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Rule of 72

Simple mental math vs. logarithmic precision

Configuration

🔒 Compounding: Annually (Fixed)
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Primary Metric
Rule of 72
TIME TO DOUBLE
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At 7% interest
Doubling Milestones
Time Date Balance
Doubling Time
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Exact (Log)
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Triple Time
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10× Time
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Real Rate
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After-Tax Rate
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rule72 ÷ r%7.0% = t10.3 yr
Visualization
Edit Benchmark Assumptions
Projected Balance
Chart: projected balance.
Chart: projected balance.

🎯 Bear / Base / Bull Scenarios

Projected outcomes at ±30% of your current rate. Updates automatically from Tab 1 inputs.

🔢 Sensitivity Matrix — Doublings

Number of times your money doubles across different rates and time periods. Your rate is highlighted.

⚡ The Power of 1%

How each additional 1% return cuts your years to double. Your current rate is highlighted in cyan.

Chart: power1chart.

🏆 Journey to $1 Million

From your current balance, how long to reach each wealth milestone at your current rate?

Milestone Years Away Calendar Year Doublings

⏰ Cost of Waiting

Your projected balance in 30 years depending on when you start investing.

📊 30-Year Growth Breakdown

How your wealth compounds over 30 years, split into principal, simple returns, and compound-on-compound growth.

Chart: stacked chart.

🪜 Contribution Ladder

How different monthly contribution amounts affect your doubling timeline and 30-year balance.

Monthly Contribution Time to First Double Balance at 20yr Balance at 30yr

What is the Rule of 72?

The Rule of 72 estimates how long it takes to double your money: divide 72 by the annual return rate. At 8% returns, your money doubles in 72/8 = 9 years. At 6%, it takes 12 years. This quick mental math works best for rates between 4-12%.

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How to Use This Calculator

1

Choose Scenario

Select whether you want to calculate Time to Double, the Required Rate for a goal, or the time needed to reach a specific Target Balance.

2

Enter Parameters

Input your balance, rate, and optional monthly contributions. The 6-stat grid and formula strip update instantly. Click "Share URL" to save your scenario.

3

Explore Deeper

Switch to Scenario Analysis to compare Bear/Base/Bull outcomes and sensitivity. Use the Wealth Projector to see your journey to $1M and the cost of waiting.

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Frequently Asked Questions

Basics What is the Rule of 72 and how is it used?
The Rule of 72 is a quick mental math shortcut to estimate how many years it will take for an investment to double at a fixed annual interest rate. Simply divide 72 by your annual return percentage. For example, at an 8% return, your money doubles in about 9 years (72 / 8 = 9).
Strategy How accurate is the Rule of 72 compared to exact math?
It is remarkably accurate for interest rates between 6% and 10%. However, as rates rise or compounding becomes more frequent, the rule deviates from the exact logarithmic formula (t = log(2)/log(1+r)). The accuracy badge in the result panel shows you exactly how much the rule deviates at your current rate.
Advanced Does the Rule of 72 work for inflation calculations?
Yes. You can use it to estimate how long it takes for inflation to cut your money's purchasing power in half. At a 3% inflation rate, $100 will only buy $50 worth of goods in approximately 24 years (72 / 3 = 24).
Basics How does compounding frequency impact my doubling time?
The standard Rule of 72 assumes annual compounding. If your interest compounds monthly or daily, your money grows faster, effectively shortening the doubling time. This calculator's 'Exact' mode accounts for different compounding schedules to show the real power of frequent compounding.
Basics What is 'Tax Drag' and how does it change the calculation?
Tax Drag refers to the reduction in your effective return rate due to taxes on investment gains. In a taxable account, you must use your after-tax return rate (Nominal Rate × (1 - Tax Rate)) to find your true doubling time, which will be significantly longer than the pre-tax estimate.
Strategy What is the 'Rule of 69.3' and when should I use it?
Mathematically, the time to double for continuous compounding is precisely 69.3 divided by the rate. 72 is used for mental math because it has many more divisors, making it easier to calculate in your head for common rates like 2, 3, 4, 6, 8, 9, 12, and 18.
Basics What does the Scenario Analysis tab show?
The Scenario Analysis tab shows Bear, Base, and Bull cases (your rate ±30%), a 5×5 sensitivity matrix showing doublings across different rates and time periods, and a "Power of 1%" chart showing how each additional 1% return reduces your doubling time.
Basics What does the Wealth Projector tab show?
The Wealth Projector shows your journey to $1 million (how long to reach each milestone), the cost of waiting (what happens if you start 5 years earlier vs later), a 30-year compound growth breakdown, and a contribution ladder comparing different monthly contribution amounts.
Basics What is the faint dashed "ghost line" I see on the growth chart?
When you click into the Rate or Monthly Contribution fields to edit them, the calculator saves a snapshot of your current projection as a faint dashed line. This "ghost" lets you visually compare your previous scenario against the new one in real time as you type.
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Formula & Methodology

