Ms. Yost has 20 boxes of markers. She buys 420% more boxes. How many boxes will she have in all?

Ms. Yost buys 20 x 4.20 = <<20*4.20=84>>84 more boxes of markers.

Thus, she will have a total of 20 + 84 = <<20+84=104>>104 boxes of markers. Answer: \boxed{104}.