Penny Doubled Every Day Calculator
A penny doubled every day for 30 days — or any amount for any number of days. See the balance on the last day, the running total, the day it passes a lump sum, and which offer wins.
How it works
Amount on day d = start × 2^(d − 1) · running total after N days = start × (2^N − 1) · day it passes a lump sum L = smallest d with start × 2^(d − 1) ≥ L
The penny-doubling puzzle (“a million dollars today or a penny that doubles every day for a month?”) is the classic demonstration of exponential growth, the same idea as the wheat-and-chessboard legend. Doubling means 100% growth per period, so after 29 doublings one cent becomes over 5.3 million — but almost all of that appears in the last few days. It is a lesson in compounding and patience, not a realistic return.
Worked example
One cent doubled every day for 30 days: on day 30 the amount is 0.01 × 2²⁹ = 5,368,709.12. If you were paid each day’s amount and kept it all, the running total would be 10,737,418.23. The doubling amount first passes a 1,000,000 lump sum on day 28, so the doubling penny is the better choice.
Sources: Wikipedia — Wheat and chessboard problem · Investor.gov (SEC) — Compound interest calculator
Frequently asked questions
How much is a penny doubled every day for 30 days?
On day 30 it is 5,368,709.12 (0.01 × 2²⁹). Adding up every day’s amount gives 10,737,418.23. On day 31 it would be 10,737,418.24.
Why is the answer so large?
Each day adds as much as all previous growth combined. Exponential growth looks tiny at first — after two weeks the penny is still under 100 — and then explodes in the final days.
Is it a realistic investment?
No. Doubling daily is impossible in real markets. The lesson is that steady compounding over long periods, at realistic rates like 5% to 8% a year, does the heavy lifting.
How long does real money take to double?
Use the rule of 72: divide 72 by the annual return. At 6% a year money doubles in about 12 years.
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This calculator is for educational purposes. Double-check important results before acting on them.