Rule of 72 Calculator
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The "Back-of-the-Napkin" Investing Trick
In the world of finance, calculating Compound Interest usually requires complex logarithmic equations or a spreadsheet. But what if you are at a dinner party, or looking at a billboard ad for a bank, and want to know if an investment is good?
You use the Rule of 72. It is the most famous mental math shortcut in investing.
This rule answers a single, powerful question: "Given a specific interest rate, how many years will it take for my money to double?"
The Formula
The math is shockingly simple. You take the number 72 and divide it by your annual rate of return.
Example 1 (The Stock Market):
Historically, the S&P 500 returns about 10% per year.
72 ÷ 10 = 7.2 Years.
If you invest $10,000 today, it will likely become $20,000 in roughly 7 years.
Example 2 (High Yield Savings):
A typical bank savings account offers 0.5% interest.
72 ÷ 0.5 = 144 Years.
This highlights the devastating cost of keeping cash in a low-yield account.
Why "72"? Why not 100?
You might think we should use 100 because percentages are out of 100. However, the math of compound interest involves natural logarithms (ln).
The actual natural logarithm of 2 (doubling) is approximately 0.693. This suggests we should use a "Rule of 69.3." However, 69.3 is a terrible number for mental math.
Mathematicians chose 72 because it is close to 69, but it has many more divisors. You can cleanly divide 72 by 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. This makes it perfect for doing math in your head without a calculator.
Accuracy Check: When does the rule fail?
The Rule of 72 is an estimation. It works best for interest rates between 6% and 10%. As you move away from that "sweet spot," it becomes less accurate.
| Interest Rate | Rule of 72 (Est.) | Exact Math | Error |
|---|---|---|---|
| 2% | 36.0 Years | 35.0 Years | Off by 1.0 Yr |
| 8% | 9.0 Years | 9.006 Years | Perfect |
| 25% (Credit Card) | 2.88 Years | 3.10 Years | Less Accurate |
| 50% (High Risk) | 1.44 Years | 1.70 Years | Very Inaccurate |
Variations: The Rule of 69, 70, and 115
Depending on what field you are in, you might hear slightly different versions of this rule.
1. Rule of 69 (or 69.3)
Used by: Bankers and Financial Analysts.
This is used for Continuous Compounding. It is mathematically the most precise version but harder to calculate mentally.
2. Rule of 70
Used by: Economists.
This is commonly used to calculate Inflation. "How long until the purchasing power of the dollar is cut in half?" At 3% inflation, 70 ÷ 3 = 23.3 years.
3. Rule of 115
Used by: Aggressive Investors.
This tells you how long it takes to Triple your money (3x).
Formula: 115 ÷ Rate = Years to Triple.
At 10% return, your money doubles in 7.2 years, but triples in 11.5 years.
The Dark Side: The Rule of 72 and Debt
Compound interest works both ways. While investors use this rule to build wealth, credit card companies use it to build their wealth off you.
If you have a credit card with a 24% APR and you don't pay it off, your debt will double in just 3 years (72 ÷ 24 = 3).
This illustrates the urgency of paying off high-interest debt. A $5,000 balance today becomes $10,000 in 3 years, and $20,000 in 6 years if left unchecked. Use our Credit Card Calculator to see the damage.
How to Reverse the Formula
You can also use the rule backwards to find the Rate you need to hit a specific goal.
"I want my money to double in 6 years. What interest rate do I need to find?"
Math: 72 ÷ 6 Years = 12%.
Now you know you need to find an aggressive investment (like stocks or real estate) rather than a passive one (like bonds) to hit your goal.