WASHINGTON—The federal government is on track to forgive at least $108 billion in student debt in coming years, according to a report that for the first time projects the full cost of plans that tie borrowers’ payments to their earnings.

The report, to be released on Wednesday by the Government Accountability Office, shows the Obama administration’s main strategy for helping student-loan borrowers is proving far more costly than previously thought. The report also presents a scathing review of the Education Department’s accounting methods, which have understated the costs of its various debt-relief plans by tens of billions of dollars.