I think the majority of people understand that if you invest money every year from age 25 or 30 or 35 onward, you will end up a "millionaire" (or whatever).
The real problem is obvious after reading the comments to this article and other articles like it. The majority of people don't believe it's possible to save enough every year, so they don't even try. And, in reality, I don't think it's possible for most people. Because most people spend at least as much as they earn every year, and don't leave room in their budget for saving for things like a retirement that they believe is at least 30 or 40 years away.
People don't need to learn that savings compounds. They need to learn how to budget properly and to always spend less than they earn.
Trust me, most people don't know that is how you become a millionair. They think you do that by becoming a CEO, starting your own super business, picking the 'right' stock, going to hollywood, the Lottery, etc.
I think pretty much everyone is already aware of exponents at this point. Talking about the "magic" of compounding is getting old as it is both fairly simple and quite intuitive. It may be interesting to show to a younger crowd, perhaps to high school students.
I actually do this for high school students. Its pretty fun. I start off asking who wants to be a millionair. I show how the Rule of 72 works, then we assume 7.2% growth so that we get nice even numbers where their account doubles every 10 years. Then I show how 1k invested at 20 turns into 32k by 70. Now add a zero, 10k turns into 320k! Invest 10k at 20, another 20k by 30 because you have a real job, another 20k by 40, another 30k by 50, and now your house is paid off so 40k by 60. (So we are talking about 1k to 4k a year in savings.... nothing really.) When I'm done it looks like...
20:10k
30:20 20k
40:40 40 20k
50:80 80 40 30k
60:160 160 80 60 40k
70:320 320 160 120 80 = $1,000,000
(I start at the top of each column and write down, then go to the next column, so they see 10k turn into 320k, then 20k turn into 320k, etc., etc.... = 1million)
It does at least get them thinking about it, and then I drill how the 90k invested between 40 and 60 only ends up being worth a little more than the original 10k invested at 20(360k vs 320k) to show how important starting early is.