NEW YORK — About half of Americans with assets of more than $250,000 say they won’t pay the entire tab for their children’s college education, according to Bank of America.

About 47 percent of those polled in the Merrill Lynch Affluent Insights Survey released Monday said they didn’t or won’t pay the full cost of higher education. Limiting access to the bank of Mom and Dad will help teach their kids financial responsibility, 29 percent of respondents said.

Tuition and fees for in-state students at public four-year institutions averaged $7,605 for the 2010-2011 school year, according to the College Board, a New York-based nonprofit. At private nonprofit four-year colleges and universities, costs averaged $27,293.

“What the numbers show is just the rising cost of college and the financial demands on middle-class and affluent families,” said Andy Sieg, head of retirement services and global investment solutions for the Charlotte, N.C.-based bank.

Having kids foot at least part of the bill for college is an example of how a “sandwich generation” is coping with caring for parents and dependent children at the same time, Sieg said.

With older generations living longer, high rates of unemployment for recent college graduates and expectations to work later in life, affluent individuals are changing their views on financial planning, he said.

Saving early for college has become a generational trend, as 60 percent of affluent parents age 35 to age 50 start college savings accounts before or within the first year of their child’s life, compared with 15 percent who were over age 65 and began saving early, the survey said.

About half of parents said “financial know-how” was a trait they hoped to impart to their children. Among parents who used a financial adviser, 64 percent said they shared some of their adviser’s guidance with their children, while almost 20 percent of parents age 51 and older had invited their children to meet with the family’s adviser.

The survey also asked respondents about health-care costs and inheritance.

About 70 percent said health-care costs were their top financial concern, and 56 percent said they’re not counting on an inheritance to help them with these costs or during general retirement.

Those results are similar to an April study by U.S. Trust, Bank of America’s private wealth management unit, said Sieg. That survey of individuals with $3 million or more in investable assets found that fewer than half said that leaving an inheritance is important to them.

“They recognize that their parents’ generation is absorbing a higher health-care cost and they will need their own financial resources to secure their own lifestyles in later life,” according to Sieg.

Braun Research, based in Princeton, N.J., contacted 1,000 Americans with investable assets of $250,000 or more on the behalf of the bank. The telephone survey was conducted in June.