FIRE variants and the maths: savings rate, the 25x rule and German cost realities
Turn a savings rate into years of work, apply the 25x rule, and compare lean, fat, coast and barista FIRE with realistic German living costs.
What you will learn
- How the savings rate, not the income, decides how many years you must work before a portfolio can carry you.
- How to derive the 25x rule from a withdrawal rate and why 3.5 percent turns it into roughly 28.6x.
- What lean, fat, coast and barista FIRE mean and which numbers separate them.
- Which German costs (health insurance, pension gap, rent) must be in the target before it is credible.
Explanation
FIRE stands for Financial Independence, Retire Early. Financial independence (FI) means that your assets can cover your living costs without wages; retiring is optional.
The savings rate is savings divided by net income. It matters twice: a higher rate builds the portfolio faster and makes the target smaller. Budgeting was covered in the course Personal Finance & Money Management; here we only use the resulting numbers.
The 25x rule says: target portfolio = yearly spending × 25. It is simply the inverse of a 4 percent withdrawal rate (1 / 0.04 = 25). The 4 percent figure comes from historical US studies that lesson 2 examines critically. At 3.5 percent the multiple becomes 1 / 0.035 = 28.6x; at 3 percent 33.3x. Compute the multiple from the rate you actually trust.
The years-to-FI formula. Set net income to 1. With savings rate s, yearly spending is (1 − s) and the target is (1 − s) / w, where w is the withdrawal rate. Saving s per year at a real return r grows to s × ((1 + r)^n − 1) / r. Solving for n:
n = ln(1 + r × (1 − s) / (w × s)) / ln(1 + r)
Using a real return (after inflation) of 4 percent and w = 4 percent, starting from zero:
| Savings rate | Years to FI |
|---|---|
| 10 % | 58.7 |
| 20 % | 41.0 |
| 30 % | 30.7 |
| 40 % | 23.4 |
| 50 % | 17.7 |
| 60 % | 13.0 |
| 70 % | 9.1 |
The table is independent of income: a nurse and a lawyer with the same savings rate need the same number of years. The 4 percent real return is an assumption; at 2 percent every row gets longer.
Variants. Lean FIRE targets a frugal budget with little room for shocks. Fat FIRE targets a comfortable budget with a safety margin. Coast FIRE means you have saved enough that, with no further contributions, compound growth should reach the target by normal pension age; you only need to earn your current spending. Barista FIRE means the portfolio covers part of the spending and a part-time job the rest, including, importantly in Germany, employer-subsidised health insurance.
German cost realities that belong in the target: (1) health and long-term care insurance, which an early retiree pays in full, typically several hundred euros per month (lesson 7); (2) the statutory pension gap, because early exit stops contributions (lesson 8); (3) rent or property upkeep; (4) taxes on withdrawals (lessons 6 and 7). A target built from today's take-home spending alone is usually too low.
Worked example
Hypothetical example: Lena, 35, net income €3,500 per month, spending €2,100, savings €1,400. All numbers are round and ignore taxes on the portfolio, fees and future salary changes.
- Savings rate: 1,400 / 3,500 = 40 percent.
- Yearly spending: €2,100 × 12 = €25,200.
- Target at 4 percent: €25,200 × 25 = €630,000. At 3.5 percent: €25,200 / 0.035 = €720,000.
- Years from zero at 4 percent real return and 4 percent withdrawal: n = ln(1 + 0.04 × 0.6 / (0.04 × 0.4)) / ln(1.04) = ln(2.5) / 0.0392 = 23.4 years, so FI at about 58.
- Realistic correction: adding €450 per month for health insurance and €150 for pension-gap savings raises spending to €2,700, the yearly figure to €32,400 and the 25x target to €810,000, which pushes the horizon well past 30 years.
- Coast FIRE check: if Lena already had €194,000 invested, €194,000 × 1.04^30 = €194,000 × 3.243 = about €629,000 at 65. She could stop saving today and still reach the original target at 65, as long as the 4 percent real return holds.
Excluded: taxes on gains, fund costs and the statutory pension, which would lower the needed portfolio after 67.
Common mistake
Practice activity
On paper: Jonas earns €4,000 net and spends €2,400. He wants a 3.5 percent withdrawal rate and expects 4 percent real return. (a) Savings rate. (b) Target portfolio. (c) Years to FI from zero with w = 0.035. (d) For coast FIRE at 40 with the target at 67 (27 years), how much must be invested at 40?
Show solution
(a) 1,600 / 4,000 = 40 percent. (b) €28,800 / 0.035 = €822,857, about €823,000. (c) n = ln(1 + 0.04 × 0.6 / (0.035 × 0.4)) / ln(1.04) = ln(1 + 1.714) / 0.0392 = 0.9985 / 0.0392 = 25.5 years. (d) €822,857 / 1.04^27 = €822,857 / 2.883 = about €285,400.
Limitations: constant real return, no taxes, fees or salary growth; real markets deliver returns in an irregular order, which lesson 3 shows is critical.
Key takeaways
- Years to FI depend on the savings rate and the assumed real return, not on the income level.
- The 25x rule is just 1 / withdrawal rate; use the multiple that matches the rate you trust.
- Coast and barista FIRE keep some earned income or time in the plan and so reduce the required portfolio.
- In Germany, health insurance, the pension gap and taxes must be inside the budget before you multiply.
Next step
Lesson 2 examines where the 4 percent figure comes from, which assumptions it carries and what international and German data say about it.
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