Good luck.
There are various kinds of "student" loans. Some are federal--yes, there are different types--and the banks aren't involved. Some are to parents but are still federal with no bank involvement. Some are private with banks involved. Each type and class has its own interest rate and way of determining it, its own payback schedule, etc.
http://en.wikipedia.org/wiki/Student_loans_in_the_United_States gives a good overview, but don't take its word for details.
LIBOR doesn't figure in. The current scheme in Congress would tie some (most? all?) of the federal loans to the 10-year T-bill rate. Right now that's lower than normal because of QE.
http://thehill.com/blogs/congress-blog/economy-a-budget/313339-senate-student-loan-bill-lets-students-down
Notice that when they say "student" they almost always mean "undergraduate student". Professional students (law, med, dental, vet) students tend to get almost no funding so they have very high loan debts although they're only in school for 3-4 years after their bachelors. STEM grad students tend to get pretty good funding, so they have fairly low loan debts. Humanities and social science students tend to have high loan debts because while they get some funding they typically are in grad school for 6 years or more
If you want to look at the current law, Thomas is the go-to place.
http://thomas.loc.gov/home/thomas.php
You'll have to figure out the search terms yourself. It was in 2010, if I'm not mistaken, and the weird thing about the student loan law was that the change officially netted no net savings to the student loan program. All the student loan savings (whatever you want to call them) were credited to the health-care law as part of it's "not contributing to the deficit" PR.