WASHINGTON — Senators are ready to offer students a better deal on their college loans this fall, but future classes could see higher interest rates.

The Senate could vote as early as today on a bipartisan compromise that heads off a costly increase for returning students. The compromise could be a good deal for students through the 2015 academic year, but then interest rates are expected to climb above where they were when students left campus this spring.

Under the deal, all undergraduates this fall would borrow at 3.85 percent interest rates. Graduate students would have access to loans at 5.4 percent and parents would be able to borrow at 6.4 percent. Those rates would climb as the economy improves and it becomes more expensive for the government to borrow money.

Undergraduates last year borrowed at 3.4 percent or 6.8 percent, depending on their financial need. Graduate students had access to federal loans at 6.8 percent and parents borrowed at 7.9 percent.

The interest rates would be linked to the financial markets, but Democrats won a protection for students that rates would never climb higher than 8.25 percent for undergraduates. Graduate students would not pay rates higher than 9.5 percent and parents’ rates would top out at 10.5 percent.

The bipartisan agreement is expected to be the final in a string of efforts that have emerged from near constant work to undo a rate hike that took hold for subsidized Stafford loans on July 1. Rates for new subsidized Stafford loans doubled from 3.4 percent to 6.8 percent, adding roughly $2,600 to students’ education costs. Lawmakers from both parties called the increase senseless but differed on how to restore the lower rates.