investing with student loans

[kdotsky]

I have about 20k in student loan debt with an interest rate of about 7%. Payments and capitalization start this summer, when I will also be starting my first full time job. I just discovered that the interest payments will not be tax deductable due to my income level.

I have about 20k saved up right now. I could just pay off all the student loan debt. However, I also could put the 20k in an agressive portfolio. Assuming the investments make 10%+, I should theoretically take as long as possible to pay off the student loans while that 20k makes a few more percent than the interest accumulating on the loan.

Is this reasonable? What practical factors might make this a bad idea?

Thanks.