The deal every kid would actually take
Here is the pitch, kid-sized: half your birthday money is still yours to blow on whatever you want, no questions asked. The other half goes to work, and it never stops working. It works while you sleep, while you are at school, while you grow up, move out, and forget about it. This page shows what that half becomes, and the answer surprises almost every grown-up who runs it, because the deposits are tiny and the result is not. The trick is not the amount. The trick is that a kid's dollars get more birthdays than anyone else's.
Worked example
Birthdays bring in $100 a year, and half gets invested from the very first one, at an assumed 7% return.
That is $50 a birthday, $900 total over 18 birthdays, and it is worth $1,700 at 18. The other $50 a year bought toys the whole way, as birthday money should.
Then the pot does its best work after the birthdays stop. Left completely alone: about $3,829 at 30, and about $40,877 at 65. From half the birthday cards. The same $900 kept in a drawer is still $900.
The birthday dollar rule
At 7%, a single dollar from the first birthday has 64 years to grow and becomes about $76 by age 65. A dollar from the 18th birthday becomes about $24. Same dollar, same rate, no cleverness anywhere: the early dollar simply attends more birthdays of its own. This is the whole secret of the page, and honestly of most long-term investing. Starting early beats starting big, beats picking brilliantly, beats every optimization a grown-up will later spend hours on. A child cannot out-earn an adult, but a child out-times everyone.
What grown-ups call the account
A kid cannot open a brokerage account alone, so the usual container is a custodial account (a UTMA or UGMA): an adult manages it, the money legally belongs to the child, and control transfers at the age of majority, typically 18 to 21 depending on the state. A 529 plan is the education-specific cousin with tax advantages if the money is for school. Which one fits is a family decision with real details (custodial money counts against financial aid more heavily than a parent's 529, for one), so treat this paragraph as a vocabulary lesson, not a recommendation. The arithmetic above works the same in any of them.
Why half, and not everything
The percentage buttons go to 100, but notice the example uses 50, and that is not timidity, it is strategy. A plan a kid resents is a plan that ends the first time they are old enough to argue. Half preserves the entire point of birthday money, which is joy, while quietly proving to the same kid, year after year, that the other half is turning into something. By the time they are old enough to understand the chart, they are the one who does not want to stop. A savings habit that survives childhood is worth more than any percentage, because the habit is the thing that will still be compounding at 40.
The fine print, said plainly
The return is an assumption you can change, and real markets never grow smoothly; some birthdays the pot will be down, which is itself a valuable lesson at low stakes. The figures are in future dollars, which will buy less than today's. Investment gains in a child's account can owe tax past certain thresholds (grown-ups: search "kiddie tax" when the numbers get large). And this page is a teaching tool, not financial advice: it exists because watching $50 become $76 per dollar is the most convincing math lesson a kid will ever get, and it costs one birthday card to start the demonstration.