This is a non-starter. Fancy schools don’t charge everyone rack-rate. If you’ve got good enough grades and are ‘interesting enough’, the fancy school pays most of the bill themselves.
My daughter went to Mount Holyoke College, which has a rack rate comparable to the Ivys, and we paid about as much as it would have cost to send her to the local state U. She had a heap of college credit earned during HS, a high GPA, and came from a ‘big square state’.
Obama, with a Kenyan father, sojourn in Indonesia, and so forth would have gotten Columbia to pay most of the cost of his attendance out of income on their endowment; Harvard Law probably threw a fat financial aid package his way, as well.