We all know that low- and middle-income workers generally don't have enough saved for retirement.

Richer folks, it turns out, might be in the same boat.

That's the takeaway from a new study by economists at the Schwartz Center for Economic Policy Analysis at the New School for Social Research.

"We always knew the bottom and the top were different and that they were growing apart," said Teresa Ghilarducci, an economics professor at the New School for Social Research and a co-author of the report. "But we were surprised that our retirement system creates winners and losers even within the same class of workers."

The researchers tracked the retirement savings of people ages 51 to 56, using the Health and Retirement Study and IRS tax data. The project took two years.

The authors found a great range in preparedness levels among people in the top-fifth of the earnings distribution, suggesting that even many prosperous Americans could struggle financially as they climb up the decades in age.