Middle English yelden, "relinquish involuntarily; submit to another's direction or rule; surrender to a foe;" from Old English gieldan (West Saxon), geldan (Anglian) "to pay, pay for; reward, render; worship, serve, sacrifice to" (class III strong verb; past tense geald, past participle golden), from Proto-Germanic *geldan "pay."
This is reconstructed to be from PIE *gheldh- "to pay," a root found only in Balto-Slavic and Germanic (and Old Church Slavonic žledo, Lithuanian geliuoti might be Germanic loan-words).
Germanic cognates include Old Saxon geldan "to be worth," Old Norse gjaldo "to repay, return," Middle Dutch ghelden, Dutch gelden "to cost, be worth, concern," Old High German geltan, German gelten "to be worth," Gothic fra-gildan "to repay, requite."
"[T]he only generally surviving senses on the Continent are 'to be worth; to be valid, to concern, apply to,' which are not represented at all in the English word" [OED, 1989].
The sense development in English comes via use of this word to translate Latin reddere, French rendre.
The sense of "produce, bear, bring forth," also "give in return for labor" is from c. 1300, later also in reference to capital invested. The intransitive sense of "give oneself up, submit, surrender (to a foe)" is from c. 1300, as is the physical sense of "give way to superior force."
Related to Middle Low German and Middle Dutch gelt, Dutch geld, German Geld "money." Related: Yielded; yielding. The old past-participle yolden, "having surrendered, submissive," produced Middle English yolden-man "prisoner of war."