FAFSA Says How Much You Can Pay for College. It’s Often Wrong.

(Families earning less than $26,000 a year can qualify for an “automatic zero” E.F.C., if they meet certain requirements.)

The formula also considers parents’ and students’ assets — and some allowances have actually become less generous over the years. Retirement savings and home equity are excluded from the federal formula, but the amount of other savings that parents can shield has plummeted over the past decade.

Take, for example, a 48-year-old parent, the median age of a person with college-age children: That parent was able to shelter $52,400 from the formula in 2009-10; now, the parent can shield only $6,000. Mr. Kantrowitz said that meant a parent with at least $52,000 saved would have an E.F.C. that is about $2,600 higher now than a decade ago.

House Democrats proposed several tweaks to the need-analysis formula in a giant bill introduced last month, which would update the Higher Education Act of 1965 for the first time in a decade. The bill would enable more families to qualify for an E.F.C. of zero by increasing the income threshold to $37,000 from $26,000.

The bill would also shield more of a student’s income from the formula, according to aides for Representative Robert C. Scott, a Virginia Democrat and chairman of the House Committee on Education and Labor. But parents with dependent children wouldn’t receive anything extra when it came to sheltering income.

Adjusting the federal formula, however, goes only so far. Even if families’ expected contributions decrease, the gulf between that figure and the cost of attendance will only widen.

“It will not be enough to just get the formula right,” said Jessica L. Thompson, director of policy and planning for the Institute for College Access & Success, a nonprofit advocacy group. “To truly bring college costs within realistic reach will require much broader federal investments in financial aid and in public colleges.”

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