I run a "Bank of Dad", tracked in a spreadsheet for my kids. They can choose to "invest" their money with me or not. To make investing meaningful for them, I pay 10% interest per month, up to a $50 balance.
To avoid bankrupting myself—and to encourage them to get a real investment account when the time comes—the rate drops as the balance increases, similar to progressive tax brackets. By the time they get to $1000 balance, the annualized rate works out to ~6%, and after that it drops fast enough that it's essentially free for me to operate.
Overall, it's been quite successful. Now whenever the kids get money, they invest it immediately. And they often delay or forego spending so that they can get more interest the next month. They haven't turned into complete misers, but it has encourage a mentality of thinking about saving, and I think the concept of interest has landed quite well. I think things really started to click for them around age 8 or 9.
If you're interested in doing something similar, I made a sanitized version of the spreadsheet. Feel free to copy: https://docs.google.com/spreadsheets/d/1f3FgHUohw26sHuCoO40s...
These kids are going to be so mad at how low interest rates are at actual banks that I wonder if this is ultimately going to teach them to borrow rather than save. I guess it’s the same thing, really: they’re learning the time value of money either way.
I've been very transparent with them that the interest rates they get from me are far more generous than out there in the real world. :)
Alternatively we’ll have hyper inflation and they’ll be even madder that all their nominal scrimping and saving was meaningless.