WASHINGTON » Senators have reached a bipartisan deal to restore lower interest rates on student borrowers. 

The breakthrough came today, one day after lawmakers huddled with President Barack Obama at the White House. Lawmakers are expected to vote as early as Thursday on the deal that would lower rates before students return to campus.

The deal would offer students lower interest rates through the 2015 academic year but then rates were expected to soar. Undergraduates could face rates as high as 8.25 percent, while graduate students would see rates as high as 9.5 percent and parents’ rates would top out at 10.5 percent.

The deal is described by Republican and Democratic aides who insist on anonymity because they are not authorized to discuss the ongoing negotiations by name.

The proposal was the latest to emerge 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 and their top aides have been tinkering with various proposal — nudging here, trimming there — trying to find a deal that avoids added red ink for students and the government alike.

The rate hike did not affect interest rates on existing student loans for undergraduate students, graduate students or parents.

Lawmakers from both parties have tried to restore subsidized Stafford loan interest rates without adding to the deficit. To accomplish that, they have been tinkering with rates on all federal direct lending programs. In most cases, they have linked rates to the financial markets; the result has been lower rates in the short-term but larger bills for future classes.

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.

Under the deal being considered, 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.

But if the economy improves as congressional economists predict, rates would climb in coming years.