WASHINGTON — A bipartisan compromise on student loans promises better deals for students and parents over the next few years but could spell higher rates if it gets more expensive for the government to borrow money as expected.

The Senate deal shifts decisions on interest rates from the whims of Congress to the financial markets and was expected to come to a vote next week, well before students returning to campus this fall would face costs to borrow money to pay for tuition, housing and books. The deal heads off a potential doubling of rates on some students loans that would cost students an extra $2,600 if Congress did nothing.

“We have gone through weeks of negotiations and we have an agreement,” said Sen. Dick Durbin, D-Ill.

Sen. Lamar Alexander, R-Tenn., said students benefited: “For every one of them, the interest rates on their loans will be lower.”

At least for now. 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 in the spring.

Even in announcing the compromise, it was clear the negotiations were dicey.

“While this is not the agreement any of us would have written and many of us would like to have seen something quite different, I believe that we have come a very long way on reaching common ground,” Durbin told reporters.

Moments later, Democratic Sen. Tom Harkin of Iowa, chairman of the Senate Health, Education, Labor and Pension Committee, said he would revisit the whole agreement this fall, when his panel takes up a rewrite of the Higher Education Act.

“Can we change it? Sure, we can change it. It’s not the Ten Commandments, for God’s sake,” Harkin said.

Harkin did little to hide his unhappiness with the compromise but said there were few options to avoid a costly hike on students returning to campus this fall.

“Students are going to have a better deal than they would have had otherwise,” Harkin said.

Under the deal, all undergraduates this fall could borrow at a 3.85 percent interest rate. 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 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 they thought the lower rates should be restored.

The Senate was likely to vote early next week on the measure.

“We should get it done as quickly as possible,” Senate Majority Leader Harry Reid said.

Democrats had urged a one- or two-year extension of the current rates, while lawmakers plan to do a complete rewrite of the Higher Education Act in the fall to address the larger issue of college costs. Reid said he would allow members of his caucus one more attempt at the tactic but urged his colleagues to back the long-term proposal.

For his part, Harkin said he could scrap the whole bill when he takes up the Higher Education Act. As a condition for his support, he would order a Government Accountability Office review of all federal student lending programs and recommendations on how to improve them.

The proposal closely hews to what House Republicans passed earlier this year. House and Senate aides alike predicted the differences could be settled quickly.

“When we see the details, I’m hopeful we will be able to put this issue behind us,” Republican House Speaker John Boehner told reporters Thursday.

Republicans in both chambers have pushed for a link between interest rates and the financial markets. Obama included that link in his budget proposal, but Democrats balked, saying it could produce government profits on the backs of borrowers if rates continued to climb.

Leaders from both parties, however, recognized the potential to be blamed for the added costs in the 2014 elections if nothing were done.

Even House Democrats who opposed the GOP-led deal there appeared ready to go along.

“While I continue to review the details of the proposal, I’m encouraged that bipartisan efforts continue in the Senate to reverse the student loan interest rate hike. Republicans’ agreement to put a cap on student loan interest rates is a positive development,” said Rep. George Miller, the top Democrat on the Senate Committee on Education and the Workforce.

Few students had borrowed for fall classes. Students typically do not take out loans until just before they return to campus, and lawmakers have until the August recess to restore the lower rates. The students who had borrowed for summer programs since July 1 would have their rates retroactively reduced.

Lawmakers and their top aides had been tinkering with various proposals — nudging here, trimming there — trying to find a deal that avoids added red ink for students and the government alike.

The deal was estimated to reduce the deficit by $715 million over the next decade.