My chances of getting into a top university?

<p>A little bit about me...</p>

<p>I didn't take high school very seriously. I was more concerned with getting it over with then enjoying the experience and getting good grades. In my freshman and sophmore year I had a 2.3 GPA. I transfered halfway through my sophmore year to a public charter school (an independant study program where you teach yourself and just come in 2x a week to take tests) and I raised my GPA up to a 3.4 and graduated early when I was only 16. I never took the SATs, just the high school exit exam. I never had ambitions or aspirations to be something great. My family has never had much money so I never thought in my wildest dreams that I would be able to go to a good university because we couldn't afford it and I would never get a scholarship with my lacking academic record in high school.</p>

<p>I started community college last year when I was 17 and my outlook on life and confidence in myself has completely changed. I have become more motivated and my work ethic has improved. I currently have a 3.9 GPA and I'm in the Honors program. I'm an applied math/finance major. My dream is to become an actuary. I have volunteered for the past 3 years at a non-profit food bank and a no-kill cat rescue. This isn't related to my major but both causes are really meaningful to me.</p>

<p>My question is what are my chances of getting into a good university? I currently live in San Diego, CA. At first I thought I wanted to go to UCSD but they only have a joint economics/math major and I'm more interested in finance than economics. I really want to transfer to a university on the East coast because I want to live somewhere new and the universities there are so highly regarded and beautiful. Also, there are more opportunities for actuaries in that area. I would be so happy if I had the opportunity to go to a university like William & Mary, U-Penn, UNC Chapel Hill, etc...</p>

<p>I know they don't accept many transfers from community colleges so do I even have a shot? Or should I settle with UCSD even though it's not my "dream school"?</p>