While an aging population will increase demand for long-term care, many Americans over the age of 40 aren’t confident they’ll be able to pay for it, and some incorrectly assume government programs will pick up the tab.

In a new poll from the Associated Press and the NORC Center for Public Affairs Research, 36 percent of respondents said they were extremely or very confident that they’re financially prepared for the costs of long-term care. While that number has steadily increased from 27 percent in 2013, most respondents didn’t report making any changes to back up this boost in confidence.

“Most say they have not set aside money to pay for long‑term care expenses, and even fewer think their current insurance will cover ongoing living assistance services. About one in three older Americans report they have set aside money for long‑term care, a figure that is unchanged from recent years despite the uptick in confidence,” the survey said.

Thirty-three percent said they had done no planning at all for long-term care, and nearly 40 percent don’t think they’ll ever need it.

Other results suggest older Americans may be basing their planning for long-term care on the mistaken belief programs like Medicare will cover the costs. Only 13 percent of respondents said they’re sure their insurance covers long-term care, but listed a variety of sources they expect to depend on for support. Medicare (40 percent) and Social Security (36 percent) top the list, even though neither program directly covers long-term care. Personal savings (32 percent) came in third. Respondents with incomes below $50,000 were more likely to expect to rely on those programs.

Setting up new forms of government assistance to support long-term care was favored by the majority of respondents. Among the many options offered to respondents were tax breaks to encourage saving (75 percent), tax breaks for purchasing long-term care insurance (70 percent), employer-sponsored programs (66 percent), and a publicly-administered plan (53 percent). Only 25 percent supported a requirement for individuals to be insured for long-term care.

While respondents may have had misconceptions about how to pay for their care, they expressed clear opinions about where they liked to receive it.

Nearly four out of five (77 percent) said they’d prefer to receive care in their own home, with only 11 percent said they’d prefer a senior community setting, and 4 percent favored a nursing home.