A Penny Doubled Every Day for 30 Days

Would you rather have $100 right now, or a penny that doubles every day for 30 days?

The doubling penny wins, and it is not close: it pays $5,368,709.12 on day 30 alone, and $10,737,418.23 in total if you keep every payment. The interesting part is not the answer, though. It is that on day 15 you are still holding less than $330, which is why almost everybody gets this question wrong.

Our post on explaining compound interest to a kid uses this as a worked exercise and tells you to run the numbers on paper together. This page is that worked-out version — every day, both columns — for when you would rather check the arithmetic than do it.

The full 30-day table

Two columns, because the question has two answers and most pages only print one. That day's amount is what you are handed that morning: $0.01 × 2(n−1). Total saved so far is what you have if you never spent any of it: $0.01 × (2n − 1).

There is a shortcut hiding in the third column worth pointing out to a kid who has just filled in a few rows by hand: the running total through any day is always one cent less than the next day's payment. Day 12 pays $20.48 and the total through day 11 is $20.47. Day 30 pays $5,368,709.12 and the total through day 29 is $5,368,709.11.

That is not a coincidence, and it is a genuinely useful thing to notice. Every payment up to today, added together, is exactly enough to cover tomorrow's payment on its own — minus the single penny you started with. It is also a free way to check the arithmetic: if the two columns ever drift apart by more than a cent, a row is wrong.

Why it feels boring, then isn't

Halfway through the month — fifteen of thirty days, the whole first half — you have $327.67. Against a final total of $10,737,418.23, those fifteen days produced 0.003% of the money. Round it and the entire first half of the exercise contributed nothing.

The last five days do 96.88% of it. Day 26 through day 30 alone move the running total from $335,544.31 to $10,737,418.23.

This is the actual lesson, and it is worth naming out loud rather than leaving it to be inferred: nothing about the first two weeks tells you what the last week looks like. A child who quits this exercise on day 12 because "it's only $20" has made a reasonable-looking judgement from the evidence in front of them and been completely wrong. That is the same reason people stop contributing to a savings account in year three.

What this does and does not prove

It proves the shape of exponential growth. It proves nothing about what a real account pays, and it is worth closing that gap before a kid walks away thinking a bank works like this.

Doubling every day is a 100% daily rate. The FDIC publishes a monthly national average rate for deposit products; as of 17 August 2026 the national rate for savings accounts was 0.38% — per year. Expressed as a daily rate to make the comparison honest, that is about 0.00104% a day, roughly one hundred-thousandth of the rate in this exercise.

Put concretely: at 0.38% a year, money takes about 183 years to double once. The penny in this table does it thirty times in a month. Leave an actual penny in an actual savings account at that rate for thirty years and it becomes about 1.1 cents.

So the honest framing for a kid is that the pattern is real — it is the reason saving early beats saving more later — but the speed is invented. Even the best savings accounts pay a small single-digit percent a year, not a day. Anything promising otherwise is not a savings account.

Try it with a rate that actually exists

The version of this exercise that transfers to real life uses a real rate and a real timeline. Put a starting balance and a plausible percentage into the compound interest calculator and let a child watch the same curve appear over years instead of days — flat for a long time, then not.

And if the question that comes back is "would it grow faster if the bank paid me every week instead of every year", that one has a surprising answer and a table of its own: Weekly vs Monthly vs Yearly Compounding: Does It Actually Matter?.