The cost to attend most colleges far exceeds the amount that students are allowed to borrow under federal loan limits, according to a recent Student Loan Hero study.

The study, which compared the costs at over 1,700 U.S. colleges to federal student loan limits for undergraduates, found that students can only borrow between $5,500 to $12,500 in federal loans per academic year.

Dependent students, which can borrow the least in their first year, have an annual federal student loan limit of $5,500. Independent upperclassmen can access as much as $12,500 in direct loans per academic school year.

Only 1.55 percent of U.S. colleges have tuition and fees low enough that a dependent freshman could afford them using only these loans. Just 27 colleges have costs that dependent freshmen can cover with direct loans. For dependent upperclassmen, this amount increase to 104 colleges.

The $12,500 limit for independent upperclassmen is high enough that far more colleges pass this bar. Of the 1,744 colleges surveyed, 532 (30.5 percent) charge tuition and fees low enough that these students can pay them with direct subsidized or unsubsidized loans alone.

The study found that tuition and fees exceed federal loan limits by $11,000 or more. Even after maxing out federal student loans, the remaining costs were $11,177 up to $18,177 on average.

Independent students, especially those in their third and fourth years, were more likely to be able to borrow enough to cover college costs. Three in 10 colleges charged tuition and fees that could be covered by the $12,500 loan limit offered to these students.

The average college cost for an in-state student at a four-year public institution is $9,650.