I've been saving a min of 15% (now 20% for the last 3.5 years) of my income for 18 years, I'm have no where near enough to retire yet.
I was a bit curious, so I made a spreadsheet that does simple compounding interest with a steady investment. Rather than dollars, I just stuck "0.15" in there to represent 15% invested.
At 15% invested, I consider 0.85 as the "magic number" for the annual return where you can retire, as it replaces the income you are used to living on. Of course, most people don't earn a steady amount through their lives, so later income increases can lower the effectiveness of compounding interest as it moves the goal posts of what you consider replacement income more than simple inflation. Speaking of which, I'm disregarding that as well. But then, most retirement calculators tend put you on living at 60% of your income at the end, so oh well. It's more examining the differences various assumptions make.
Investing 15% at a 5% return, you hit 0.86 at 40 years. 15 years in, compounding interest starts to be a larger factor than your continuing deposit of 15%.
Change that to a 10% return, .86 is hit after 22 years. Retire early, perhaps? But then, that would have implications for health care, so it might be better to wait to retire early 2 more years, at which point your investment would return 1.07 times your income. Or, even safer, 29 years, when you could switch from probably highly risky(on an annual basis) 10% return investments to much safer 5%.
If you do 20%? At 10% that's hitting 0.8 at only 18 years. 1.6 times your income at 24.
I've averaged 9% with my investments, which would be 23 years for 0.85, 31-32 for full replacement income.
It's really quite astonishing how much faster you hit various "retirement points" if you are able to save a good chunk of your income - and that depends more on your spending, I think, than your income.
Of course, keep in mind that the cheaper you live now, the less you can potentially save during retirement. Sure, you can save money not driving to work every day, but what if your idea of "retirement" is packing into a RV and driving around the country?