Government officials are trying to rein in increasingly popular federal programs that forgive some student debt, amid rising concerns over the plans' costs and the possibility they could encourage colleges to push tuition even higher.

Enrollment in the plans—which allow students to rack up big debts and then forgive the unpaid balance after a set period—has surged nearly 40% in just six months, to include at least 1.3 million Americans owing around $72 billion, U.S. Education Department records show.

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