Sen. Tom Harkin, D-Iowa, center, chair of the Senate Education Committee, announces Thursday to reporters that a bipartisan agreement was reached on lowering rates for government student loans.

WASHINGTON — A compromise deal on student loans that could hold down loan rates in the short term was expected to come to a vote next week, well before students returning to campus this fall have to sign their loan agreements.

While the deal could lower rates for students and parents over the next few years, it could spell higher rates as the economy improves.

The Senate deal pegs the interest rates on new loans to the financial markets. Under the deal, undergraduates this fall could borrow at a 3.9 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.

The compromise undoes the doubling of rates on some student loans that took hold on July 1, and one analysis of the Senate deal suggests incoming freshmen would save more than $3,300 in interest.

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

At the White House, spokesman Jay Carney said President Barack Obama was “glad to see that a compromise seems to be coming together.”

And 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.