Graduate in three years and then apply for Ph.D. programs? This is a question that I've been pondering for a long time and badly needs advice and different perspectives. Background: I'm an international student attending a modestly reputable college in the US. I'm a rising junior majoring in math and minoring in chemistry and psychology, with a GPA of 4.0/4.0 and pending publications in computational chemistry and psychology. I'm interested in Ph.D. programs in computational neuroscience (since this is a inter-disciplinary field, mostly I will apply to math or neuroscience programs).

So here is the problem: I really want to graduate early in three years, but should I? There are four reasons supporting this decision. First, due to some poor financial choices of my parents, it is risky if I stay in college for the total four years (getting a degree in three years is surely better than no degree at all!) Secondly, there is no professor here who works in the field of computational neuroscience, and the lack of relevant research opportunity is disappointing to say the least. Third, I find myself under-challenged by the curriculum. I'm taking the maximum course load with a lot of "hard" classes, but I find myself getting nothing out of the classes besides more facts and techniques. Finally, from the limited internship opportunities and readings I've done in computational neuroscience, I know that I will enjoy immersing myself in this field.

On the other hand, I can see how graduating in three years can put me in a huge disadvantage for Ph.D. application, and this is why I'm hesitant to make the final decision. One more year means more higher-level classes to take, more time to do better research, more time to prepare for GRE general and subject tests, and more time to grow as a person in general. I feel like even though I'm one of the best student in my college, but I'm certainly far from being one of the best in the country (which means diminished probability of being accepted by one of the better programs). I just want some more time to further challenge myself before I leave the college for good.

I would really appreciate some different opinion on this matter, and I thank you for reading through this long question.
If it really is a risk that you might not graduate at all if you stay on another year, then maybe you could consider graduating early and hedging your bets. There are other ways to catch up and make yourself both more prepared and more desirable to PhD programs of your choice. For example, you could try and apply for a research position if you see any openings in labs, and either take courses simultaneously or or as someone else suggested, apply to a non PhD program first. 

Either way, if there is an academic you know you would want to work with, it doesn't hurt to write them an email and ask them if they would be willing to take someone with only three years of college and if not, what would kind of skills and strengths they might be looking for. I did this when I switched fields right after college, and I was told that though I did not have quite enough qualifications, if I managed to do x, y, z I would be considered. That's what I ended up doing while working part time and two years later I got into the program (of course if you need a visa to work that's a different story).

However, if you can manage it financially, I would probably advise staying in college the extra year, and prepping for the GRE, taking courses relevant to your field, and getting those very important recommendation letters by making an impression on your professors. Also, most colleges have the option of doing a senior thesis, and if you want to go into a research career, while not a deal breaker, writing one can be very beneficial, no matter what area you write it in. Showing that you have the ability to do independent work is always a good thing when applying for doctoral programs. And it gives you a chance to work one-on-one with your advisors and can be as challenging and fulfilling as you make it! 

Everyone is different, so you will have to decide on your own, but I'm always in favor of a little bit more rather than less time between college and grad school to be both psychologically and academically prepared. But that's just me. Good luck to you!