When it comes to college, most families assume public schools are far more affordable. That's only partly true. At public, four-year institutions, costs for the 2017-18 school year hit $20,770, according to the College Board. Tuition plus room and board at four-year private universities was much higher: $47,000, on average, in the current academic year. However, about two-thirds of all full-time students receive aid, which can bring the sticker price significantly down. Your net price is a college's tuition and fees minus grants, scholarships and education tax benefits, according to the College Board. To that end, The Princeton Review ranked colleges by how much financial aid is awarded and how satisfied students are with their packages. The report is based on data collected from fall 2016 through summer 2017. The schools that fared the best were all private schools, many of which have sky-high prices, but very generous aid packages.

"We look at sticker price but also academics and financial aid. And that's really where the value comes in," said Robert Franek, The Princeton Review's editor-in-chief and author of "Colleges That Pay You Back." When it comes to offering aid, private schools typically have more money to spend, he added. "These schools have been very clear about their commitment to making college costs affordable and giving out massive amounts of aid to students and families that need it." Here are the schools that made The Princeton Review's top 10:

10. Colgate University

Colgate University, with Taylor Lake in the foreground, is shown in Hamilton, N.Y. Source: Wikimedia Commons

Location: Hamilton, N.Y.

Tuition, fees, room and board: $67,500

Average need-based scholarship: $45,724

Out-of-pocket cost: $21,776 Students here have a healthy dose of school spirit, with good reason: Colgate is one of the best liberal arts schools in the country even though it has very high tuition. Still, students receive over $45,000 in grant aid, on average, making it a much more affordable place to matriculate.

9. Yale University

The Sterling Memorial Library on the Yale University campus in New Haven, Connecticut. Craig Warga | Bloomberg | Getty Images

Location: New Haven, Conn.

Tuition, fees, room and board: $66,900

Average need-based scholarship: $47,960

Out-of-pocket cost: $18,940 This Ivy puts its money where its mouth is: Committed to meeting 100 percent of each applicant's demonstrated need, Yale spends more than $100 million on student financial aid each year. As a result, more than 10 percent of the student body will have $0 expected parent contribution in 2018.

8. Vassar College

Vassar College Source: Vassar College

Location: Poughkeepsie, N.Y.

Tuition, fees, room and board: $68,060

Average need-based scholarship: $45,109

Out-of-pocket cost: $22,951 Vassar is one of most expensive colleges in the country but also one of the most generous. The average scholarship is just over $45,000, making the total cost less than $23,000 for a top liberal arts school with a stunning campus.

7. Princeton University

Students walking to classes at Princeton University, Princeton, NJ Barry Winiker | Getty Images

Location: Princeton, N.J.

Tuition, fees, room and board: $60,090

Average need-based scholarship: $47,497

Out-of-pocket cost: $12,593 This elite Ivy League school makes the top of many college lists, but it's also highly regarded for its war on student debt. Princeton has eliminated all loans for students who qualify for aid. Instead, awards come in the form of grants that do not need to be repaid.

6. Pomona College

Pomona College Source: Wikipedia

Location: Claremont, Calif.

Tuition, fees, room and board: $67,225

Average need-based scholarship: $41,443

Out-of-pocket cost: $25,782 As a member of the Claremont Colleges, a group of highly regarded schools just outside of Los Angeles, admission to Pomona is tough but also need-blind. The goal is to achieve "significant socio-economic diversity," according to Adam Sapp, Pomona's senior associate dean and director of admissions.

5. Washington University in St. Louis

Brookings Hall at Washington University in St. Louis. Stephen Ehlers | Getty Images

Location: St. Louis, Mo.

Tuition, fees, room and board: $67,539

Average need-based scholarship: $40,509

Out-of-pocket cost: $27,030 At first glance, Wash U. is another one of the pricier schools on Princeton Review's list but it is similarly committed to helping defray the cost without relying on loan debt. For starters, all aid to families earning $75,000 or less a year is grant-based, which means it does not have to be paid back.

4. Cooper Union for the Advancement of Science and Art

Cooper Union for the Advancement of Science and Art Source: Cooper Union

Location: New York, N.Y.

Tuition, fees, room and board: $61,370

Average need-based scholarship: $15,394*

Out-of-pocket cost: $45,976 In the heart of New York City is a small school making a big promise to provide an affordable education. Aside from the aid available to help cover housing, food, books and supplies at Cooper Union, all students receive a half-tuition scholarship worth over $20,000 a year*.

3. Vanderbilt University

Vanderbilt University Vanderbilt | Collegiate Images | Getty Images

Location: Nashville, Tenn.

Tuition, fees, room and board: $60,572

Average need-based scholarship: $41,331

Out-of-pocket cost: $19,241 In addition to gift assistance, Nashville's Vanderbilt is known for its three signature scholarships which all cover full tuition and offer summer stipends to study abroad, complete service projects or conduct research. And they are renewable for all four years of college.

2. Williams College

Chapin Hall at Williams College Barry Winiker | Getty Images

Location: Williamstown, Mass.

Tuition, fees, room and board: $67,700

Average need-based scholarship: $48,885

Out-of-pocket cost: $18,815 One of the nation's very best schools also gets extremely high marks for its ability to finance its students' educations. The school meets 100 percent of demonstrated need for all undergrads for all four years.

1. Bowdoin College