The open secret of higher education is that private colleges competing for students often slash prices for families wealthy enough to pay full tuition.

Some dangle “merit aid” to lure academic stars. Others use discounts to ensure that they enroll enough affluent students to meet their revenue targets.

Washington University in St. Louis provides grants unrelated to financial need or athletics to 14 percent of freshmen, a Washington Post analysis found. George Washington University gives them to 20 percent, and Tulane University to 37 percent. Those three are among dozens of prominent private schools that offer significant largesse to students without need.

But as prices climb past $60,000 a year at many private colleges, debate over student debt and subsidies for the affluent has led some schools to rethink how they dole out funds.

Franklin & Marshall College is a case in point. The liberal arts school here in Pennsylvania’s Amish region ended almost all merit aid a few years ago and expanded grants for those in need, launching a recruiting revolution that has drawn national attention.

List: College grants for the affluent

The share of freshmen in high need soared, while the share who pay full price shrank. Test scores of incoming students held steady. This year the school cracked the top 40 in the U.S. News & World Report ranking of liberal arts colleges, rising to 37th.

[List: College grants for the affluent]

People here avoid the word “merit” and its connotation of subsidies for the affluent. Instead, F&M President Daniel R. Porterfield talks of a “talent strategy” targeting students from all family incomes. Full charge for tuition, fees, room and board at the school is $60,799. Need-based aid, he said, “makes it possible for super-qualified kids to pursue the education they’ve earned.”

Financial aid, like selective admissions, baffles college-bound students. Fears abound of stratospheric sticker prices at private colleges. Real prices, often far lower, are maddeningly hard to pin down.

Students wonder why some schools offer merit aid and others don’t, why their “expected family contribution” varies from place to place, and why some schools require them to take out large loans and others don’t.

Michael DiAntonio III, 22, of Wildwood Crest, N.J., was a merit aid target when he was applying to college. A graduate of a private boarding school and the oldest of four brothers, he said he chose F&M, at full price, over several well-regarded colleges that offered discounts of $10,000 to $12,000 a year.

F&M’s intimate atmosphere, he said, hooked him. The school, 90 miles northeast of Washington, enrolls about 2,300 students and has a tranquil campus of red-brick buildings. It is easy to talk with professors here, students say, but hard to get an A. Students are called Dips, short for Diplomats. That’s the mascot of the 227-year-old school, named for an 18th-century Founding Father (Benjamin) and a 19th-century Supreme Court chief justice (John).

Grace Jeong, 21, of Chantilly, Va., meets with professor Danel Draguljic on Nov. 18 in Lancaster, Pa. The Franklin & Marshall senior receives need-based grants of more than $55,000 a year. (Katherine Frey/The Washington Post)

DiAntonio, a senior majoring in creative writing, works as a campus tour guide and takes other jobs to pay for books, gas and other items. He has no student loans and receives no financial aid. His father is a businessman, and his parents and grandparents pay most of his expenses. “I make sure to thank them on a frequent basis,” he said.

Students like DiAntonio are the fiscal bedrock of most private colleges. At F&M, the share of freshmen without financial need has fallen from 63 percent in 2008, when the college changed its aid policy, to 43 percent this year. College officials say the share probably can’t fall much more without busting the budget.

Expanding need-based aid

F&M has taken several steps to support the expansion of need-based aid. What it used to spend on merit aid — $1.7 million for 2007-2008 freshmen — now flows into a need-based aid fund of nearly $13 million for the latest entering class. The school also has raised tuition, added students, contained spending and launched a fundraising campaign.

In 2008, 1 of every 20 freshmen here qualified for a need-based federal Pell grant. Now the share is 1 in 5.

This pivot helped make it possible for Grace Jeong, 21, of Chantilly, Va., to come here to study public health.

Jeong, a senior, said F&M and the government provide her grants of more than $55,000 a year. She also has student loans and works 12 hours a week as a caregiver for an elderly woman. The oldest of four children in a Korean immigrant family, Jeong said her father is a chef and her mother a tailor. Their annual income is modest. She has a younger sister at private Bowdoin College in Maine. “I definitely wouldn’t be here if the financial aid wasn’t generous,” she said.

