An Etymological Dictionary of the German Language/Annotated/Kost
Kost (1.), feminine, ‘cost,’ from Middle High German koste kost, feminine and masculine, ‘value, price, expense,’ even in Old High German kosta, feminine; borrowed in the Old High German period from Middle Latin costus, masculine, costa, feminine (compare Italian costo, masculine, French coût, masculine, Spanish costa, feminine; ultimate source Latin constare, ‘to come to, cost’). From Romance are derived Middle English costen, English to cost, whence Scandinavian kosta, ‘to cost.’
Kost (2.), feminine (in the 16th century also masculine), ‘board,’ from Middle High German koste, kost, feminine, ‘living, food, victuals’; compare Scandinavian kostr, masculine, ‘victuals, provisions.’ In Scandinavian as in the German word, the meanings of (1) and (2) overlap; at all events (2) is a later development of (1). We must certainly assume that the Scandinavian loan-word kostr, ‘expense, victuals,’ was confused with an Old Teutonic word which would be most closely connected with Gothic kustus, masculine, ‘trial, proof,’ and gakusts, ‘test’; Old Icelandic kostr, masculine, ‘choice, condition, circumstances.’ With regard to these nouns see kiesen.