The Washington Mentorship Program is a full pay program for which American will not give financial aid towards the costs. You have to come up with the money on your own. You and your parents either have to pay it or borrow it. I think American makes that very clear. In addition to paying for the program, you need to finish payment for room/board as American requires it that term. You’ve already made a deposit towards that. That’s just the first payment.
You need to talk to American University about your situation or you and the school are going to go through the very unpleasant experience of kicking you out for lack of payment. There are students each year at many colleges that undergo the painful process of being evicted from a school due to lack of payment. For most, it’s a matter of parents who fall behind in payments or ‘fess up they cannot pay for the school. A loan gets declined. In your case, you are going head on, knowing full well you have no way to pay the cost of the program. If you want to do this, hoping some miracle happens, as it appears you are doing, understand that you are likely to be removed unceremoniously and painfully.
American is a private school. It had no responsibilities in paying for programs someone wants. . They have declined your request to subsidize you. You want to go there, you have to pay, as most people do. It’s like shopping, you can’t just take what you want. You need to pay for it.