The millions of college students and parents who will borrow money from the federal government for the coming school year can plan on much lower interest rates than originally offered, as the U.S. House overwhelmingly voted 392 to 31 on Wednesday to approve a Senate plan that would allow interest rates to move with the financial markets.

The plan now goes to President Obama, who has already voiced support. House Republican leaders have deemed this a long-term solution, while many Democrats have said this plan will probably need tweaking in future years.

Undergraduates who take out federal loans for the coming school year can expect an interest rate of 3.86 percent, while the rate for graduate students will be 5.41 percent. The interest rate for PLUS loans, available to graduate students and parents of students, will be 6.41 percent. All of those rates are lower than current fixed rates of 6.8 percent for Stafford loans and 7.9 percent for PLUS loans.

These rates will apply to loans taken out since July 1 and will lock in for the lifetime of the loan. The plan calls for limits on how high the rates can go: 8.25 percent for undergraduates, 9.5 percent for graduate students and 10.5 percent for PLUS loans. If the economy improves, rates on future loans are expected to surpass the current rates. Democrats have said they hope to again take action before that happens.

This rate change has been in the works for months, prompted by the July 1 expiration of a reduced interest rate on one type of loan taken out by mostly low- and middle-income undergraduates. In May, the House approved a plan that would tie interest rates to the market but allow those rates to change over the lifetime of the loan. The plan was also expected to generate hundreds of millions of extra dollars for the government over a decade. Obama threatened to veto that plan if it advanced.

In the Senate, a bipartisan group spent weeks negotiating under ever-increasing pressure from the White House. The final compromise was approved by the Senate last week.

House GOP leaders have seized upon this issue as an opportunity to declare victory and criticize Senate Democrats. At a Wednesday morning news conference, House Speaker John A. Boehner (Ohio) said: “I congratulate the Senate for finally getting this bill over to us.” House Majority Leader Eric Cantor (Va.) said he was “very, very excited the Senate and White House decided to set politics aside and come down on the side of the students.” And House Majority Whip Kevin McCarthy (Calif.) praised his colleagues for acting “early, long before the deadline.”

House Minority Leader Nancy Pelosi (D-Calif.) has brushed off such celebration.

“The bill passed by the Senate is far superior to what happened here in the House,” Pelosi said at a news conference last week. “And if they want to take credit for calling attention to the shortcomings of the bill that were corrected in the Senate, well, they can take credit for that.”