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WASHINGTON — A bipartisan group of U.S. senators reached a deal late Wednesday night on a long-term change to interest rates on all new federal student loans — an agreement that had remained elusive for months, even as pressure mounted when the rates on some new loans doubled last week.

The agreement would tie the interest rate on new student loans to market conditions, a change that both the Obama administration and Congressional Republicans sought this year. Rates, based on the yield on 10-year Treasury bills, would vary from year to year, but be fixed over the life of the loan.

Rates would be capped so they couldn't rise indefinitely if interest rates spike: undergraduate loans would be capped at 8.25 percent, and graduate loans at 9.25 percent.

The compromise would be retroactive, so students taking out loans after July 1 would get the new interest rate. 

The plan is similar to several proposals put forward earlier this year as a July 1 deadline loomed. Last week, the interest rate on new, federally subsidized student loans increased to 6.8 percent from 3.4 percent -- the result of legislation passed in 2007 that gradually lowered rates over five years but then allowed them to rebound.

The increase was scheduled to occur last year, but an election-year coalition of student groups and the Obama administration pushed Congress to pass a one-year delay. This year, President Obama proposed a long-term fix in his budget for fiscal year 2014, and Republicans in Congress pushed for a similar, market-based plan.

But the issue got bogged down in Congress, as Democrats fought for another one-year extension so they could address the issue when Congress takes up the Higher Education Act, the massive law governing federal financial aid programs.

As the July 1 deadline approached, the House of Representatives passed a bill for student loan interest rates based on market conditions, varying over the life of the loan -- which Obama vowed to veto. A bipartisan group of senators proposed a long-term, market-based change to interest rates. But the Senate's Democratic leadership continued to support a one-year extension.

Wednesday's compromise, though, included Senator Tom Harkin – the Iowa Democrat and chairman of the Senate Committee on Health, Education, Labor and Pensions, who had opposed the previous plan — as well as Senator Richard Durbin, the majority whip, indicating a shift in the leadership's position.

Final details on the interest rate are awaiting a score from the Congressional Budget Office, expected midday today. But late Wednesday night, the group agreed that all undergraduate loans would be set at the 10-year Treasury yield plus 1.8 percentage points. For graduate loans, the rate would be the 10-year yield plus 3.4 percent; for Parent PLUS loans, the 10-year yield plus 4.5 percent. 

If rates were based on Wednesday's Treasury yield, undergraduate loans issued today would have an interest rate of 4.5 percent; graduate loans, 6.1 percent; and PLUS loans, 7.2 percent. All are lower than the rates for those loans under current law. (Note: This paragraph and the previous paragraph have been updated with new information on the interest rate.)

Setting a single rate for all undergraduate loans means that subsidized loans, which go to students determined to have financial need, would no longer have lower rates than unsubsidized loans, which are available to all undergraduates regardless of need. From 2007 until last week, subsidized loans had lower interest rates. The rate for unsubsidized loans has been 6.8 percent.

If the plan passes the Senate, the House of Representatives is likely to follow suit, said a senior Republican aide familiar with the negotiations. A vote on the measure has not yet been scheduled.

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