Formula & Methodology

Rule of 72

Doubling Time ≈ 72 ÷ Annual Return Rate

A mental math shortcut accurate for rates between 6-10%. Uses 72 because it has many convenient divisors (2, 3, 4, 6, 8, 9, 12).

Exact Logarithmic

Doubling Time = ln(2) ÷ ln(1 + r) = 0.6931 ÷ ln(1 + r)

The mathematically precise calculation. For 7% annual return: ln(2) ÷ ln(1.07) = 10.24 years vs Rule of 72 estimate of 10.29 years.

Rule of 69.3 (Continuous)

Doubling Time = 69.3 ÷ Rate

More accurate for continuous compounding since ln(2) ≈ 0.693. Used in academic finance but less practical for mental math.

Goal Time with Contributions

FV = PV × (1+r)^n + PMT × (((1+r)^n − 1) / r)

When monthly contributions are added, the future value combines compound growth on the initial balance with the annuity formula for regular payments.

About this calculation · Accuracy & Methodology

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Key Terms Explained

Rule of 72 A simplified formula for estimating investment doubling time. Divide 72 by the annual return rate to get approximate years to double.
CAGR Compound Annual Growth Rate — the annualized return that smooths out volatility. The rate used in Rule of 72 calculations for real-world investments.
Doubling Time The number of years required for an investment to grow to twice its current value at a given fixed rate of return.
Tax Drag The reduction in effective return caused by taxes on investment gains. Lengthens doubling time in taxable accounts vs tax-advantaged accounts (401k, Roth IRA).
Real Return The investment return after subtracting inflation. If nominal return is 8% and inflation is 3%, real return is approximately 5%.
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Real-World Examples

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Alex

Example 1: S&P 500 Index Fund

Rate: 10% historical average. Rule of 72: 72 ÷ 10 = 7.2 years to double. Exact: ln(2) ÷ ln(1.10) = 7.27 years. Starting with $10,000, you reach $20,000 in ~7.3 years.

Doubling Time at Various Rates

Annual ReturnRule of 72Exact (years)ErrorContext
2%36.0 yrs35.0 yrs+2.9%Government bonds
4%18.0 yrs17.7 yrs+1.9%Corporate bonds
7%10.3 yrs10.2 yrs+0.5%Balanced portfolio
10%7.2 yrs7.3 yrs-0.5%S&P 500 average
15%4.8 yrs5.0 yrs-3.2%Growth stocks
25%2.9 yrs3.1 yrs-7.3%Speculative (less accurate)
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The Rule of 72: A Complete Guide

Why 72?

The number 72 is not mathematically precise — ln(2) is approximately 69.3. However, 72 is used because it is divisible by 2, 3, 4, 6, 8, 9, and 12, making mental math fast for common interest rates. The error between Rule of 72 and exact calculation is less than 1% for rates between 6-10%, which covers most real-world investment scenarios.

Beyond Doubling

The Rule of 72 can be extended. To estimate tripling time, use 114 ÷ rate. For quadrupling, use 144 ÷ rate (since quadrupling is two doublings). These extensions maintain the same level of approximation accuracy and are useful for long-term retirement planning projections.

The Power of Starting Early

The Rule of 72 powerfully illustrates why starting early matters. At 8% annual return, money doubles every 9 years. Starting at age 25 gives you roughly 5 doublings by age 70 (a 32x multiplier). Starting at 35 gives you only 4 doublings (16x). That single decade difference means having half as much wealth at retirement, even with identical contributions and returns.

Adjusting for Reality

The basic Rule of 72 uses nominal returns, but real wealth creation requires adjusting for inflation and taxes. If your nominal return is 8%, inflation is 3%, and your effective tax rate is 15%, your after-tax real return is approximately (8% × 0.85) − 3% = 3.8%. Doubling time jumps from 9 years (nominal) to 19 years (real after-tax). This reality check is essential for honest financial planning.