APR Desk · Growth

Rule of 72 calculator

A shortcut for doubling, next to the exact time

The rule of 72 is a mental shortcut: divide 72 by the annual percent and you get a rough number of years for money to double. It is not the compound-interest formula. This page shows the shortcut and the exact time, which is the natural log of 2 divided by the natural log of one plus the rate.

Inputs

Result

Fill in the fields and press Calculate.

Disclaimer: Doubling time for a constant rate. It is not a return you will earn.

How to use

  1. Enter one annual rate as a percent. 8 means 8 percent a year.
  2. Press Calculate. The hero is the exact years to double.
  3. The other line is 72 divided by that percent.
  4. Use the compound-interest calculator if you want a balance, a contribution, or a compounding frequency.

How it's calculated

Shortcut years = 72 ÷ rate. Exact years = ln(2) ÷ ln(1 + rate ÷ 100). The exact line assumes the rate compounds once per year.

The shortcut is close for rates people often quote, and it drifts as the rate gets very small or very large. That is why both numbers are on the page.

Worked example

At 8 percent, 72 ÷ 8 = 9 years. The exact annual compound time is about 9.01 years. At 6 percent the shortcut is 12 years and the exact time is a little longer. The page prints both so you can see the gap for the rate you typed.

Assumptions

One constant annual rate, compounded yearly for the exact line. No contributions, no taxes, and no fees. A rate of zero or less is rejected because money would not double.

FAQ

Is the rule of 72 exact?

No. It is a shortcut. The hero number is the exact years at annual compounding.

Does this work for inflation?

You can type an inflation rate and read it as years for prices to double. It is the same arithmetic. It is not a forecast.

What about the rule of 69 or 70?

Those are other shortcuts. This page only divides by 72, and it always shows the logarithm beside it.

Can I see the dollar balance?

Not here. The compound-interest calculator takes a starting amount and a contribution.

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