Nearly two-thirds of adults over 40 have no idea how they’ll pay for long-term care when they’ll need it.

That’s one of the dismal findings from a recent survey exploring the state of aging and caregiving.

More than half of those interviewed admitted they’d done virtually no planning for their long-term care needs. The poll was conducted as a joint effort by the University of Chicago’s NORC Center for Public Affairs Research along with the Associated Press.

One in five respondents didn’t know whether their health insurance covered nursing home care, with over 25% unsure about the same coverage by Medicare – the federal health insurance plan largely for those 65 and over.

Neither private insurance nor Medicare cover long-term care – only, in some cases, short-term emergency rehabilitation.

“The need for long-term care services is expected to dramatically increase over the coming decades, as the senior population is expected to nearly double,” summarizes the report. “In 2000, Americans age 65 or older made up only 12 percent of the national population, but by 2040, it is expected that seniors will comprise about 22 percent.”

Perhaps optimistically – or because of a shortage in savings – the percentage of Americans who think they’ll eventually need ongoing care fell from 65% in an earlier poll from 2013 to just over half.

Another key finding of the poll is that nearly 1 in 10 Americans over 40 are being squeezed tightly as part of the “Sandwich Generation” – caring for at least one child along with an elder loved one, typically a parent or grandparent.