If you want to study applied math and go into the workforce, then my point still stands, going to Princeton vs. Michigan simply doesn't matter. If you want to go to graduate school, it's unclear if it matters all that much. Princeton tends to draw the most talented young mathematicians in the world, and has for decades. Presumably if a student of that caliber went to Michigan, they would do just as well, because Michigan also has talented mathematicians who do good research and can write good letters of recommendation for graduate school.