WASHINGTON — More than 3,000 former Corinthian College students will have their college loans erased, the first wave of debt relief tied to the collapse of the for-profit higher education chain. The potential cost to taxpayers if all Corinthian students seek relief: $3.2 billion.

So far, almost 12,000 students have asked the federal government to discharge their college loan debt, asserting that their school either closed or lied to them about job prospects, according to a report released Thursday by the Education Department.

About 3,100 closed-school claims have so far been approved – totaling about $40 million in student loans, the department said.

While unprecedented, the figures represent just a fraction of the students who might qualify for debt relief.

Education Undersecretary Ted Mitchell told reporters in a press call that processing remaining claims will take some time.

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