Most Americans grossly underestimate the cost of nursing homes or assisted living, and a substantial number don't have a dime set aside for elder care, according to a new survey for MoneyRates.

The report found two-thirds of Americans do not have enough set aside for even one year in a nursing home. Even worse, 40 percent have set aside nothing for it.

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MoneyRates used an old saying to illustrate the situation: “We grow too soon old, and too late smart.”

“That phrase is an old Pennsylvania Dutch saying, and it accurately describes how people tend not to recognize the full cost of elder care until it is too late.”

Safety nets such as Medicaid only offer limited protection, MoneyRates said. It noted Medicaid kicks in only after someone has substantially depleted their net worth, and limits which facilities can be used and the level of privacy.

A study by MetLife found the actual cost of a semi-private room in a nursing home in the U.S. adds up to an average of $81,030 a year. For a private room, the figure goes up to $90,520. In some areas, the average can be much higher. A semi-private room in the New York metro area was calculated at $141,620.

The MoneyRates survey found men and women are nearly equally ignorant when it comes to nursing home costs. Fifty-six percent of women and 58 percent of men wrongly believed a year in a nursing home costs less than $75,000.

Some Americans believe their long-term care insurance will take care of them in their old age, but MoneyRates cautioned they should read the fine print to find out which services are actually provided.

The cost of staying in an assisted living facility is about half the price of a nursing home, but MoneyRates said many Americans thought they were the same.

“Why is it important for people to realize this? Some wise planning could allow you to stay in assisted living longer and thus preserve more of your savings.”

Genworth Financial’s 2014 Cost of Care report found the median monthly average cost for assisted living in the U.S. is $3,500.

The median hourly rate for homemaker services is $19, the median home health care aide hourly rate is $20, and the median day rate for adult day care centers is $65, according to Genworth.

“Multi-generational living is becoming mainstream again. There has been a 70 percent increase in the past decade of parents moving in with the kids,” Dee Lee, a certified financial planner, told CBS Boston.

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