Sen. Tom Harkin, the Iowa Democrat who chairs the Senate's Education Committee, returns to the chamber at the Capitol in Washington, Tuesday, July 16, 2013. As a bipartisan group of senators inched closer Wednesday to a compromise that would reduce interest rates on student loans before classes resume, Harkin insists that the caps on interest rates were still too high. The U.S. Capitol is seen in Washington, Sunday night, June 23, 2013. WASHINGTON (AP) - A bipartisan compromise on student loans promises better deals for students and parents over the next few years but could spell higher rates as the economy improves. The Senate deal pegs the interest rates on new loans to the financial markets and was expected to come to a vote next week, well before students returning to campus this fall had to sign their loan agreements. 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. The compromise heads off the doubling of rates on some students loans, which would cost students an extra $2,600. "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." 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," Harkin said. It's not the Ten Commandments, for God's sake. 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. As part of the compromise, Democrats won a protection for students that capped 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. Using Congressional Budget Office estimates, rates would not reach those limits in the next 10 years. Lawmakers engaged in 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. On Wednesday, the Consumer Financial Protection Bureau estimated outstanding student debt at $1.2 trillion - up 20 percent in just two years. Student loans are now the largest form of consumer debt behind mortgages. The rapid growth in debt is raising alarm among experts, and there is growing evidence student debt is weighing down the economy - for instance, by delaying the ability of young graduates to buy homes. The increase follows the jump in the cost of higher education. The tuition sticker price at public four-year colleges is up 27 percent beyond overall inflation over the last five years, according to the latest figures from the College Board. This past year it rose nearly 5 percent to an average of $8,655 nationwide. Only about one-third of full-time students pay that published price, and the average net price - what the average student does pay after financial aid - is just $2,910. But net prices have been rising, too, and tuition is just part of the cost of college. Including room and board, the average sticker price at public colleges is now $17,860, and students pay on average $12,110. At private four-year colleges, the average full tuition price is now just under $40,000, with the average student paying $23,840. The bipartisan student loan compromise 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. 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 House Committee on Education and the Workforce. 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. Associated Press Higher Education Writer Justin Pope in Ann Arbor, Mich., contributed to this report.