# The rule of 72

> Work out how long money takes to double, in your head.

Lesson 2 of 6 in [How money grows](https://learnfold.app/learn/money/), a free course from Learnfold.

How long does money take to double? Divide 72 by the yearly growth rate. That's the whole rule.

| Growth per year | 72 divided by the rate | Actual doubling time |
| --- | --- | --- |
| 3% | 24 years | 23.4 years |
| 6% | 12 years | 11.9 years |
| 8% | 9 years | 9.0 years |
| 12% | 6 years | 6.1 years |

Close enough to do on a walk, with no calculator.



Try 6%, then 24%. The blue estimate stays close, but the purple exact answer shows where the shortcut drifts.

### Doublings stack

The rule gets interesting when you count doublings. At 6%, \$10,000 becomes about \$20,000 after 12 years, \$40,000 after 24, and \$80,000 after 36.

Look at what each doubling adds. The first adds \$10,000. The third adds \$40,000. Each doubling adds more than all the earlier ones put together. That's why cutting a timeline short hurts so much. The years you lose come off the end, where the doublings are biggest.

It also explains why a small difference in rate turns into a big difference in money. Over 36 years, 4% a year doubles your money twice, so you end with 4 times what you started with. At 8% it doubles four times, and you end with 16 times. Twice the rate, four times the result.

### Why 72

The exact answer takes logarithms. For very small rates the magic number is closer to 69, and at the rates people usually care about, 72 lands close. It also divides evenly by 2, 3, 4, 6, 8, 9, and 12, which is the real reason people use it. The rule drifts at high rates. At 24% it says 3 years, and the real answer is a little over 3.

### It works against you too

Anything that compounds follows the rule, including things that cost you.

- Credit card debt at 24% a year doubles in about three years if none of it is paid off.
- Prices rising 3% a year double in about 24 years, which means cash buys half as much. The next lesson is about this.
- Fees compound against you as well. They get their own lesson in the next chapter.

### Try it in your head

At 9%, how long does money take to double? 72 divided by 9 is 8 years.

How much does money grow in 40 years at 6%? It doubles every 12 years, so that's three and a third doublings. Two, four, eight, and a bit more. Roughly ten times what you started with. The exact figure is 10.3.

Once this clicks, you'll start doing it everywhere. A loan rate, a pay rise, a headline about prices. Divide 72 by the number and you know how fast it doubles.

### Rabbit holes

> How do I flip the rule of 72 to find the rate I'd need to double my money by a certain age?

> Why does the rule of 72 get less accurate at very high rates?

> How long would it take a country's economy to double at 2% growth versus 7%?

Read online: https://learnfold.app/learn/money/rule-of-72/