<p>That totally narrows down your college list. If you’re aiming for top 20 and you can pay ~10k, you’ll be aiming mostly at the need-blind colleges. MIT, Princeton, Dartmouth, Harvard, etc.
Frankly, admission to those schools is very competitive. MIT, for example, admits about 3% of international applicants. No one has a sure chance of being admitted to those schools. Applying only to the top 20 and asking for 80% aid is a HUGE risk. I would not recommend it.
What people normally do is go to a tier 2/3 university that will offer them aid (about rank 70 and up). They can then transfer, if they want to, to a better university.</p>