The higher rates of education may explain why these parents are so gung-ho about helping their kids pay for college: these parents understand the benefit. An earlier Pew study found that 86 percent of college graduates felt their own education was a good investment, even as the majority of Americans (57 percent) said the higher education system fails to provide good value for the cost.

While they may not be saving enough, the millennial parents polled have done many things right, Bernhardt said. The vast majority of millennials saving for college put money aside monthly (79 percent), compared to 72 percent of GenX college savers and 66 percent of Boomer savers. Most millennial savers (57 percent) started saving before their children turned six, compared to 47 percent of GenXers and 37 percent of Boomers.

Forty-three percent of millennials polled use 529 college savings plans to save (Fidelity just so happens to offer 529s), compared with 37 percent of GenX and Boomers.

One thing parents are still getting wrong, though, is being afraid that saving for college will hurt their kids' ability to get financial aid. Fidelity found 53 percent had that fear, even though money saved in a parent's name-such as in a 529-has only a small impact on aid. Financial aid formulas expect parents to use less than 6 percent of their non-retirement savings for college. Incomes factor far more into financial aid formulas than assets. "If you save $10,000, you'll lose just $600 in financial aid," Bernhardt said. "They want people to save."

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