Rutgers New Brunswick is good college to have as a nearby commutable college. However, it looks like in-state tuition and fees are about $15k, plus $1-2k books. That may be doable if your parents will pretend that your live-at-home (food and utilities) and commuting costs are $0, but would be an issue if those costs are added for the purpose of determining affordability. Of course, it could be more affordable if you earn a scholarship (if you have the option of commuting, you may not need as big a scholarship than if you did not have the commuting option).
RVCC would be about $10k cheaper than Rutgers for the first two years, but you appear to be quite advanced in several subjects, so it may not be a particularly good option from an academic standpoint (seems like if you have already completed calculus BC, you may be taking college sophomore math like multivariable calculus, linear algebra, and differential equations at RVCC during 12th grade).
An hour commute is doable, but generally considered undesirable.
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I think Rutgers would be good since with merit aid, the price would drop.
With your stats and activities, you would want to try for a top program like MIT or Caltech although it can be like a lottery given their low admissions rates. A state school might offer merit aid. Maybe try asking for recommendations where you had your research project or looking where some professors had their undergraduate education. Good luck!
So you’re middle class, won’t get financial aid but need a full-ride? Can you at least afford room and board?
I don’t think top schools like MIT give merit scholarships, just need based financial aid. Same with Ivy schools. No merit. All need based aid.
You’ll have to look a little lower to get full tuition scholarships but they do exist. If you also need room and board paid for then I think it gets tougher.
URM status will help but not sure it will get you to full-ride. Does your school have a guidance counselor?
Here’s a pretty good thread from the previous cycle. It’s long but you can get full rides. You just might have to look around.
You are competitive for any college. However, the most competitive colleges do not have much merit aid. However. some of the college which have really good physics departments also have really good scholarships for high-stats URM students
There are a few lists online for large merit scholarships out there. Do some searching online, and see which of the colleges that you like has a scholarships or has scholarships for which you would like to apply.
I would suggest NJIT as a safety. They have some very attractive merit scholarships. If you are stretching your budget for college costs, out of state travel can be an additional financial burden. Especially in times of emergency - like a pandemic.