Rule of 72 calculator

The rule of 72 is a quick way to guess how long money takes to double: 72 ÷ the yearly rate. Enter a rate to check the guess against the exact answer, or enter the years you have to see the rate it takes.

For any fixed yearly rate: savings, loans or inflation · Free, no sign-up · The formula

What do you know?

Your yearly rate

Use a fixed yearly rate, like an account's APY or a loan's APR.

At the 4% a year you entered, compounded yearly, money would double in

17.7 years

The quick rules, next to the exact answer:

Rule of 7218.0 years0.3 years too long

Rule of 7017.5 years0.2 years too short

Rule of 69.317.3 years0.3 years too short

Hypothetical illustration based on your inputs. Not a prediction, a recommendation, or the performance of any Amaltash strategy.

How it works: the exact answer uses the fixed yearly rate you enter, compounded once a year. The rules of 72, 70 and 69.3 are quick estimates. Real rates change over time.

Results change each time you change an input.

Real rates change. Fees, taxes and penalties are not included, and a rate you are offered can differ from this one.

What is the rule of 72?

The rule of 72 is a shortcut for doubling. It tells you about how many years an amount needs to double at a fixed yearly rate:

t \approx \dfrac{72}{R}

In words: Split 72 by the yearly rate, written as a plain number. The answer is roughly how many years it takes to double.

$t$: the years to double
$R$: the yearly rate as a plain number: 9% is 9

At 9% a year, 72 ÷ 9 = 8. So $1,000 would grow to about $2,000 in 8 years, if it earned a steady 9% that compounded each year.

How long will it take to double my money?

Find the yearly rate on your account or loan. If it shows an APY, use that.
Drop the percent sign. 4% becomes 4.
Split 72 by that number: 72 ÷ 4 = 18.
That is about 18 years. The calculator above gives the exact answer: 17.7 years.

Why 72?

First, 72 is easy to split. It divides evenly by 1, 2, 3, 4, 6, 8, 9, 12, 18, 24 and 36, so you can do the math in your head.

Second, it sits close to the true math. Here is the exact time to double:

t = \dfrac{\ln 2}{\ln(1 + r)}

In words: Take the natural log of 2. Divide it by the natural log of 1 plus the rate. That gives the exact years to double.

$t$: the exact years to double
$\ln$: the natural log, a key on most phone calculators
$r$: the yearly rate as a decimal: 6% is 0.06

ln 2 is about 0.693, and for small rates ln(1 + r) is close to r. That makes the answer close to 69.3 ÷ rate. Moving up to 72 makes up for interest added only once a year, and makes the rule fit best near 8%.

Where the rule of 72 is off

The rule is a guess. It hits closest near 8%. Below that, it says a little longer than the truth. Above it, it says shorter, and the miss grows as rates climb. Here are the guesses next to the exact years, with interest added once a year:

Rate per year	72 ÷ rate	70 ÷ rate	Exact years
1%	72.00	70.00	69.66
3%	24.00	23.33	23.45
5%	14.40	14.00	14.21
9%	8.00	7.78	8.04
12%	6.00	5.83	6.12
18%	4.00	3.89	4.19
24%	3.00	2.92	3.22
36%	2.00	1.94	2.25

At 36%, the rule says 2 years, but it really takes 2.25. That is a quarter of a year too soon.

The rule of 70 and the rule of 69.3

Some people put 70 or 69.3 on top instead of 72. It is the same idea with a different number.

Rule of 72: best when interest is added once a year, and the easiest to split.
Rule of 70: a round number that splits evenly by 2, 5, 7 and 10. Its answers land between the other two.
Rule of 69.3: exact when interest is added nonstop, called continuous compounding. 69.3 is 100 times ln 2. With daily or monthly interest, it comes very close too.

The rule of 114 and 144: tripling and quadrupling

The same trick works for bigger goals. Divide 114 by the yearly rate to guess the years to triple. Divide 144 by it to guess the years to grow four times.

Why those numbers? Growing four times is doubling twice, so 144 is 72 times 2. And 114 fits tripling best near 8%, just as 72 fits doubling best there. The exact years to triple use the same formula, with 3 in place of 2:

t = \dfrac{\ln 3}{\ln(1 + r)}

In words: Take the natural log of 3. Divide it by the natural log of 1 plus the rate.

