This answer is better served as a comment but I don't have enough rep.
It is not guaranteed that they 'do not accrue interest while you are a full time student'. Some student loans can capitalize the interest - before pursuing leveraged investing, be sure that your student loan is not capitalizing.
Capitalized interest is a second reason your loan may end up costing
more than the amount you originally borrowed.
Interest starts to accrue (grow) from the day your loan is disbursed
(sent to you or your school). At certain points in time—when your
separation or grace period ends, or at the end of forbearance or
deferment—your Unpaid Interest may capitalize. That means it is added
to your loan’s Current Principal. From that point, your interest will
now be calculated on this new amount. That’s capitalized interest."
If you accrue interest while you are in school – as with Direct
Unsubsidized, FFELP Unsubsidized, Direct and FFELP PLUS Loans, and
Private Loans – you will have capitalized interest if it is unpaid.
Unpaid accrued interest is added to the principal amount of your loan
after you leave school and finish any applicable grace period.
Simply put, there will be interest to be paid on both the principal of
the loan and on the interest that has already accumulated.
To minimize the effects of the capitalized interest on the amount you
will pay overall, you can pay the interest during college instead of
waiting until after graduation. That way, you start with the original
principal balance (minus any fees) when you begin repayment.