Penny Doubled Daily Calculator
See how a penny doubled every day grows exponentially.
Calculate how much any starting amount becomes when doubled daily for any number of days.
The classic “penny doubled every day for 30 days” puzzle is one of the most powerful demonstrations of exponential growth — a concept that is fundamental to investing, compound interest, and understanding how wealth accumulates over time.
The Famous Example
Would you rather have $1,000,000 today, or a penny doubled every day for 30 days?
Most people instinctively choose the million dollars. The math reveals why that is the wrong choice:
| Day | Amount |
|---|---|
| 1 | $0.01 |
| 5 | $0.16 |
| 10 | $5.12 |
| 15 | $163.84 |
| 20 | $5,242.88 |
| 25 | $167,772.16 |
| 29 | $2,684,354.56 |
| 30 | $5,368,709.12 |
A penny doubled daily for 30 days becomes over $5.3 million — more than 5 times the million dollar alternative.
The Formula
For a starting amount A doubled for n days:
Final Value = A × 2ⁿ
For continuous compounding more generally: Final Value = A × (1 + rate)ⁿ
Why This Matters for Investing
This example illustrates why compound interest is so powerful in long-term investing. While no investment doubles every day, the principle holds:
- 7% annual return → doubles every ~10 years (Rule of 72: 72 ÷ 7 ≈ 10)
- 10% annual return → doubles every ~7 years
- 14% annual return → doubles every ~5 years
Starting early — even with a small amount — is far more valuable than starting later with a larger amount.
The Rule of 72
To quickly estimate how long it takes to double money at a given interest rate: Doubling Years ≈ 72 ÷ Annual Interest Rate (%)
Example: At 6% per year, money doubles in 72 ÷ 6 = 12 years.