WASHINGTON — Senators negotiating a bipartisan deal to keep student loan rates low reached a deal on Wednesday night that could end the partisan feud on Capitol Hill that has threatened to permanently double interest rates.

Two Senate aides said that the new proposal, which had been the subject of tense negotiations since the rates doubled on July 1, would include both a cap on federal Stafford and PLUS loans and a relatively low interest rate pegged to Treasury notes. Undergraduates would pay the 10-year Treasury note rate, 2.49 percent on Wednesday, plus 2.05 percent, with a cap of 8.25 percent, to protect them from inflation. Graduate students would pay the 10-year Treasury rate plus 3.6 percent, with a cap of 9.5 percent.

Loans to parents of students would be given a rate of 4.6 percent plus the 10-year Treasury rate, with a cap of 10.5 percent.

Because the Senate proposal hews closely to the one the House approved in May, the chances for a deal that can become law have greatly improved. That may not happen until after Congress returns from its summer recess after Labor Day, and House and Senate negotiators have an opportunity to reconcile their plans.