Divide 72 by the annual percentage rate to estimate the years until money doubles. At 8%, that is about 9 years.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Why it works
It is a shortcut for the logarithm that solves the compound interest equation. It is accurate enough for rates between about 4% and 12%.
It runs both ways
The rule also gives doubling time for debt, and, using inflation, how long until prices double.
Doublings compound
Four doublings is sixteen times, not eight. Each doubling acts on everything accumulated before it.
Start early
The last doubling adds more than all the earlier ones combined. Reaching one extra doubling is what an early start buys.
Its limits
The rule assumes a steady rate and no deposits. It estimates rather than computes.
The rule of 72
Dividing 72 by the annual percentage rate approximates the years to double. At 6%, roughly twelve years. It is an approximation that works well for rates between about 4% and 12%.
Why it works
It comes from the logarithm in the compound growth formula, with 72 chosen because it divides evenly by many small numbers. It is a mental arithmetic convenience derived from an exact relationship.
It applies to debt as well
An unpaid balance at 24% doubles in about three years. Applying the rule to a credit card rate is one of the quickest ways to see why carried balances become unmanageable.
Time is the dominant variable
In compound growth, the number of doublings matters more than the rate, and doublings depend on time. That is the arithmetic reason starting earlier has such a large effect on a long-horizon balance.
Step 2: Try It Yourself
Tap and try it out.
Start
1 doubling
2 doublings
3 doublings
3 doublings has the most. It has 7 more than Start.
Step 3: Watch an Example
One step at a time.
Watch Sana Compare Two Starting Ages
Two savers each put in $10000 at 8%, one at 25 and one at 34. Both stop at 61.
- Step 1
At 8% the doubling time is 72 ÷ 8 = 9 years.
Step 4: Your Turn
Practice makes it stick.
The Doubling
Problem 1 of 2
At 6% a year, how many years until money doubles?
years
The Four Doublings
Problem 2 of 2
$10000 after 4 doublings. What is the amount, in dollars?
dollars
Estimate the Time
1 of 8
At 8%, years to double?
2 of 8
At 9%, years to double?
3 of 8
At 4%, years to double?
4 of 8
$5000 after 3 doublings. Amount in dollars?
5 of 8
At 8% over 36 years, how many doublings?
6 of 8
At 3% inflation, years until prices double?
7 of 8
Match each rate with its doubling time.
Tap a card on the left to start.
8 of 8
$2000 after 4 doublings. Amount in dollars?
Step 5: Quick Check
Show what you know.
Question 1 of 2
At 12% a year, how many years until money doubles?
Question 2 of 2
Why does starting early matter so much?
What You Learned
- Divide 72 by the rate to estimate years until doubling.
- Doublings compound: four doublings is sixteen times.
- The final doubling is the largest, which is why starting early wins.