One-quarter of Americans believe their best chance to build wealth for retirement is by playing the lottery, not by patiently saving and investing, a survey says.  Those living paycheck to paycheck are even more likely to feel that way.

Misconceptions about how small amounts of money can grow keep millions of people from taking the steps that could greatly improve their lot, say sponsors of the survey released Thursday -- the Consumer Federation of America and the financial services firm Primerica.

"If Americans understood that their chances of winning a big lottery jackpot were 10 to 20 million to one but that they could accumulate hundreds of thousands of dollars through regular saving, more families would put $ 50 away rather than spending it on gambling or unneeded consumption," said Primerica Chairman Joseph Plumeri.

Invested for 40 years a 9 percent annual yield, $50 a week would add up to $ 1,026,853.

Stephen Brobeck, the consumer group's executive director, said banks and brokerage firms must take some of the blame for the fact that many Americans don't realize there are ways to invest profitably even small amounts of money, such as in savings bonds or mutual funds.

"I don't think they've done an adequate job in publicizing those products to the low- and middle-income households," Brobeck said.   "There are decent savings options out there for any household."

The poll indicated 27 percent of Americans believe winning a lottery or sweepstakes is their "best chance to obtain a half a million dollars or more in your lifetime."

Among households with annual incomes of $35,000 or less, those holding that belief jumped to 40 percent.

Overall, fewer than half -- 47 percent -- of all those surveyed said saving and investing some of their income was the most reliable route to wealth. 

People were also asked how much $25 invested weekly for 40 years at 7 percent annual yield would amount to.

Fewer than a third guessed over $150,000.  The correct answer is $286,640.

A series of similar questions found that younger and lower income Americans, along with women, tend to most undervalue how savings can add up.

But, that $ 286,640 is still not the half-million dollars the survey asked about.

The telephone poll of 1,010 Americans 18 and older conducted July 22-25, has an error margin or plus or minus 3 percentage points.