Here are both rules next to the exact years, with interest added once a year:

Rate per year	114 ÷ rate	Exact years to triple	144 ÷ rate	Exact years to quadruple
3%	38.00	37.17	48.00	46.90
6%	19.00	18.85	24.00	23.79
8%	14.25	14.27	18.00	18.01
12%	9.50	9.69	12.00	12.23

See what money grows to after any number of years with the future value calculator →

The rule of 72 and inflation

Inflation is how fast prices go up. The rule works on it too: split 72 by the inflation rate to see how long until prices double. When prices double, each dollar buys half as much.

Say prices rose 3% every year. 72 ÷ 3 = 24, so in about 24 years, $100 would buy what about $49 buys today. Cash that earns less than inflation loses buying power, even while the number in the account goes up.

How fast debt can double

On debt, the rule works against you. Say a card balance grows at 24% a year and you make no payments. 72 ÷ 24 = 3, so the balance doubles in about 3 years. Many cards add interest daily, which is a bit faster: about 2.9 years. Fees make it faster still.

Most cards skip interest on new purchases when you clear the whole statement balance on time. Paying more than the minimum shrinks the amount that interest is charged on.

See what a card APR costs in a year with the APR calculator →

Working backward: the rate to double in a set time

Flip the rule to find a rate. Split 72 by the years you have. To double in 10 years takes about 72 ÷ 10 = 7.2% a year. The exact rate comes from this formula:

r = 2^{1/t} - 1

In words: Find the number that, multiplied by itself once for each year, makes 2. Take away 1. That is the exact yearly rate.

$r$: the exact yearly rate, as a decimal
$t$: the years you have to double

For 10 years, that is 7.18% a year. Here are a few more:

To double in	72 ÷ years	Exact rate
5 years	14.40%	14.87%
10 years	7.20%	7.18%
15 years	4.80%	4.73%
20 years	3.60%	3.53%

This is arithmetic, not a target. No rate is promised, and higher rates usually come with more risk of loss.

Try a plan on past market prices with the investment calculator →

The rate that links a start value to an end value has a name: CAGR, the compound annual growth rate.

Find the yearly rate between any two values with the CAGR calculator →

See how a fixed rate adds up year by year with the compound interest calculator →

Questions people ask

Is the rule of 72 accurate?

It is close for most everyday rates, and closest near 8%. Below 8% it guesses a little long. Above 8% it guesses short. At 36%, it says 2 years, but the exact answer is 2.25 years.

Can I use the rule of 72 for stocks?

Only as a what-if. The rule needs a steady rate. Stock prices move by a different amount each year, and they can fall, so no rule can tell you when a stock will double.

Does the rule of 72 work with monthly compounding?

Yes, but it guesses a little long. Money doubles a bit sooner when interest is added monthly. At 6%, that takes 11.6 years, not the 11.9 it takes with yearly interest. The rule of 69.3 lands closer: 69.3 ÷ 6 = 11.55.

Does it count taxes and fees?

No. Taxes and fees take a slice of the growth each year, so doubling takes longer. Use the rate you keep after them for a closer guess.

How long does it take to triple money?

Divide 114 by the yearly rate. At 5% a year, 114 ÷ 5 = 22.8 years. The exact answer, with interest added once a year, is 22.5 years. Some people use 115 instead, which gives 23 years.

Is the rule of 72 the same as compound interest?

No. Compound interest is how your money grows when interest is added to it. The rule of 72 is a shortcut that pulls one number out of that growth: the years to double. A compound interest calculator shows the balance for each year.

More calculators

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Reviewed by Tavish Sharma, CFA · Last reviewed Nov 12, 2026

Published by Amaltash Advisors LLC, an SEC-registered investment adviser

Sources

What is compound interest? (Rule of 72), Investor.gov, US Securities and Exchange Commission
What is a credit card interest rate? What does APR mean?, Consumer Financial Protection Bureau
How does my credit card company calculate the amount of interest I owe?, Consumer Financial Protection Bureau
What is a "daily periodic rate" on a credit card?, Consumer Financial Protection Bureau