WASHINGTON (AP) — A bipartisan Senate compromise on student loans is heading to House, where lawmakers there already have voted to link interest rates with the financial markets.

If lawmakers can iron out the relatively small differences between the House student loan bill and the version the Senate passed Wednesday, students and their parents will find interest rates lower than the ones they faced last year.

President Barack Obama encouraged the House to vote quickly on the legislation so returning students can enjoy lower rates across the board.

"I urge the House to pass this bill so that I can sign it into law right away," Obama said in a statement.

Critics, including some in the president's Democratic caucus, said borrowing for tuition, housing and books would be less expensive this fall, but the costs could soon start climbing under the Senate bill. The compromise would be a good deal for all students through the 2015 academic year. After that, interest rates are expected to climb above where they were when students left campus in the spring, if congressional estimates prove correct.

The White House and its allies said the new loan structure would offer lower rates to 11 million borrowers immediately and save the average undergraduate $1,500 in interest charges.

The bipartisan Senate bill links interest rates to the financial markets. It is similar to the bill that already had passed the Republican-led House and is like the proposal in Obama's budget earlier this year.

Undergraduates this fall would borrow at a 3.9 percent interest rate. Graduate students would have access to loans at 5.4 percent, and parents would borrow at 6.4 percent. The rates would be locked in for that year's loan, but each year's loan could be more expensive than the last. Rates would rise as the economy picks up and it becomes more expensive for the government to borrow money.

As part of the compromise, Democrats won a protection for students by capping rates at a maximum 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.

If Congressional Budget Office estimates hold true, rates would not reach those limits in the next 10 years.

For the moment, most lawmakers were emphasizing the low costs immediately available, while a few were already looking for a fix in coming years.

"This bipartisan agreement is a victory for students, for parents and for our economy, and it is consistent with the House Republican bill passed in May," House Speaker John Boehner said in a statement.

"The House will act expeditiously," Boehner, R-Ohio, pledged.

The Republican chairman of the House Education Committee, Rep. John Kline of Minnesota, predicted "the bill's swift passage." And the top Democrat on the panel, Rep. George Miller of California, similarly urged Boehner to bring up the Senate bill and pass it quickly.

All seemed to portend lower rates for students, a reversal from less than a month ago.

Rates on new subsidized Stafford loans doubled to 6.8 percent on July 1 because Congress could not agree on a way to keep them at 3.4 percent. Without congressional action, rates would have remained at 6.8 percent — a reality most lawmakers called unacceptable.

"This permanent, market-based plan makes students' loans cheaper, simpler and more certain," said Sen. Lamar Alexander of Tennessee, the top Republican on the Senate education panel. "It ends the annual game of Congress playing politics with student loan interest rates at the expense of students planning their futures."

The measure's supporters suggested that the compromise was better than the status quo for students returning to campus for fall classes.

Sen. Tom Harkin, the Iowa Democrat who chairs the Senate education panel, said the legislation was not what he would have written had he had the final say. But he also said he recognized the need to restore the lower rates on students before they return to campus.

"It's the best that we can do," Harkin said.

Harkin added that a rewrite of the Higher Education Act this fall could include a comprehensive review of college costs and could revisit the loan rates for future classes.

The Congressional Budget Office estimated the bill as written would reduce the deficit by $715 million over the next decade. During that same time, federal loans would be a $1.4 trillion program.