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Keith So
Keith So

Posted on • Originally published at boring-math.com

The Math Behind Early Retirement (FIRE) And What Most Calculators Get Wrong

You've probably seen the FIRE pitch: save aggressively, invest, retire at 40. The subreddits are packed with spreadsheets and projections. But most back-of-napkin FIRE math makes the same mistakes, and they compound badly over a 20-year horizon.

Let's break down the actual math, where the popular shortcuts fail, and how to run the numbers properly.

The Core FIRE Equation

FIRE boils down to one question: how many years until my investment portfolio covers my annual spending?

The classic rule of thumb is the 4% rule (from the 1998 Trinity Study). If your annual expenses are X, you need 25X saved. That's it. Simple division.

FIRE number = Annual expenses / 0.04
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Spending 30,000/year? You need 750,000.

But this formula hides three assumptions that quietly wreck projections.

Mistake #1: Ignoring Inflation During Accumulation

The 4% rule accounts for inflation-adjusted withdrawals in retirement, but most people forget inflation during the savings phase.

If you earn 60K and spend 30K today, you're saving 30K/year. But in 15 years at 3% inflation, that same lifestyle costs 46,739. Your FIRE number just jumped from 750K to 1.17M.

Future expenses = Current expenses x (1 + inflation)^years
Adjusted FIRE number = Future expenses / withdrawal_rate
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This alone adds 3-7 years to most projections. Try it with real numbers

Mistake #2: Using Average Returns Instead of Sequence of Returns

Markets don't return a steady 7% per year. They crash, they spike, they go sideways.

A portfolio averaging 7% over 30 years might look like:

Scenario Year 1-5 avg Year 6-30 avg Final value (500K start)
Steady 7% 7% 3.81M
Early crash -8% 9.4% 2.94M
Late crash 9.4% 5.2% 3.12M

Same average. Different outcomes. The early crash scenario is the killer during retirement because you're selling low to fund expenses.

This is called sequence of returns risk, and it's why a single number like "7% growth" is dangerously misleading.

Mistake #3: Treating the Withdrawal Rate as Fixed

The 4% rule assumes a 30-year retirement. If you're retiring at 35, you need that money to last 50-60 years. The safe withdrawal rate drops.

Research from Wade Pfau and others suggests:

Retirement length Safe withdrawal rate
30 years 4.0%
40 years 3.5%
50 years 3.25%
60 years 3.0%

At a 3% withdrawal rate, your FIRE number for 30K/year spending isn't 750K. It's 1,000,000. That's a 33% increase from a single variable change.

Putting It All Together

A proper FIRE calculation needs:

  1. Current savings and monthly contribution
  2. Expected return (use real returns, net of inflation, around 4-5% historically)
  3. Current annual expenses inflated to your target retirement date
  4. Withdrawal rate adjusted for your expected retirement length
  5. Tax treatment of withdrawals (ISA vs pension vs general account matters hugely in the UK)

The formula for years to FIRE, accounting for compound growth on contributions:

Years = ln((FIRE_number * r + C) / (P * r + C)) / ln(1 + r)

Where:
  P = current portfolio value
  C = annual contribution
  r = real annual return (after inflation)
  FIRE_number = annual expenses / withdrawal rate
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This is a log equation, which means the relationship between savings rate and years to retirement is non-linear. Going from a 30% savings rate to 50% doesn't cut your timeline by a third. It might cut it in half.

The Savings Rate Curve

Here's what the numbers look like at a 5% real return, starting from zero:

Savings rate Years to FIRE (4% rule) Years to FIRE (3% rule)
20% 37 years 42 years
30% 28 years 33 years
40% 22 years 26 years
50% 17 years 21 years
60% 12 years 16 years
70% 9 years 12 years

The jump from 50% to 70% savings rate saves you 8-9 years. The math heavily rewards higher savings rates.

Run Your Own Numbers

I built a FIRE calculator that handles all of this: inflation-adjusted expenses, variable withdrawal rates, and compound growth on ongoing contributions. No signup, runs in your browser.

If you want to explore the components separately:

The Honest Take

FIRE math isn't hard. It's logarithms and compound growth. The hard part is the inputs: predicting returns, inflation, tax policy, and your own spending over decades.

Anyone who gives you a single number without showing sensitivity analysis is selling you a fantasy. Run the numbers yourself, stress-test the assumptions, and plan for the version where things don't go perfectly.

The spreadsheet doesn't care about your feelings. That's what makes it useful.

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