An Etymological Dictionary of the German Language/Miete
Miete, f., ‘pay, hire, rent,’ from MidHG. miete, OHG. mieta, miata, earlier méta, f., ‘payment, wages'; the orig. form is preserved by Goth. mizdô, ‘reward,’ the z of which, however, by the lengthening of the ĭ to ê has been lost in Teut.; OHG. mêta, OSax. méda, AS. méd (once with the normal change of s into r, meord), E. meed. Goth. mizdô, from pre-Teut. mizdhdâ, is primit. allied to Gr. μσθός, ‘wages, hire,’ OSlov. mǐzda, f., ‘wages,’ Zend mîžda, n., ‘wages,’ OInd. mîdhá (for miždhá), ‘contest, match, booty’ (orig. sense probably ‘prize,’ by inference from the Sans. adj. mîdhvás, ‘distributing lavishly’). Hence the primit. Aryan form of the cognates is mizdho-, mizdhâ-, orig. meaning ‘wages, prize.’