I've noticed that the Mongolian word for "new" is "шинэ" (or in traditional script, "ᠰᠢᠨᠠ"). Since final vowels are not pronouned it's spoken as "shin".
The Han character for "new", "新" is also pronounced pretty much as "shin" in Mandarin, Korean, and Japanese.
Is the Mongolian word also derived from Chinese? It seems like it ought to be core vocabulary but as its been borrowed into Korean and Japanese it seems quite possible though those other languages facilitated a greater degree of borrowing due to using the Chinese writing system.