late 14c., pensioun, "payment for services," especially "a regular reward or annual payment out of a will or benefice" (early 14c., in Anglo-Latin), from Old French pension "payment, rent" (13c.) and directly from Latin pensionem (nominative pensio) "a payment, installment, rent," from past-participle stem of pendere "to hang, cause to hang; weigh; pay" (from PIE root *(s)pen- "to draw, stretch, spin"). For the financial sense of the Latin verb, see pound (n.1).
Meaning "regular payment to a person in consideration of past service" is from 1520s, hence "periodic payment made to a person retired from service on account of age or disability" (originally especially government pay to soldiers and sailors). Meaning "boarding house, boarding school" is attested from 1640s, from a sense in French based on the meaning "money paid for board," and in English it is usually in reference to places in France or elsewhere on the Continent.