“There are trade-offs everywhere,” he said. “The reality is there’s not enough money for everyone you want to enroll.”

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Ms. Muse in Colorado is trying to piece together how she will pay for Lydia’s next three years at RISD, and is considering selling her house to do so. But that’s likely only to get her through two years with financial aid. Ms. Muse said her daughter considered less expensive in-state options, but a specialized art school “is more congruent with her interests in animation and illustration.”

While families may manage to fill the gap in financial aid the first year of college, tuition prices are set one year at a time, limiting the ability to plan ahead. That’s what Nancy and John Flaherty face.

Their daughter, Courtney, is a sophomore at the College of William & Mary in Virginia, which charges more than $60,000 to out-of-state students. The Flahertys’s expected family contribution was about half that, and William & Mary’s aid package fell about $5,000 short the first two years, which the couple paid for by drawing from their savings.

Now, to plan for the next two, they may tap into their home equity, take out a loan through a state program or borrow from retirement savings. The decision was made more difficult by a recent surprise: Their expected contribution for junior year jumped by $10,000 because of John’s overtime pay in the year covered by FAFSA.

How exactly that change will impact their aid remains unclear. After the first year, aid packages typically arrive just weeks before the first tuition bill comes due.