Some people assume that every dollar spent on no-need aid takes away a dollar that could have been spent on need-based aid. College officials say that is not necessarily true.

Jon Boeckenstedt, associate vice president for enrollment management and marketing at DePaul University in Chicago, said discounts for upper-income families help many colleges collect the revenue they need to help students who are less affluent. “It’s not a zero-sum game,” he said. DePaul, the nation’s largest Catholic university, reports giving an average of about $10,000 a year in no-need aid to 22 percent of freshmen. But it also gives an average need-based grant of more than $11,000 to 61 percent.

Most of the nation’s ultra-selective schools — think top 20 in the U.S. News rankings — offer few or no grants to students without need. But some use merit aid to snare top scholars.

A Post analysis of information schools reported in a survey called the Common Data Set 2013-14 found that Duke University provided scholarships worth an average of about $56,000 a year to 67 freshmen with no financial need — nearly 4 percent of the class.

“They help us enroll some of the most talented students in our applicant pool,” said Christoph Guttentag, Duke’s longtime admissions chief. The takeaway for these recipients: Goodbye, Cambridge, Mass., and Palo Alto, Calif. Hello, Durham, N.C.

Washington University’s awards to freshmen without need averaged about $10,700. GWU’s averaged about $18,300, and Tulane’s $22,400.

Merit aid is not just a private-school phenomenon. The Post review found that about 3 percent of freshmen at the University of Virginia and the College of William and Mary received aid without showing any need. About 20 percent did at the University of Maryland.

But unlike public colleges, those in the private sector are not state-funded. The vast majority rely mainly on tuition revenue to cover costs. That raises the stakes for practically every pricing decision for every admitted student among colleges below the top 20.

“A lot of them are basically trying to get students in the doors,” said Stephen Burd, an analyst at the New America Foundation. “And if they can get wealthier students, that’s even better.”

A tuition price war

In some regions, colleges are engaging in what looks like a price war. In Ohio, the Post analysis found, public Miami University and Ohio State University both gave no-need grants or scholarships to about 30 percent of freshmen. The rate was 25 percent or higher at the private College of Wooster, Oberlin College, Case Western Reserve University and Denison University — a sign of an intense scramble for money and talent in that state.

Here in Pennsylvania, the scrum for enrollment is also intense. Dickinson College gave no-need grants to 13 percent of freshmen. The rate was 7 percent at Bryn Mawr College and 8 percent at Bucknell University and Lafayette College.

Starting in about 1990, F&M plunged into the merit aid competition, too. But college officials said they discovered several years ago that no-need awards were doing little to raise the school’s academic stature. So they ended them. At the same time, they widened their search for top students nationwide, regardless of need, teaming up with organizations such as the Posse Foundation to find highly qualified candidates from low-income families.

None of that would have worked, college officials say, without an aggressive expansion of aid to those in need. F&M showed The Post details of nine offers it made to assemble its freshman class, with proposed college grants ranging from $0 to $13,000 to nearly $51,000 a year.

College-bound students find huge variations in how schools size up their family resources.

Michelle Bailey, 19, a sophomore from Alexandria, Pa., learned that lesson when she was considering offers from several private colleges. Her father, a retired ironworker, works in food service on a college campus. Her mother is a bookkeeper. She did not qualify for Pell grants. F&M asked her family to pay $5,000 a year out of pocket, she said, on top of student loans of a few thousand dollars a year — a “fantastic” package, she said. Another college in Pennsylvania asked the family to pay $9,000. A third in Massachusetts offered her no aid.

Her father said F&M’s cap on expected family contribution was crucial. “To be honest with you, any more than that would have been almost impossible,” Michael Bailey said. “Not impossible. But I don’t know what we would have done.”

Michelle Bailey said F&M has a knack for helping students from diverse backgrounds blend in. “There is no divide,” she said. But that doesn’t mean aid policies are uncontroversial. “Trust me — it is a point of contention for some of the students who pay full tuition,” she said. “A lot of them do feel they are entitled to some form of merit aid.”