Several examples were stated showing the big effect of time on savings and investing. Starting that saving plan early is key. Also think about taxes. IRA's and 401K's generally allow you to choose between a regular (original) version or a Roth version. The regular version allows you to invest a portion of your earnings (income) each year without paying taxes on that money that year. Taxes are deferred until you make withdrawals. The Roth version is based on investing/saving a portion of your earnings, but you do have to pay income taxes on that money before you invest it. But, your withdrawals will never be taxed. Many people take advantage of the immediate tax break and use a regular version - paying less taxes each year.
The thing to consider is that all that growth and increase in value over a long time will get taxed with a regular account when you withdraw it many years later. If you invest in a Roth account, only your contributions get taxed. All that growth over time is tax free to you. If you retire with $500,000 of regular IRA/401k savings, you will have to pay taxes as you withdraw it for your living expenses. That $500,000 is not all yours - the tax man wants his share. That same $500,000 in a Roth IRA or 401k is all yours - no taxes to be paid. That person with the Roth account ends up with a lot more spending money that that person with the regular account, even with the same account balance. If you end up with a few million in a regular account, the tax bill gets very big every year when the minimum distribution kicks in. You are forced to withdraw (and pay taxes on) the minimum distribution amount for a regular account - even if you don't need that much money to live on. Investing after tax money in a Roth account seems like the best plan - certainly if you max out your contributions each year. If you already have a regular IRA or 401k, you can probably transfer/convert it to a Roth version a little at a time each year - but you have to pay taxes on the amount converted each year. But, if you are 10+ years to taking withdrawals, this will probably save you money (on taxes) overall. General issue is that when you are young, you might not put much effort into all this. By the time you understand all the options and the importance of it, there is less time to take advantage of it.