# Rule of 72 Calculator — How Long Until Money Doubles

> How many years until money doubles at any rate — and how fast a card balance doubles at its APR, or prices at inflation. The Rule of 72 vs the exact answer.

Canonical: https://thebrinklabs.com/tools/rule-of-72/  
Source: The Brink Labs · support@thebrinklabs.com · Last reviewed 2026-09-25

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Instrument 09 · Grow

## Rule of 72 Calculator — The Doubling Clock.

The Rule of 72 estimates doubling time by dividing 72 by the annual rate: at 8%, money doubles in about 9 years (exactly 9.01). It works for anything that compounds — investments, inflation and debt. At a 24% card APR, an unpaid balance doubles in about 3 years; compounded monthly, exactly 2.92.

Runs in your browser · Nothing uploaded or stored · Last reviewed 25 Sep 2026

### 01 — What Is Compounding

- **Annual rate of return** — Between 0.01% and 100%.
- **Starting amount**
- **Compounding** — Card debt compounds monthly; most return and inflation figures are quoted yearly.

### The Doubling Clock

Rule of 72

9.00

years

Exact

9.01

years

$10,000 becomes $20,000 in 9.01 years.

**−0.01 yrs · −0.1%** The rule’s error

**Rule of 72** Closest at this rate

| Milestone | When | Amount |
| --- | --- | --- |
| ×2 | 9.01 years | $20,000 |
| ×4 | 18.01 years | $40,000 |
| ×8 | 27.02 years | $80,000 |

Exact figures use ln 2 over the compounding factor; the rule divides 72 by the rate. Quadrupling is two doublings, eightfold is three.

In MyneWallet

## Compounding Starts With The Amount You Keep.

MyneWallet does not forecast markets. It does the part that makes doubling possible: finding a monthly amount to invest, and keeping the debts that double against you — with their rates — in plain view. On your phone, offline.

[Get MyneWallet on Google Play](https://play.google.com/store/apps/details?id=com.thebrinklabs.mynewallet.expensetracker&referrer=utm_source%3Dthebrinklabs.com%26utm_medium%3Dbridge%26utm_campaign%3Drule-of-72)

Android. Free to use; one-time unlock for the full engine. No subscription, ever.

Reading Your Result

## What The Number Is Telling You.

- **Error under 2%** — The mental shortcut is good enough at this rate.
- **Error 2–5%** — Close; use the exact figure for decisions.
- **Error above 5%** — Rates this high break the shortcut — trust the exact answer.

The Model

## The Formula, In Full.

The arithmetic this instrument runs, with a worked example. Its test cases are published on the [methodology page](https://thebrinklabs.com/methodology/#rule-of-72)

```text
Rule of 72: t ≈ 72 ÷ r (r in per cent)
Exact, yearly compounding: t = ln 2 ÷ ln(1 + r ÷ 100)
Exact, monthly compounding: t = ln 2 ÷ (12 × ln(1 + r ÷ 1200))
Continuous compounding: t = 69.3 ÷ r
```

**Worked example.** 8%: 9.00 (rule) vs 9.01 (exact). 24% debt, monthly: 3.00 vs 2.92. 3% inflation: 24.00 vs 23.45. 1%: 72.00 vs 69.66 — at low rates the Rule of 70 is closer.

**Assumptions and edge cases**

- The rate is constant for the whole period.
- No additions or withdrawals — pure compounding of one amount.
- Growth rates are inputs you choose, not forecasts; nothing here is investment advice.

| Edge case | Behaviour |
| --- | --- |
| Rate ≤ 0 (Growth, Debt) | "Never doubles at this rate"; no logarithm of zero. |
| Negative inflation | "Prices do not double while they fall." |
| Rate above 100% | Input capped at 100 with a note. |
| Very low rate (0.1%) | 693 years is shown plainly, not hidden. |

Questions

## Rule of 72, Answered Plainly.

### What is the Rule of 72?

The Rule of 72 is a shortcut for estimating how long something growing at a fixed annual rate takes to double: divide 72 by the rate. At 6 per cent, 72 ÷ 6 = 12 years. It works for investments, for debt that is not being paid down and for prices rising with inflation. It is an approximation of the exact formula, ln 2 ÷ ln(1 + r), and it is remarkably close for everyday rates.

### How accurate is the Rule of 72?

Very accurate between about 6 and 10 per cent, where it is within roughly 1 per cent of the exact answer, and most accurate near 8 per cent. It drifts at the extremes: at 1 per cent it overstates doubling time by 3.4 per cent, and at 24 per cent it understates it by about 7 per cent with yearly compounding. The calculator above shows the rule and the exact figure side by side.

### Should I use the Rule of 72, 70 or 69.3?

Use 69.3 for continuous compounding, 70 for low rates such as inflation or savings interest, and 72 for typical investment returns between about 6 and 12 per cent. The numbers differ because the true constant depends on how often interest compounds and on the rate itself. 72 survives as the favourite because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12.

### How do I use the Rule of 72 for inflation?

Divide 72 by the inflation rate to see how long it takes prices to double — which is also how long it takes cash to lose half its purchasing power. At 3 per cent inflation, prices double in about 24 years; at 6 per cent, in about 12. Money held in cash for those periods buys half as much at the end, which is why long-term savings need to earn more than inflation.

### How fast does credit card debt double?

Divide 72 by the APR. At 24 per cent, an unpaid balance doubles in about three years; with monthly compounding the exact figure is 2.92 years. That is the same arithmetic that makes investments grow, running against you. The [debt payoff calculator](https://thebrinklabs.com/tools/debt-payoff/) shows what it takes to stop it, and which balance to attack first.

### Who invented the Rule of 72?

The earliest known reference is in Luca Pacioli's Summa de arithmetica, published in Venice in 1494. Pacioli states the rule without deriving it, which suggests merchants of the time already knew it. The rule works because the natural logarithm of 2 is about 0.693, and 72 is a convenient number close to 69.3 that suits annual compounding.

### How long does it take to triple or quadruple money?

Use the same idea with a different constant: about 114 divided by the rate to triple, and 144 divided by the rate to quadruple. At 8 per cent, money triples in roughly 14.3 years and quadruples in 18. The exact versions are ln 3 ÷ ln(1 + r) and ln 4 ÷ ln(1 + r); quadrupling is simply two doublings.

Related Instruments

## Where People Go From Here.

- [Debt Payoff Calculator](https://thebrinklabs.com/tools/debt-payoff/) — Instrument 08 · Borrow. Avalanche or snowball, priced to the month and the cent.
- [Savings Goal Calculator](https://thebrinklabs.com/tools/savings-goal/) — Instrument 06 · Protect. One monthly figure for every known future cost.
- [Net Worth Calculator](https://thebrinklabs.com/tools/net-worth/) — Instrument 10 · Grow. Everything you own against everything you owe — and where it is heading.

Next in sequence

[Net Worth Calculator](https://thebrinklabs.com/tools/net-worth/)

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Educational and illustrative. Rates are assumptions you choose, not forecasts, and nothing here is financial or investment advice. The Brink Labs is a software lab, not a financial adviser.

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