WASHINGTON — A bill that would give college students better loan rates immediately is finally on its way to President Barack Obama.

The House voted 392-31 Wednesday in favor of a Senate deal to lower the interest rates on federal Stafford loans by tying them to the 10-year Treasury note. The plan is in some ways similar to a previous House version, but would lock the rate through the life of the loan rather than make it variable as previously proposed by the GOP.

Under the new deal, undergraduate borrowers this fall would pay roughly 3.9 percent interest rates, while graduate students would pay 5.4 percent and parents 6.4 percent. It also would set caps on the loans – 8.25 percent for undergraduates, 9.5 percent for graduates and 10.5 percent for parents.

The current rate for undergraduate is 6.8 percent after the doubling on July 1.

“After many weeks of delay, I’m pleased we finally have a bipartisan agreement to address the student loan interest rates problem. My colleagues and I have been fighting for months for long-term market-base solution that serves students and taxpayers, and the legislation before us today will do just that,” said Rep. John Kline, the chairman of the House Committee on Education and the Workforce.

House passage came after one last round of congressional finger pointing. While Kline emphasized that the new bill is almost identical to the House’s earlier plan, the committee’s top Democrat, Rep. George Miller, argued that it is not and is “worth the wait.”

Miller brought a chart showing that under the Senate bill, a freshman entering college this year would pay approximately $11,400 of interest for five years of loans with the maximum amounts. The individual would have paid around $16,500 under the House’s previous bill.

“It would have subjected students to a bait-and-switch scheme. It offers students teaser rates that balloon annually, leaving students … deeper in debt and guessing what they will owe,” Miller, D-Calif., said.

The White House said the bill would save 11 million borrowers an average of $1,500 each, and Obama said he wants to sign it into law.

Amid concerns that the market will push the rates high, the Congressional Budget Office projected that they would not exceed 7 percent for at least five years.

Some student loan experts, however, worried that the rates will start to climb quickly as early as 2015.

“The root problem is that the cost of education is so high,” said Heather Jarvis, a North Carolina-based student loan expert. “The current system of financing higher education, which is dependent on student loans, is not serving the needs of low-income students and families as it had been hoped.”

Recent research by College Board showed the number of Stafford loan borrowers almost doubled in the past decade to nearly 10.5 million in the 2011-12 school year.

Jarvis called for more government investment in higher education to ensure larger access to grants and scholarships, arguing that those funds are not helping the most needy students.

“We’ve seen some trends towards grant and scholarship aid being directed for so called merit-based scholarships to compete for certain kinds of high-performing students rather than distributed based on need of the students and families,” she said.