Jenna Johnson / The Washington Post

WASHINGTON — 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 on Wednesday overwhelmingly voted 392 to 31 to approve a Senate plan to allow interest rates to move with the market.

The plan now goes to President Barack Obama, who has already voiced support. House Republican leaders have deemed this a long-term solution, while many Democrats have said this plan will do for now but will likely 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 in coming years, rates on future loans are expected 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 press conference, Speaker John Boehner, R-Ohio, said: “I congratulate the Senate for finally getting this bill over to us.” Majority Leader Eric Cantor, R-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.”