President Obama's latest effort to ease repayment for student loans will benefit 2 million borrowers and cost the government $15.3 billion, according to new estimates from the administration.

The Department of Education, as detailed in a rule posted to the Federal Register website Wednesday, will expand eligibility for a program that caps federal student loan payments as a share of the borrower's income and forgives debt after a period of time.

The program, called Pay as You Earn, or PAYE, is the most generous of several income-based repayment plans available to student borrowers and was introduced by the Obama administration in 2012. The Labor Department's new rule, requested by Obama last year, expands the program retroactively for students who took out loans before 2007, as well as making other changes to eligibility criteria.

Now, those borrowers will be able to cap payments at 10 percent of their income and have remaining debts forgiven after 20 years.

Six million borrowers would become eligible for the sweetened terms under the proposed new rule, according to the Labor Department's estimates. But only 2 million are expected to enter the program.

Updating the program would cost $8.3 billion for borrowers who took out loans in between 1994 to 2015 and $7 billion for people who will take out new loans from 2016 to 2025.

PAYE and income-based repayment plans are favored by many student advocates to help graduates avoid falling behind on their debts. Repayment of college debt has become a major concern on Capitol Hill as aggregate U.S. student debt has eclipsed $1.1 trillion. Of that debt, 11.3 percent is delinquent, according to the Federal Reserve Bank of New York, a rate that has roughly doubled since before the recession.

Such plans have traditionally seen relatively low enrollment. But they have grown rapidly in popularity in the past year, nearly doubling. Just under 3 million borrowers were in PAYE or other income-driven repayment plans in the second quarter of 2015, according to the Department of Education, up from 1.6 million a year earlier.

Higher-than-expected enrollment caused the Obama administration to announce a $22 billion write-down on its federal student loans in February.

At the time, experts suggested that more credit losses could follow if PAYE gains notice and increases enrollment.

The federal government's total student loan portfolio is more than $1.1 trillion.