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BlogFIRE outside the US: which parts of the maths travel, and which don't

Savings rate and years to financial independence: the arithmetic in any currency

The share of take-home pay that is saved sets most of the years to financial independence, whatever the currency or income. One table from 10% to 70% at three real returns, with the working one click away.

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The share of your take-home pay that you don’t spend decides most of how long you work. Saving 50% from zero takes about 16.6 years at a steady 5% real return (the return after inflation), or about 20.5 years at 2%. Both assume the pot is 25 times a year’s spending, which is a 4% withdrawal rate. This is arithmetic, not a forecast. How the 4% has held up is history: in Wade Pfau’s 19-country data (half stocks, half bills, retirements starting 1900–1981), it lasted 30 years in 96.3% of start years for a world portfolio and 78.0% for the world excluding the US (Pfau). Currency and the size of the pay don’t change the answer.

The table

Savings rate (share of take-home pay) Years at 5% real return Years at 3.5% Years at 2%
10% 51.4 63.5 86.1
20% 36.7 43.7 55.5
30% 28.0 32.3 39.0
40% 21.6 24.4 28.3
50% 16.6 18.3 20.5
60% 12.4 13.4 14.5
70% 8.8 9.3 9.8

Years from zero savings until the pot reaches 25 times a year’s spending, with the same real return every year. The 4% rate lasted 30 years in 96.3% of historical start years for a world portfolio and 78.0% for the world excluding the US (Pfau, above).

The see-saw

Saving is a see-saw. Every unit moved from spending to saving pushes on both ends at once: more goes into the pot each year, and the pot needed gets smaller, because there is less spending to cover. At 20%, a household spends 80 of every 100, so the target is 80 × 25 = 2,000 and it adds 20 a year. At 50%, the target is 50 × 25 = 1,250 and it adds 50 a year. That is why the years fall so fast as the rate rises.

Only ratios go into the calculation, so the currency drops out. Two households taking home 2,000 euros and 600,000 yen a month, both saving half, need the same number of years. Tax is already inside take-home pay; tax on later withdrawals is a separate matter, covered in Does the 4% rule work outside the US?

The three columns are real returns after inflation, from sources. 5% is the assumption in Mr. Money Mustache’s 2012 table (post; his text says about 16 years at 50%, his table rounds to 17), close to world equities’ 5.2% a year from 1900 to 2024 (Cambridge Judge Business School on the UBS Global Investment Returns Yearbook 2025). 3.5% is what world equities returned from 2000 to 2024 (UBS Yearbook 2025, summary edition, p. 13). 2% is an example of a low return; world bonds returned 1.7% from 1900 to 2024 (Cambridge write-up). The return matters most to people who save little: going from 5% to 2% adds 34.7 years at a 10% savings rate, but 1.0 year at 70%.

The working, step by step

Show the working for one row: 40% saved, 5% real return, 4% withdrawal rate

An example household saves 40 of every 100 it takes home.

  1. Spending: 100 − 40 = 60 a year.
  2. Target: 60 × 25 = 1,500. (25 is 1 ÷ 0.04.)
  3. Saving: the same 40 at the end of every year, invested at 5% a year after inflation. It is a fixed yearly payment, not one that grows.
  4. The question: after how many years does 40 a year reach 1,500? A fixed yearly payment P invested at rate r for n years reaches P × ((1 + r)ⁿ − 1) ÷ r.
  5. Set it equal: 40 × (1.05ⁿ − 1) ÷ 0.05 = 1,500.
  6. Divide by 40: (1.05ⁿ − 1) ÷ 0.05 = 37.5.
  7. Multiply by 0.05: 1.05ⁿ − 1 = 1.875, so 1.05ⁿ = 2.875.
  8. Solve for n: n = ln(2.875) ÷ ln(1.05) = 1.0561 ÷ 0.0488 ≈ 21.6 years.

A spreadsheet gives the same answer: =NPER(0.05, -40, 0, 1500) returns 21.6. At a 2% return: 1.02ⁿ = 1 + 37.5 × 0.02 = 1.75, so n = ln(1.75) ÷ ln(1.02) ≈ 28.3 years.

Every cell in the table uses years = ln(1 + r × T ÷ s) ÷ ln(1 + r), where s is the savings rate, T = (1 − s) ÷ 0.04 is the target in years of take-home pay, and r is the real return.

Other withdrawal rates change the target. At 3.5% (about 28.6 times spending), the 50% row at a 5% return takes about 18.2 years, not 16.6. At 3%, about 20.1. Both rates are below the world portfolio’s highest safe rate in Pfau’s table (3.58%), so for that portfolio they lasted 30 years in every start year from 1900 to 1981.

What the table leaves out

  • Steady returns. Real returns jump around: across the Yearbook’s countries, the yearly real return on equities since 1900 had an average standard deviation of 23.0% (UBS Yearbook 2025, summary edition, p. 7). No row is a date anyone can count on.
  • A start from zero. Existing savings shorten every row.
  • Tax on withdrawals, fees and public pensions. The hub shows the arithmetic.
  • The 4% rate. It lasted 30 years in 96.3% of start years for a world portfolio and 78.0% for the world excluding the US.

What these figures are, and what they leave out, is on the limitations page. None of this is a recommendation to save at any particular rate.

How we calculated this

  • Method: the end-of-year savings formula above, solved for years with a short script and checked against NPER; rounded to one decimal.
  • Fixed assumptions: a start from zero, a 4% withdrawal rate, pay and spending flat in real terms.
  • Sourced inputs: 5.2% and 1.7% (Cambridge), 3.5% and 23.0% (Yearbook summary, pp. 13 and 7), Mr. Money Mustache’s assumptions (2012), Pfau’s failure shares for 4% (world 3.7%, world excluding the US 22.0%; success = 100% minus these) and the world portfolio’s highest safe rate (3.58%).
  • Illustrations: the 2% return and the households.

This article is part of FIRE outside the US.

Written with AI assistance and reviewed by the Draupne editorial team. Published by Fri Vei AS.

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