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STORY: A psychology major at Howard University, Moniest Cardell said a weight was lifted off her shoulders as the $20,000 of erased debt would mean relief for her whole family.

Given the stress debt can cause in many people, the measure means "a little bit of breathing room" according to computer science major Jie Reid.

Biology student Alexis Horton said the news "sounds really good", since she was planning to go into medical school, which means she would "rack up a lot of loans at school."

The government will cancel $10,000 in student loan debt for borrowers making less than $125,000 a year, or $250,000 for married couples. Students who received Pell Grants, low-interest federal loans to benefit lower-income college students, will have $20,000 of their debt canceled.

Canceling $10,000 in student loan debt for every borrower would cost the U.S. government $321 billion, the New York Fed calculated in April, but the income cap means the actual cost will be lower than that.

The New York Fed estimated that forgiving $10,000 per borrower would eliminate student debt for 11.8 million borrowers, or 31% of the total number. The White House said that figure will be 20 million borrowers. Nearly 90% of those borrowers will make under $75,000 a year, the White House said.