Government-backed student debt is big business: About one in six U.S. adults has a student loan owned or guaranteed by taxpayers, and the feds pay their contracted loan servicers and debt collectors close to $2 billion annually to counsel borrowers on their repayment options and collect monthly payments on nearly $1.3 trillion of federal student debt.

The U.S. Department of Education updates the public every three months on how borrowers are faring with their federal student loans. Bloomberg crunched the numbers on where the federal student loan portfolio stood as of June 30. Here's what we found.

Fewer Borrowers Are Falling Behind

Late payments, when measured by loan balances in arrears, have fallen significantly in recent years. In 2013, a quarter of student loans were at least 31 days late. Delinquency rates have steadily dropped since then, falling to about 19 percent as of June 30.

The figure likely reflects the Obama administration's expansion of generous repayment plans that let borrowers make monthly payments based on how much they earn, rather than how much they borrowed, and improved service by federal loan contractors.

But Many Are in Distress

A closer look at the broader pool of borrowers expected to be making payments—everyone except students still in school or in mandatory six-month grace periods after leaving college—shows the improved delinquency rate isn't quite as rosy.

Less than $3 of every $5 is being repaid on time. More than 42 percent of loan balances are either delinquent, temporarily postponed, in default or in bankruptcy, or borrowers are seeking to shed the debt by convincing the feds that their disability prevents them from ever repaying what they owe.

Defaults Continue to Climb

More than 1.1 million borrowers defaulted on student loans direct from the Education Department last year.