English ham "dwelling place, house, abode, fixed residence; estate; village; region, country," from Proto-Germanic *haimaz "home" (source also of Old Frisian hem "home, village," Old Norse heimr "residence, world," heima "home," Danish hjem, Middle Dutch heem, German heim "home," Gothic haims "village"), from PIE *(t)koimo-, suffixed form of root *tkei- "to settle, dwell, be home." As an adjective from 1550s. The old Germanic sense of "village" is preserved in place names and in hamlet.

'Home' in the full range and feeling of [Modern English] home is a conception that belongs distinctively to the word home and some of its Gmc. cognates and is not covered by any single word in most of the IE languages. [Buck]

Slang phrase make (oneself) at home "become comfortable in a place one does not live" dates from 1892 (at home "at one's ease" is from 1510s). To keep the home fires burning is a song title from 1914. To be nothing to write home about "unremarkable" is from 1907. Home movie is from 1919; home computer is from 1967. Home stretch (1841) is from horse racing (see stretch (n.)). Home economics as a school course first attested 1899; the phrase itself by 1879 (as "household management" is the original literal sense of economy, the phrase is etymologically redundant).

Home as the goal in a sport or game is from 1778. Home base in baseball attested by 1856; home plate by 1867. Home team in sports is from 1869; home field "grounds belonging to the local team" is from 1802 (the 1800 citation in OED 2nd ed. print is a date typo, as it refers to baseball in Spokane Falls). Home-field advantage attested from 1955.

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loan-translation (n.)
"process by which a word or phrase is translated literally from another language, keeping its original connotation," 1931, from German Lehnübersetzung (by 1905), properly "lend-translation," from lehnen "lend" (see lend (v.)). An earlier word for it was calque.
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loan-word (n.)
"word taken untranslated from one language into another," 1860, a translation of German Lehnwort, properly "lend-word," from lehnen "lend" (see lend (v.)) + Word (see word (n.)).
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home page (n.)
also homepage, 1993, from home (n.) + page (n.1).
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