Want to retire with $1 million? Here's what researchers say is the ideal age to start saving.

Americans say they'll need about $1.8 million to retire comfortably, a pie-in-the-sky figure for most households given that the average retirement fund holds just over $113,000. But a nest egg of over a million dollars isn't out of reach — as long as you start saving early enough, according to new research. 

The optimal age to start socking away money for your golden years is 25 years old or younger, according to a new report from the Milken Institute, an economic think tank. And there's a very simple mathematical reason for that number. Due to the power of compounding, starting a retirement savings while in one's early 20s, or even younger, can help ensure your assets grow to at least $1 million by age 65. 

"The message of early investing needs to be conveyed in ways that resonate with Americans across the board," the report noted. 

Compounding — famously ascribed by billionaire investor Warren Buffett as one of the keys to his success — is the reason why it pays to save as early as possible. The term refers to the accrual of interest earned on an initial investment, which is then reinvested with the original savings. That combined savings amount goes on to earn more interest, with the original investment snowballing in value as the pattern continues year after year. 

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For instance, a 25-year-old who saves $100 a week in their retirement account, and receives a 7% return on that investment will retire with $1.1 million at age 65, the analysis noted. 

While that may seem like an easy recipe for investment success, reaching that $1.1 million investment egg becomes much harder when starting to save at a later age, due to the smaller time period for compounding to work its magic. A 35-year-old who begins saving that same $100 per week will end up with $300,000 at age 65, the report said. 

Unfortunately, some generations of Americans began saving much later in their careers, the study found. For instance, baby boomers — the generation that's now retiring en masse — typically started saving for their golden years at age 35, while Generation X began at a median age of 30, it said. There's more hope for younger generations: millennials began saving at age 25 and Gen Z, the oldest of whom are now in their early 20s, at 19.

A growing retirement gap

Also, the retirement gap, or the difference between what one needs to stop working versus what they have saved, is growing for some American workers. 

Retirement savings rates are lower for women and people of color, for instance. Part of that is due to lower earnings for women and people of color, the Milken report notes. Women are also more likely than men to take time off from work to care for children and elderly relatives, which hurts their ability to save for retirement. 

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And low-wage workers are going backward, with just 1 in 10 low-income workers between the ages of 51 and 64 having any funds put away for retirement in 2019, compared with 1 in 5 in 2007 prior to the Great Recession, according to a recent analysis by the U.S. Government Accountability Office.

To be sure, saving for retirement is easier if you've got a job that offers a 401(k) with a company match, something to which half of all workers don't have access. Expanding access to such accounts would help more Americans achieve their retirement goals, the reported added.

"The lack of savings vehicles for many workers is one of the most important issues that policymakers and the private sector must address," the Milken report noted.