The bulk of colleges are unaffordable for most families, even taking financial aid and student work into account.

That’s according to an analysis published Thursday by the Institute for Higher Education Policy, a nonprofit focused on equity in higher education. The study took 10 fictional students with incomes ranging from $2,706 for a student living independently from his parents to $162,995 for a student living with her family and calculated whether they could afford the net price — tuition minus any grant and scholarship aid — at more than 2,000 schools.

What did they find? Even a student from a family earning more than $100,000 a year could only afford 41% of the schools. Students from poorer backgrounds couldn’t afford more than 90% of the colleges. The analysis defined affordability as being able to pay for college through a combination of savings — 10% of discretionary income for 10 years leading up to college — and earnings from a student working 10 hours a week.

“What we found is a pretty bleak picture of the state of college affordability,” said Mamie Voight, the vice president of policy research at IHEP and one of the authors of the report. “There’s a huge disparity there in terms of high-income students having a world of opportunity available to them and then low-income students having limited options on the table.”

Low-income students can’t afford more than 90% of colleges, according to IHEP’s analysis. IHEP

The findings illustrate how the rising cost of college has impacted families of varying incomes. Over the past several decades, declining state funding for public colleges has shifted the cost burden onto students and families, putting a four-year public college degree or even a community college education out of reach. The latest example of that trend played out on Wednesday when the board of trustees at the California State university system — the biggest public university system in the country — voted to raise tuition 5% amid declining state funding.

Some schools and policy makers have taken a stab at trying to make college more affordable, but often those efforts wind up benefiting very few low-income students. Elite universities, like Stanford, cover the tuition for students coming from families earning $125,000 a year or less, but they tend to education a small share of the low-income students going to college.

Policy makers in states like New York have also proposed making public college free for students from families earning $125,000 or less, but the structure of that proposal means that it largely benefits middle-class instead of poor students, the study notes. The plan uses what is called a “last dollar” model, which means it kicks in to fund the remainder of the cost of tuition after other state and federal grants are taken into account. Since most poor students already have their tuition covered by state and federal grants, these kinds of programs provide them with little extra money then what’s already available.

“The free tuition proposal does not actually invest any additional funding in that student,” Voight said. “What it does do is devote more resources to high income students who can already afford college.”

Supporters of these proposals say that providing just a promise of free college does more to help low-income students get to school than our current financial aid system, which requires students to navigate a sometimes complicated set of steps to prove their eligible for funding. But Voight said she’d like to see more free college proposals that target funds to low-income students and provide them with the funds necessary to cover the other costs associated with attending college, like room and board.

“We think there are some real equity issues at play,” she said.