Being Canadian, I have no idea what an Associate's Degree is. I suspect that it's probably a 2-year Community College / Vocational / Tech Diploma sort of thing. I'll go against the grain because I like playing devil's advocate, and because I tend to be cautious / conservative in what I do.
As an undergrad, I took Intro Economics (for Engineers!) Two concepts from there seem to come to mind:
1) Sunk Costs
2) Opportunity Cost
Sunk Costs are time / money you've invested into something that you're never going to get back. It's gone, finito, non-recoverable, and shouldn't factor into your economic decision making, in order to allow you to evaluate (economic) decisions on their own merits (and maximize utility, or economic benefit), without regards to what you've already done. Basically, gussied up formulation of "Don't go chasing good money after bad"
Wasn't I going to take a contrary position? You've already spent 3 semesters taking this, why waste another semester? Because, unless you've already been accepted and are about to start classes in a few months, your possible alternatives are:
- Do nothing (vacation)
- Spend another semester finishing this degree
- Work (or work more), while biding your time
Hedging against the possibility that the physics thing might not work out, and on the assumption that an AA in business admin would get you a better job (doing business admin) than without, and lead to greater economic benefit than just working (or working more) at whatever job you have / can get, finishing off the degree (in light of the assumptions made above) is the good economic decision. It's the equivalent of passing go, and collecting $200; a fall-back plan, just in case.
That of course presumes that your utility (a.k.a. personal benefit / happiness) won't be severely hampered, and leave you extremely depressed or some such. Or that the 'vacation' won't improve that utility.
Opportunity Cost is closely related to the above. Basically, how much benefit would you get from doing the next best thing (and identifying what that next best thing, or ranking of next best things, happens to be). If you've already been accepted to Physics School, great, go for it!--It'll maximize your utility, if not necessarily your earnings potential (if you decide to go the academic route, and not go to Wall Street or some such).
If you haven't been accepted (or are guaranteed admission), and aren't starting your degree in September, then would you be working, or working more at whatever job you have / get? Would you instead be doing nothing? Would you perhaps be preparing for your SATs? (in an ideal world, you wouldn't be able to prepare for the SATs, and should get consistent results; however, we live in a non-ideal world). Would you be working through Physics textbooks and problems, and try to understand what's going on? (This might have the added benefit of telling you whether or not you want to do math / physics problems, and self-learning, or whether or not your interest in Physics is just a passing interest). Are these better (in terms of your utility) than going for a final semester?
So ultimately, good luck, don't count your chickens before they hatch, and all the best, whatever you decide. Also, thanks for letting me dig out my first-year Econ material!
