About the Penny Doubled Every Day Calculator
This calculator answers the classic riddle: would you rather have a million dollars today, or a penny that doubles every day for 30 days? Enter the starting amount and the number of days, and it shows what the amount is worth on the final day, the running total if you kept every day’s amount, and the day on which the doubling amount first overtakes the lump sum you choose. A day-by-day table and chart show the shape of exponential growth.
Teachers use the penny puzzle to explain exponents and compound interest, and it is a memorable way to show why starting to save early matters: for most of the month the penny looks hopeless — it is still under $11,000 on day 21 — and then the last week delivers almost everything. Half of the final amount arrives on the very last day, because each day’s amount equals all the previous days combined plus one cent.
The calculation treats day 1 as the starting amount (one cent), day 2 as two cents, and so on, so day 30 is the penny doubled 29 times. No real investment doubles daily — it is the equivalent of an interest rate of 100% per day — but the same arithmetic drives long-term compounding at ordinary rates.
With the default inputs, the amount on the final day is $5,368,709.12. Change any value above to recalculate instantly.
How to use the penny doubled every day calculator
- 1Enter the starting amount — one cent for the classic puzzle.
- 2Enter the number of days to keep doubling.
- 3Enter the lump sum you want to compare against.
- 4Read the final day’s amount, the running total and the day it overtakes the lump sum.
- 5Scroll the table to see how slowly it starts and how fast it ends.
Formula and method
Each day the amount doubles, so after n − 1 doublings the day-n amount is the starting amount a multiplied by 2 raised to n − 1. With one cent, day 30 is 0.01 × 2^29 = $5,368,709.12.
If instead you received every day’s amount and kept it, the running total is a geometric series: a + 2a + 4a + … + 2^(n−1)a = a × (2^n − 1), which is always one starting amount less than double the final day. The day the amount passes a lump sum L is the first n with a × 2^(n−1) ≥ L, i.e. n = ⌈log₂(L/a)⌉ + 1.
- a
- Starting amount on day 1
- n
- Day number
- L
- Lump sum used for comparison
Worked examples
A penny doubled for 30 days vs $1 million
One cent doubled 29 times is $5,368,709.12 on day 30 — more than five times the $1 million. The doubling amount only overtakes $1 million on day 28, and if you kept every day’s amount you would have $10,737,418.23.
A 31-day month
One more day doubles the result again: day 31 is worth $10,737,418.24 and the running total passes $21.4 million.
$1 doubled for 20 days vs $100,000
Starting with $1, day 20 is 2^19 = $524,288. The daily amount first exceeds $100,000 on day 18 ($131,072).
Frequently asked questions
How much is a penny doubled every day for 30 days?+
On day 30 a penny doubled every day is worth $5,368,709.12 (one cent × 2^29). If you add up every day’s amount, the total is $10,737,418.23.
Would you rather have $1 million or a penny doubled for a month?+
Take the penny if the month has at least 28 days: it passes $1 million on day 28 and reaches $5.37 million on day 30 and $10.7 million on day 31. For a 27-day doubling it would be only about $671,000.
Why does the penny grow so slowly at first?+
Exponential growth adds a fixed percentage, not a fixed amount. While the base is tiny, doubling adds only cents or dollars; by day 20 it is still $5,242.88. Most of the value arrives in the final week, which is why patience matters with compound interest.
What interest rate would double money every day?+
Doubling daily is a 100% daily return, equivalent to an astronomically large annual rate. Real savings and investments compound at a few percent a year, so money takes years to double — about 72 ÷ rate years, by the rule of 72.
Is day 1 one cent or two cents?+
This calculator counts day 1 as the original penny, so day 30 is the penny doubled 29 times. If you double on day 1 as well, the final amount is twice as large ($10.7 million) — the riddle is usually told the first way.