Rule of 72: how long money takes to double.

01How it works

In plain words.

The exact doubling time is ln 2 divided by ln(1 + r). For everyday rates that is close to 0.72 divided by r, so 72 divided by the rate in percent gives the years. The same trick gives tripling (114) and quadrupling (144) times.

02Worked example

The default numbers, by hand.

At 12% a year: 72 / 12 = 6 years; the exact answer is ln 2 / ln 1.12 = 6.1 years. Over 30 years that is about 4.9 doublings: Rs 1 lakh becomes about Rs 30 lakh.

03Key concepts

What to know before you use it.

It works for anything that compounds

Prices at 6% inflation double in about 12 years. A credit card balance at 36% a year doubles in about 2 years.

Where it is accurate

The rule is closest between about 6% and 10%. At 1% or 25% use the exact figure on the right.

Good to know

• Compare doubling times instead of rates: 9.8% (the Nifty 50 TRI figure on this page, with its date) doubles in about 7.4 years; a 7% deposit assumption in about 10.2 years.
• The number of doublings, not the rate, is what makes long horizons so different.

04Assumptions

What the calculator assumes.

• A constant compound rate.

05Questions

Asked about the Rule of 72.