Does college pay off? For many, it only takes a few years, study says.

One of the major questions facing families today is whether a college degree is worth the expense, given rising tuition and fees that can saddle graduates with tens of thousands in student loan debt. Today, a majority of Americans don't think the cost can be justified.

But a new analysis finds that most post-secondary degrees provide a payoff within less than five years after graduation for low- and moderate-income students, although that time frame can largely depend on the type of school and program that a student chooses. The analysis, from the HEA Group and the educational nonprofit College Futures Foundation, focuses on graduates in California, the state with the largest number of enrolled college students.

The study examined families earning $75,000 or less given that these students may be more likely to skip higher education due to fears that pursuing a post-secondary degree may not pay off, even though a college degree could help them get an economic foothold. For this group of students, almost 4 of 5 California colleges and other higher education institutions provide a return on investment within five years, the research found.

"The No. 1 deterrent for a student not to pursue a college degree is affordability — they simply think they can't afford the cost of a higher education," HEA Group founder Michael Itzkowitz told CBS MoneyWatch.

But the study found that many low- and middle-income students are getting "an affordable education that allows for enough of an earnings premium that they can pay down their college education very quickly," he added.

The schools with the best return on investment for low- and middle-income students include many of California's state colleges, which tend to be lower-priced than nonprofit private universities, he noted. Itzkowitz said he believes the findings have applicability across the U.S. because students across the nation likewise have access to state colleges and universities that offer lower-cost degree programs compared with private institutions.

The findings echo recent a recent analysis of 1,500 colleges by Bloomberg News, which found that Ivy League universities like Yale and Harvard provide the best return on investment due to high salaries earned by their grads. But students who don't gain acceptance to one the Ivies are often better off attending state colleges, rather than high-priced private institutions, given that public institutions' lower cost of attendance result in a better return on investment.

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