Penny Doubled Daily Calculator
See how a penny doubled every day grows exponentially.
Calculate how much any amount becomes when doubled daily for any number of days — the power of compounding visualized.
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.