I would not worry too much about this. Most schools will want you to spend most of the "extra cash" you have on tuition before they will provide you grants. This is reasonable when you consider that, usually, all applicants are treated equally and that you'll be walking in the door a little richer then some other applicants.
Depending on the school, you may be able to "hide" any extra money you have in a house or some types of investment. Of the few schools I applied to last cycle, it semed that where as it was possible to hide cash in accets at public schools, the private schools wanted to see everything.