The Obama administration proposed Tuesday to expand the Pell grant program for college students in financial need, giving them new incentives to take a full schedule of courses year-round in an effort to boost graduation rates.

Full-time students who qualify would be able to receive the grants three semesters a year, instead of two, under the proposal. The so-called year-round Pell, which had been eliminated in 2011 through a federal budget cut, would enable students to enroll during the summer. The administration estimated that the proposal would help nearly 700,000 students in the coming year, providing them with an additional $1,915 on average to pay college bills.

In addition, the administration proposed an incentive for students to “stay on track or accelerate progress” by raising the maximum Pell award $300 for those who take 15 or more credits per semester in a school year. The current maximum annual award, depending on financial need and cost of school, is $5,775. Officials said this proposal would benefit an estimated 2.3 million students. Typically, a bachelor’s degree requires amassing 120 credits over four years.

Getting the proposals through the Republican-controlled Congress would be a tall order. The administration said the measures, if approved, would expand Pell grants by $2 billion in the next fiscal year. There was no estimate available on how much the proposals would cost the government over 10 years.

The government spends about $30 billion a year on the grants, which have been a cornerstone of federal education policy for more than 40 years. Recipients do not have to pay them back. They provide access to college for millions of students in financial need.

“We look forward to working with Congress to make these proposals a reality,” said Acting Education Secretary John B. King Jr., speaking with reporters by telephone from Orlando, Fla.

Ted Mitchell, under secretary of education, said one college student in Florida told officials Tuesday that money is an overriding concern for students.  “That resonated with the group,” Mitchell said, “and I know it resonates with students around the country.”

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