How the result is calculated
A number thirty-seven years away is hard to judge: will two and a half million dollars be a lot or a little? That is why the calculator shows every figure in today's money as well as on the statement, and why this guide spends as long on the inflation and withdrawal assumptions as on the growth loop itself.
B(t)B(t − 1) × (1 + g) + C(t)
Real balance(t)B(t) ÷ (1 + i)t
IncomePortfolio × w
FIRE numberDesired income ÷ w
- B(t)
- the balance at the end of year t; B(0) is what you have saved today
- g
- the annual return, as a decimal
- C(t)
- the contribution in year t, which rises each year by the contribution-increase rate
- i
- the inflation rate
- w
- the withdrawal rate in retirement
The return you enter is nominal, the percentage your statements will show. Inflation eats part of it, and the honest real return is not simply return minus inflation:
Real return(1 + g) ÷ (1 + i) − 1
Worked example
| Item | Amount | How it is obtained |
|---|---|---|
| Year 1 balance, age 31 | $68,425.00 | 52,500 × 1.07 + 12,250 |
| Year 2 balance, age 32 | $85,464.75 | 68,425 × 1.07 + 12,250 |
| Year 15 balance, age 45 | $452,679.68 | the same step repeated; growth that year is $28,813, more than twice the contribution |
| Portfolio at 67 | $2,605,873.13 | after 37 steps |
| Of which contributions | $453,250.00 | 37 × 12,250 |
| Of which growth | $2,100,123.13 | 2,605,873.13 − 453,250 − 52,500 |
| Portfolio at 67 in today's money | $872,923.03 | 2,605,873.13 ÷ 1.0337 |
| Annual income at 4% | $104,234.93 | 2,605,873.13 × 4% |
| Annual income in today's money | $34,916.92 | 104,234.93 ÷ 1.0337: the number to judge |
The income target of $59,500 in today's money needs 59,500 ÷ 4% = $1,487,500 in today's money, or $4,440,524.68 at the prices of the year you retire. On these inputs the portfolio reaches it at 80, thirteen years after the planned retirement age.
| Annual contribution | Portfolio at 67 | In today's money, and the age the target is reached |
|---|---|---|
| $6,000 | $1,603,764 | $537,234; target reached at 93 |
| $12,250 | $2,605,873 | $872,923; target reached at 80 |
| $18,000 | $3,527,813 | $1,181,757; target reached at 73 |
| $24,000 | $4,489,838 | $1,504,019; target reached at 67, the planned retirement age |
Reading the result
The headline is the portfolio at your retirement age, with its value in today's money directly beneath it. The Contribution shown selector sets how the contribution is entered and displayed, per month or per year; the projection itself is annual, so a monthly figure is the year's contribution divided by twelve, and the yearly amount is shown under the field so the two never drift apart. Annual income applies the withdrawal rate to that portfolio, again in both forms. You contribute and investment growth split the final balance into what you put in and what the market did, and the growth line carries the real return the Fisher relation gives.
The chart plots two lines. The nominal balance climbs steeply; the today's-money balance climbs more gently, and the gap between them is inflation. If you set a desired income, a dashed line marks the FIRE number in today's money, and the point where the lower line crosses it is your independence age. The table lists each year: your age, that year's contribution, the growth the portfolio earned, the nominal balance and its real value. Notice how growth overtakes the contribution, in the opening example around age 38, after which the portfolio adds more each year than you do.
What changes the result
The 4% rule is an American result
The withdrawal rate is the single most consequential assumption here, and the familiar 4% figure comes from the Trinity study, which used United States stock and bond returns since 1926 over a 30-year retirement. American markets had an unusually good century. Studies that repeat the exercise on other countries' returns generally land lower, so this calculator opens on 3.5% outside the United States and says why. The difference is not small: on 40,000 of income a year, 4% needs a million and 3.5% needs about 1.14 million.
The retirement age opens on the country's own pension age, which is not a constant either: it ranges from 60 to 67 across the countries here, and in several of them it is still moving, either on a published timetable or with life expectancy. Each country's page gives its age and the rule behind it.
What the state provides is not modelled
Every country here has a public pension, and in several of them it is the larger part of retirement income rather than a supplement to it. In the United States, Social Security is the floor underneath a 401(k) or an IRA, and the portfolio this calculator projects sits on top of it. Elsewhere the balance between the public scheme and your own savings can be very different; each country's page says how.
None of it is projected here, because doing so properly needs a contribution history this tool does not ask for. Treat the state pension as reducing the income your own portfolio has to provide: work out what the state will pay, subtract it from what you need, and enter the remainder as your income target.
Time, contribution and return
Small, early changes move the result far more than large, late ones, because every dollar contributed at 30 compounds for 37 years. A later retirement age adds both contribution years and growth years at the top of the curve, where each year is worth the most. A one-point change in the return, held for 37 years, moves the final balance by roughly a quarter.
What is not included
- Tax. Contributions may be pre- or post-tax and withdrawals may be taxed. The projection is gross; a rough adjustment is to reduce the income by your expected retirement tax rate.
- State pensions and Social Security. They reduce the income your portfolio has to provide. Subtract them from the income you enter.
- Employer matching. Add it to your contribution; it is money going into the account.
- Fees. A fund charging 0.5% a year turns a 7% return into 6.5%. Enter the net figure.
- Sequence of returns. Markets do not return 7% every year. A bad run just before retirement hurts far more than the same run twenty years earlier. Treat the result as a central estimate and test lower returns.
- Contributions after retirement. The FIRE-age search assumes you keep contributing at the same rate past your planned retirement age; if you would stop, the real independence age is later.
Using the result
Look at the today's-money figures first: the real balance and the real income. If they fall short of what you want, the calculator makes the trade-offs visible: a later retirement age, a higher contribution, a rising contribution as your salary grows, or a lower income target. Raise the contribution a little and watch the age at which the target is reached move; it is the most direct lever you have.