Washington ? Maximum federal grants for low-income students would rise from $4,310 to $5,400 a year by 2011 under legislation passed Friday by the Senate.

College students also may find it easier to apply for government-backed loans under another bill the Senate is planning to consider next week. That bill would simplify the federal financial aid application process and would address conflicts of interest in the student loan industry.

The legislation that passed Friday in a 78-18 vote would cut roughly $18 billion in federal subsidies to banks that issue government-backed student loans.

Budget rules require that more than $700 million of that savings go toward reducing the federal deficit, but the rest would go to help students pay for college.

“This legislation does not cost the taxpayer. It saves the taxpayer because we are taking the money from the banks and providing it for the … students themselves,” said Sen. Edward M. Kennedy, D-Mass., chairman of the Senate education committee.

The bill does not cut interest rates on federally backed student loans to poor and middle-class students, something that is in a House-passed version of the bill. A House-Senate committee will now have to forge compromise legislation.

“I don’t think we’re going to have much trouble in the conference working through the differences,” Kennedy said.

The two bills differ in how much they would give to Pell grant recipients. Other legislation also moving through Congress, including a spending bill that passed the House on Thursday, also seeks to increase aid for Pell grant recipients.

Both the House and Senate student loan bills cap annual payments for students at a percentage of their income, which is aimed at preventing people from having to pay back more than they can afford.