And the problem is escalating, with people close to retirement more likely to be in debt, and to be deeper in debt, than earlier generations were. While part of the problem lies in the complexity of financial products these days, another part—and a large one—is the lack of understanding people have of basic financial principles.

No longer driven to pay off mortgages prior to retirement, as earlier generations did, today's preretirees are carrying far larger mortgage debt loads thanks to larger loans that required little or no down payment on more expensive homes.

That means, according to a Wall Street Journal blog post by Mitchell, that older people today are more likely to file for bankruptcy than in the past, and they are far more likely to report feeling financially fragile.

However, those who learned about finance—either in school or in the workplace—not only do better at saving and investing, they end up with greater lifetime wealth and are less likely to run out of money in retirement.

The study, says Mitchell, "shows that substantial wealth inequality arises in this framework compared to the conventional approach where returns on wealth simply depend on portfolio composition alone rather than financial knowledge."

And the difference is not small, she adds: "people who invest in financial knowledge can save better, invest better and manage their money better during retirement, while those who do not, do worse." In fact, "some 30 percent to 40 percent of retirement wealth inequality is … explained by differences in financial knowledge."

While poorer segments of the population that will derive a greater benefit from Social Security when they age are perhaps less driven to invest in financial education, people who are better paid and won't get as much benefit from Social Security "are incentivized more to invest in financial knowledge."