It's no secret that many Americans aren't saving enough for retirement, but a big chunk of households have saved nothing at all.

Nearly a third, or 31% of U.S. adults said they had no savings or pension to help them afford retirement, according to the Federal Reserve Board.

Even more alarming: 19% of those very close to retirement age, between the ages of 55 and 64, said they had no savings.

As a result, more than half of these respondents said they planned to either work full-time or part-time during their retirement years.

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Meanwhile, a quarter of those surveyed said they didn't know how they would afford their golden years.

A big part of the problem: many low- and middle-income households "have little financial cushion at all" and often lack even basic emergency savings, the Fed survey found.

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Plus, around half of workers and the majority of part-time workers don't receive retirement benefits at work, making it even harder to save.

The Federal Reserve Board survey, which took place last year, polled more than 4,000 working and retirement-age Americans on everything from retirement savings to student loan debt.