An Etymological Dictionary of the German Language/Annotated/Miete
Miete, feminine, ‘pay, hire, rent,’ from Middle High German miete, Old High German mieta, miata, earlier méta, feminine, ‘payment, wages'; the original form is preserved by Gothic mizdô, ‘reward,’ the z of which, however, by the lengthening of the ĭ to ê has been lost in Teutonic; Old High German mêta, Old Saxon méda, Anglo-Saxon méd (once with the normal change of s into r, meord), English meed. Gothic mizdô, from pre-Teutonic mizdhdâ, is primitively allied to Greek μσθός, ‘wages, hire,’ Old Slovenian mǐzda, feminine, ‘wages,’ Zend mîžda, neuter, ‘wages,’ Old Indian mîdhá (for miždhá), ‘contest, match, booty’ (original sense probably ‘prize,’ by inference from the Sanscrit adjective mîdhvás, ‘distributing lavishly’). Hence the primitive Aryan form of the cognates is mizdho-, mizdhâ-, originally meaning ‘wages, prize.’