# What does the rule of 72 say?

Uses the rule of 72 to estimate how many years money takes to double at a yearly return, or the return that doubles it in a given time, with the exact answer and the rules of 70 and 69.3.

- Page: https://www.acalculator.org/finance/rule-of-72-calculator
- JSON spec: https://www.acalculator.org/finance/rule-of-72-calculator.json
- Version: 9b13e71a96ab

## Default answer

Example with the default inputs (Find Years to double, Yearly rate of return 9%, Rule 72): By the rule of 72, the answer is about 8 years; exactly 8.04 with yearly compounding.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| find | Find | The years to double at a rate, or the rate that doubles in a number of years. |
| r | Yearly rate of return | The yearly interest rate or return, in percent. |
| t | Years to double | The number of years in which the money should double. |
| rule | Rule | The number to divide: 72 (the usual rule), 70, or 69.3 (close to continuous compounding). |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| estimate | Rule estimate | The rule number ÷ the rate (years), or ÷ the years (percent). |
| exact | Exact, compounded yearly | ln 2 ÷ ln(1 + r) years, or (2^(1/t) − 1) × 100 percent. |
| continuous | Exact, compounded continuously | ln 2 ÷ r years, or ln 2 ÷ t × 100 percent. |
| difference | Rule minus exact | The rule estimate minus the yearly-compounding answer. |
| unit | Answer in | Whether the answers are years or a yearly percent. |

## Method

Years ≈ 72 ÷ r and rate ≈ 72 ÷ t (or 70, 69.3). Exact, yearly: t = ln 2 ÷ ln(1 + r/100), r = (2^(1/t) − 1) × 100. Continuous: t = ln 2 ÷ (r/100), r = ln 2 ÷ t × 100.

## Assumptions

- The rate stays the same every year and all growth is reinvested.
- Taxes, fees and inflation are not taken off.

## Worked examples

1. find = years, r = 9%, rule = 72 gives estimate = 8, exact = 8.043232, continuous = 7.701635, unit = years. Source: SEC, Tips for Teaching Students About Saving and Investing: divide 72 by the expected rate of return; at 9% money doubles about every 8 years, https://www.sec.gov/investor/students/tips.htm.
2. find = years, r = 6%, rule = 72 gives estimate = 12, exact = 11.895661, difference = 0.104339. Source: SEC, Tips for Teaching Students About Saving and Investing: divide 72 by the expected rate of return; at 9% money doubles about every 8 years, https://www.sec.gov/investor/students/tips.htm.
3. find = rate, t = 10, rule = 72 gives estimate = 7.2, exact = 7.177346, continuous = 6.931472, unit = percent a year. Source: SEC, Tips for Teaching Students About Saving and Investing: divide 72 by the expected rate of return; at 9% money doubles about every 8 years, https://www.sec.gov/investor/students/tips.htm.
4. find = years, r = 7%, rule = 70 gives estimate = 10, exact = 10.244768. Source: SEC, Tips for Teaching Students About Saving and Investing: divide 72 by the expected rate of return; at 9% money doubles about every 8 years, https://www.sec.gov/investor/students/tips.htm (the same rule with 70).

## FAQ

### What is the rule of 72?

A quick way to estimate doubling time: divide 72 by the yearly rate of return in percent. At 9% a year, money doubles in about 72 ÷ 9 = 8 years (the SEC uses this example).

### How accurate is the rule of 72?

Close for rates from about 5% to 12%. At 9% the exact doubling time with yearly compounding is 8.04 years against the rule’s 8. At 2% the rule gives 36 years and the exact answer is 35.0; at 30% the rule gives 2.4 years and the exact answer is 2.64.

### How do I find the rate that doubles my money in a set time?

Divide 72 by the years. To double in 10 years you need about 72 ÷ 10 = 7.2% a year; the exact rate with yearly compounding is (2^(1/10) − 1) × 100 = 7.18%.

### What are the rules of 70 and 69.3?

The same idea with a different number. ln 2 × 100 = 69.3, so 69.3 ÷ r is almost exact for continuous compounding, and 70 is a round number close to it. 72 is popular because it divides evenly by 2, 3, 4, 6, 8, 9 and 12, and it is closer for yearly compounding at common rates.

### Does the rule of 72 work for inflation or debt?

Yes, for anything that grows at a steady percent. At 3% inflation prices double in about 24 years. A credit card balance at 18% that is not paid doubles in about 4 years.

### Why is the exact answer ln 2 ÷ ln(1 + r)?

Money growing at r a year is multiplied by (1 + r)^t after t years. It has doubled when (1 + r)^t = 2, so t = ln 2 ÷ ln(1 + r).

## Sources

- U.S. Securities and Exchange Commission (SEC), Tips for Teaching Students About Saving and Investing: the Rule of 72, divide 72 by the expected rate of return; at 9% an investment doubles about every 8 years. Retrieved 2026-10-02. https://www.sec.gov/investor/students/tips.htm