---
title: "Rule of 72 Calculator vs the Exact Answer | Interest Grove"
description: "How long until money doubles? Compare the rule of 72 with the exact ln 2 ÷ ln(1 + r) answer and the rules of 70 and 69.3, with an error table."
url: https://interestgrove.bond/rule-of-72-calculator/
---

# Rule of 72 calculator

Divide 72 by a yearly growth rate and you get roughly how many years it takes to double. Here is how rough, next to the exact answer and the rules of 70 and 69.3.

## Where 72 comes from

Money growing at a yearly rate r doubles when (1 + r)^n = 2, so the exact time is n = ln 2 ÷ ln(1 + r). For small rates ln(1 + r) is close to r, which gives 0.693 ÷ r: the rule of 69.3, exact for continuous compounding. With yearly compounding the true time runs a little longer, so of the three rules 69.3 is closest only below about 1%, 70 from about 1% to 5%, and 72 from about 5% up. It is exact near 7.85%, and 72 divides neatly by 2, 3, 4, 6, 8, 9 and 12.

Exact years to double = ln 2 ÷ ln(1 + r)Rate needed to double in n years = 2^(1 ÷ n) − 1

The rule is old: it appears in Luca Pacioli's *Summa de arithmetica*, printed in Venice in 1494.

Example: at 6% the exact time is ln 2 ÷ ln 1.06 = 11.90 years. 72 ÷ 6 = 12 is 0.9% too long; 70 ÷ 6 = 11.67 is 1.9% too short.

## Sources

- Investor.gov (U.S. Securities and Exchange Commission), glossary: [compound interest](https://www.investor.gov/introduction-investing/investing-basics/glossary/compound-interest), the growth the rule describes.
- ICAEW Library, [Summa de arithmetica](https://www.icaew.com/library/library-collection/historical-accounting-literature/highlights-of-the-collection/summa-di-arithmetica) (Luca Pacioli, Venice, 1494).

## Questions

**Does the rule work for inflation too?**

Yes. At 3% inflation prices double in about 72 ÷ 3 = 24 years (exactly 23.4), after which money buys half as much.

**What about monthly compounding?**

At the same stated rate, monthly compounding grows a little faster, so doubling comes slightly sooner, closer to the rule of 69.3. For an exact answer enter the effective yearly rate.

**Can I find the rate needed to double in a set time?**

Yes, with the second field. The exact rate is 2^(1 ÷ years) − 1; the shortcut is 72 ÷ years.