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.

Senate Budget Committee Chairman Mike Enzi (R., Wyo.) ordered the report last year amid a sharp increase in enrollment in income-driven repayment plans, which the Obama administration has heavily promoted to help borrowers avoid default. The most generous version caps a borrower’s monthly payment at 10% of discretionary income, which is defined as any earnings above 150% of the poverty level.

That formula typically reduces monthly payments of borrowers by hundreds of dollars. Any remaining balance is then forgiven after 10 or 20 years, depending on whether the borrower works in the public or private sector.

Congress approved the plans in the 1990s and 2000s, and President Barack Obama has used executive actions to extend the most-generous terms to millions of borrowers.

Enrollment in the plans has more than tripled in the past three years to 5.3 million borrowers as of June, or 24% of all former students who borrowed directly from the government and are now required to be making payments. They collectively owe $355 billion.

The GAO estimates that $137 billion of that figure won’t be repaid. Most of it—$108 billion—will be forgiven because of borrowers fulfilling their obligations under income-driven repayment plans. The $108 billion only covers loans made through the current school year, however. The overall sum could continue to grow alongside enrollment increase.

The other $29 billion will be written off because of disability or death, the GAO projects, the only other circumstances under which the government takes a loan off its books. The government can garnish wages and Social Security checks for those in default.

Supporters say the plans offer a lifeline to borrowers who are unemployed or earning little, while the Obama administration has credited the programs for leading to a reduction in the number of new graduates defaulting on their loans. Supporters also point out that under current law, any amount forgiven would be taxed as ordinary income for private-sector workers, limiting the benefits for individuals. Public-sector workers aren’t taxed on forgiveness.

The overall government loan program—currently totaling $1.26 trillion of debt outstanding, including privately issued loans backed by the government—continues to generate a profit, though these projected revenues are dwindling as more people go into income-based repayment.

The government has a separate program, not included in the $108 billion estimate, to forgive loans to students who prove their colleges lured them to enroll by deceptive practices.

Critics, including academics across the political spectrum, say the income-based repayment program isn’t targeting the neediest borrowers and instead bestows big benefits on those who attend pricey colleges and graduate schools and earn high incomes.

Education Department data show that most borrowers with high debt balances have attended graduate school. Roughly 8 million borrowers are currently in default on their loans, most owe under $10,000, government data shows. But Wednesday’s report suggests the average balance of borrowers in income-driven repayment plans is nearly $67,000.

President Obama has called for capping how much debt an individual can have forgiven, but Congress hasn’t acted on the proposal.

While Republicans such as Sen. Enzi have criticized the debt-forgiveness plans, President-elect Donald Trump said during his campaign that he supported the idea of helping student-loan borrowers. He has proposed setting payments at 12.5% of income and forgiving balances after 15 years.

Meanwhile, the GAO report also criticizes how the Education Department has produced budget estimates for the loan program. For example, it said the department has failed to account for inflation when estimating borrowers’ future earnings. And it said the agency failed to account for further increases in enrollment in income-driven repayment plans.

“Due to growing IDR-plan popularity, improving [the Education Department’s] estimation approach is especially important,” the report says. “Until that happens, IDR-plan budget estimates will remain in question, and Congress’s ability to make informed decisions may be affected.”

The GAO said it could take 40 years to know full costs of the programs.

In a recent sign of that uncertainty, the Education Department in November reduced the projected revenue from all loans issued before the 2015 fiscal year. It reduced estimated revenues by $23.35 billion from a prior estimate because of higher-than-expected default rates, a different assumption on interest rates and growing enrollment in income-driven repayment programs.