The definition of compounding interest is something they should be teaching to first graders. It is not a difficult principle to grasp, once explained.
Compounding interest is interest calculated on initial principal, as well as on the accumulated interest from previous periods. Think of it as interest on interest.
It's an important financial lesson because it teaches children how money can make more money. The idea of taking your $5 allowance and saving it for a year instead of buying a toy and a candy bar is silly, unless you can grasp that saving that $5 now means you'll have more than $5 later on. Of course, telling them to open a savings account at the bank with you, in order to deposit that $5 at .1% interest (average savings account rate), is not going to cause many squeals of delight.
Hint: Don't use numbers like .1% or even 1% compounding with kids. Telling them if they save their 100 M&Ms for a year they'll have 101, and after two years they'll have 102 and a tiny flake of M&M chocolate coating, just isn't going to cut it. Kids need serious returns on their M&Ms. Let's say 50%. That's better. And let's make it compounding daily, not yearly.
So listen kids, if you save your 100 M&Ms today, tomorrow you'll have 150 M&Ms. You made 50 M&Ms in just one day. Awesome, right? But get this, if you wait one more day, then that second day you won't get 50 M&Ms, you'll get 75! So now you have 225 M&Ms, just for saving those first 100. Hold your horses, kids, it gets better. On day 3 you would earn 112.5 M&Ms! That's right, because of compounding interest you are now earning more M&Ms in one day than you started out with!
Once they begin to grasp this concept, you can then discuss it as it pertains to investing in stocks. This could be more accurately described as compounding growth, since you are not simply earning a fixed interest rate.
Let's say it's Christmas Day 2010 and Grandpa gives you 1 share of Amazon stock as a gift. You're ten years old, so you probably give Grandpa a hug and say thank you, while simultaneously rolling your eyes behind his back. But, let's talk about why that was such an awesome gift. With the magic of hindsight we get to see what would have happened to that share of AMZN by the time you turned eighteen.
You start off with a $182 share of Amazon stock that Grandpa gives you on Christmas morning 2010. You're only ten, so you ask Dad if you can just have the money instead, so you can buy whatever you want—the answer is no. You pout, storm off to play with your Legos, and promptly forget about that piece of paper that says you own a share of Amazon stock.
But each year Dad shows you what that share is now worth.
At the end of year one it's worth $179 and you say, "See, you should have given me the money last year. Can I have it now?" And the answer is no, again.
Another year goes by and now it's worth $257. Hmmm, things are getting interesting. Now you're twelve years old, and maybe you start to ask Dad what the price of the stock is a little more often.
One year it goes from $403 down to $306. But by the next year it is $664 and now you're really starting to understand. You aren't making the same fixed amount of money every year, you are earning different amounts. The stock price growth is based on the value at the end of the last, not just on the initial $182. So a 10% increase today is worth more than a 10% increase the day you received the stock. The same growth rate on AMZN stock when you are 18 is worth far more money (in dollar terms) than it was when you were ten.
Eight years after Grandpa gave you a $182 share of stock it is worth $1,344. You did nothing but let your money/stock work for you. Your share of Amazon earned an annual compound growth rate of over 28%. It didn't go there in a straight line. Some years it went down, some years up, but over time it grew.
I know it's not exciting, and that's why it's hard for so many adults—much less their children—to come around to saving/investing instead of spending each check in full as it comes in. Compounding takes time, something we seem less and less inclined to accept these days (perhaps because we weren't taught how it works when we were young). But this is a valuable lesson, and one that if it is learned early on in life, will pay off greatly in your kid's future.
If they grasp this early on, using small numbers, then they will eventually realize how the concept works when they increase the numbers. By the time your child is eighteen they "get it." When they start earning money of their own they will consider investing some of it so it will work for them. They will understand what a difference socking away 10% of their earnings can make. And then, because they understand compounding, they'll realize what a difference doubling to 20% would make, while making just a small difference to their current lifestyle. Kids understanding compounding investing now will set them up for great financial success when they are 20, 30, 40—instead of coming to the grim realization that they haven't done enough when they are 40, 50, 60. Put them on that path.