The percentage of borrowers who defaulted on federal education loans within the first three years of payments rose to an average of 13.4 percent last year — 22.7 percent for those who attended for-profit colleges — according to statistics released on Friday by the Department of Education.

With tuition rising steadily, and family income falling, the number of borrowers with federally guaranteed student loans has increased by about a third in the last five years, to more than 37 million. The number of borrowers in default has risen to about 5.9 million, and together they owe a total of $76 billion on loans.

“We continue to be concerned about default rates and want to ensure that all borrowers have the tools to manage their debt,” said Education Secretary Arne Duncan. “In addition to helping borrowers, we will also hold schools accountable for ensuring their students are not saddled with unmanageable student loan debt.”

The rate of students defaulting on federal loans within two years, also released on Friday, increased to 9.1 percent, the highest level in more than a decade.