Personally, I think the best age to start saving for retirement is when you get your first allowance payment as a kid. Even if you set aside $1, the key is to get in the habit of saving and living on less than you make. As you get older and make more money (even if it is summer jobs through high school and college), starting by setting aside at least 10% of your gross income is a great habit to get into.
When you start working after college (or whenever you start working "full time"), if you can target at least 15% of your gross income, that will likely put you on the path to a pretty solid retirement. It won't guarantee it because there are too many unpredictable variables between the time you start working and the time your retire (likely 30-40+ years depending on your situation), but it is a good goal to aim for.
Obviously, the more you can set aside, the better - while I've heard people complain about not setting aside and saving enough money, I've never heard someone complain that they saved too much. So, if you can eventually get to a 20% savings rate, that is better than 15%, which is better than 10%, all of which are certainly better than nothing.
If you can achieve an annualized return of just over 7% (which is in no way out of the realm of possibility if you put together a properly allocated, well diversified portfolio and stick to your plan and let it grow for 30 or 40 years), your money will double approximately every 10 years or so. So, if you set aside $5,000 at age 20, and average an annualized return of just over 7%, it would be worth roughly $80,000 at age 60 (and that is without adding another dime to it along the way). If you set aside $5,000 at age 30 and averaged the same annualized return as above, it would only be worth about $40,000 at age 60. So, that shows you how powerful time is when it comes to compounding your money.
While there may not be a "best" age at which to start saving, if I was pressed on the issue, I would definitely not say that 30 is the "best." Thirty is certainly a better starting point than 35, or 40 (or even 31), but I would suggest that in your teens or 20s is better than 30. The earlier you start, the more time your money has to grow and compound and the better off you will be in the long run.
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