WASHINGTON, DC - MAY 12: Graduate students sit to the right as undergraduate students sit to the left during the commencement ceremony for American University's School of International Service (Eva Russo/FOR THE WASHINGTON POST)

Jason Delisle is director of the Federal Education Budget Project at the New America Foundation. Alexander Holt is an education policy analyst at the foundation.

Since its inception, the federal student loan program has operated under an implicit contract: Students get loans to go to college at reasonable interest rates, with no previous credit history required, but when they graduate, they have to pay them back. But that agreement is shifting. This month, the Obama administration admitted that loan forgiveness under a program known as income-based repayment would cost $21.8 billion more than previously anticipated.

It would be one thing if the new costs were to benefit struggling borrowers who drop out of some predatory trade school. But too much of that increase likely would come from changes, won by the Obama administration, that boost benefits for middle- and even upper-income borrowers — with the biggest benefits reserved for those who go to graduate school.

To be clear, it’s not as though the administration was looking to create a big handout for wealthy graduate students. The changes to the program looked innocuous at the time — borrowers would be asked to pay 10 percent of their income for no more than 20 years instead of 15 percent of their income for no more than 25 years. That hardly sounds like a loan-forgiveness giveaway for the well-to-do. Congress never debated the changes, which were tucked into a giant, unrelated bill — the Affordable Care Act — just weeks after the president proposed them.

So why would this program now provide so much more in loan forgiveness and to many more borrowers than anticipated?

By cutting monthly payments by a third, the administration disproportionately increased benefits for borrowers with higher incomes. Under the new plan, low-income borrowers either still owed nothing (due to an exemption) or had their payments cut by no more than $20 per month. Borrowers earning $70,000 per year, on the other hand, saw their monthly payments fall by $174.

And while both groups of borrowers now pay for five fewer years before having their debt forgiven, that change disproportionately helps higher-income borrowers more because low-income borrowers, by definition, would pay little during those last five years.

Still, even 10 percent of income for 20 years sounds like it should be enough money to pay back a student loan. The problem is that almost no one, not even wealthy borrowers with graduate degrees, pays anything close to that rate.

Take a hypothetical law school graduate, Robert, who graduates with $150,000 in debt (the average for a law school student with loans) and lands a job making $70,000 a year. Let’s say Robert has a wife who earns $80,000 and one child. His monthly payment would be $238 under income-based repayment. If that seems too low to be 10 percent of his income, that’s because it is.

Robert’s payment would be calculated not from his total income but rather his adjusted gross income of $59,500. After that, he would subtract another $30,900, which is the cost-of-living exemption for himself, his wife and his child under income-based repayment. Though his wife earns a higher income than he does, none of that is counted because they file their income taxes separately.

So, Robert’s payment would actually be calculated off only a $28,600 income. He wouldn’t make loan payments equal to 10 percent of his total household income of $150,000; he would pay only 1.9 percent. (More information on this calculation is online at EdCentral.org.) In fact, he would make interest-only payments for 20 years and then have all of what he borrowed forgiven. (And, just to be clear, our projections assume that Robert receives annual raises of 4 percent and, eventually, a big promotion that brings his salary to $150,000 in year 10 of his repayment plan.) Under the old income-based repayment parameters, he would have fully repaid the loan.

Wealthy graduate students, not undergraduates, will reap a larger share of the loan-forgiveness benefits under this program because they can borrow a lot more. The government limits how much undergraduates can borrow to as little as $5,500 a year and cuts them off after $31,000 in total. Graduate students, on the other hand, can take out federal loans for the entire cost of their educations with no annual or lifetime limit. Loans to grad students are already the fastest-growing category of federal student borrowing, the Education Department reports, and of those who take out more than $20,500 per year, half are repaying through the income-based program.

With large loan-forgiveness benefits going to graduate students earning decent incomes, the Obama administration has managed to turn the student loan system upside down. Borrowers with graduate and professional degrees should be the last people the government subsidizes — they do have high debt levels, but they also have higher incomes and undergraduate degrees to fall back on. They are also far less likely to be unemployed than just about any other group.

It’s curious that an administration so focused on everyone paying their fair share created a program that will provide billions of dollars in windfall benefits to the most elite, highly educated segment of society.