But it also generates your expected family contribution or E.F.C. – A number that can easily be misleading. It is frequently higher than many households can afford, and yet in many cases, as with the Phipps family, it is still not enough.

"For a long time, there was this growing gap between the formula of needs analysis and the precise representation of a student's and his family's solvency," said Justin Draeger, president of the National Association of Student Financial Aid Administrators, members at nearly 3,000 schools.

The gap has widened not only due to the exponential rise in college prices, but also due to the E.F.C. Formula itself. The 36-page formula often assumes that families have far more college income than they actually have, financial aid experts said, especially in high-cost areas. The reason is based on the basic assumptions: A family of four can live on less than $ 30,000, for example, regardless of where they live.

"Students have a lot more needs than we realize," he said Eddy Conroy, deputy director at the Hope Center for Society, Higher Education and Justice at Temple University. "But the system doesn't get it right."

Universities use the E.F.C. Determining a student's financial needs – the difference between college attendance costs and expected family contributions. Then the schools come with a financial aid package. (Around 400 schools and programs, mostly private universities, also use a different formula, the so-called CSS profile, to determine institutional assistance, according to the college committee that did the calculation.)

But unless a student attends a college that promises to meet 100 percent of their needs – and the vast majority don't – students and their families are likely to pay more than the FAFSA estimates.