The 10 richest universities in America hold nearly a third of the total wealth, in cash and investments, amassed by about 500 public and private institutions. The 40 richest hold almost two-thirds of the total wealth.

And their financial edge is widening. These schools are drawing an outsized share of gifts to colleges and universities. Their assets grew at at a far faster rate from 2009 to 2014 than the portfolios of schools in the middle and bottom of the pack.

Those are the findings from Moody’s Investors Service, released Thursday, in a study of the balance sheets of 503 institutions in the portfolio of the credit-rating firm. The study illuminates the disparity between the haves and the have-nots in higher education.

“This growing gap will pose increasing competitive challenges for institutions that do not have the resources to invest in facilities, financial aid, and other strategic initiatives at the same level as their wealthier counterparts,” Moody’s said.

This point is worth remembering as many schools scramble to cut expenses and recruit students. Some are laying off employees. A few have opted to close. The battle over the planned shutdown of Sweet Briar College in rural Virginia has become a symbol of these financial struggles and the fallout for students and faculty.

The top 40 in the Moody’s wealth analysis had median cash and investments worth $6.3 billion. The median for the rest of the schools analyzed was $273 million. Assets of the top 40 grew 50 percent from 2009 to 2014. Assets of schools deemed to be of moderate to very high credit risk grew 22 percent in that time.

Donors gravitate to the wealthiest schools. Nearly 60 percent of gifts last year to the schools that Moody’s analyzed flowed to the top 40.

Who are the rich?

The top 10 private names are familiar: Harvard University ($42.8 billion in cash and investments in fiscal 2014), Stanford University ($31.6 billion), Yale University ($25.4 billion), Princeton University ($21.3 billion), Massachusetts Institute of Technology ($15.2 billion), University of Pennsylvania ($11.9 billion), Duke University ($11.4 billion), Northwestern University ($10.4 billion), Columbia University ($9.9 billion) and University of Notre Dame ($9.5 billion).

The top 10 public names: University of Texas system ($36.7 billion), University of California ($28.6 billion), University of Michigan ($11.5 billion), State University System of Florida ($9.7 billion), University of Virginia ($8.1 billion), Pennsylvania State University ($6.7 billion), California State University ($5.7 billion), Texas A&M University system ($5.0 billion), University of Washington ($4.9 billion) and Ohio State University ($4.8 billion).

Note: An earlier version of this article inadvertently attached a full copy of the Moody’s report, which was intended to be limited in distribution to Moody’s subscribers.