When asked how much they should have put away in order to fund a comfortable retirement, a whopping 61 percent of Americans choose the answer, "Don't know," according to a new survey from Bankrate.

Another 8 percent under-estimate by a lot: They say that they'll only need $250,000 or less, which is a fraction of the $1 million financial experts typically recommend. But even the 15 percent of respondents who say they'll need between $250,000 and $1 million could be missing the mark as well, given that $1 million doesn't stretch as far as it used to.

On average, respondents estimate they'll need around $650,000, which could leave them broke in their old age. Older generations are more likely to give a lower number: Both boomers and those aged 73 and above say they'll only need $500,000 in the bank for retirement. Those in Gen X predict they'll need $1 million, while millennials say $800,000.

Not only are Americans failing to understand how much they need to put away for their golden years, they aren't saving much, either. A Bankrate survey from March found that 20 percent of Americans don't save any of their annual income at all.

Only 16 percent of survey respondents say that they save more than 15 percent of what they make, which is what experts generally recommend. A quarter of respondents report saving between 6 and 10 percent of their income and 21 percent say they sock away 5 percent or less.