Growth of a balance with regular contributions

A nominal annual rate compounded m times a year becomes an effective annual rate of (1 + r/m)^m − 1. We convert that to an equivalent monthly growth factor g = (1 + effective)^(1/12) so that monthly contributions are handled correctly whatever compounding frequency you choose.

Each month the contribution is added first and the balance is then multiplied by g - the standard annuity-due treatment, which matches a standing order paid at the start of the month. Balance after n months = P·gⁿ + C·((gⁿ − 1)/(g − 1))·g, where P is the starting amount and C the monthly contribution.

Inflation and real values

Real value = nominal value ÷ (1 + i)^years, where i is the inflation rate you enter. This is what the 'today's money' line on the retirement chart shows, and it is applied to the target income before the gap analysis compares it with your projection.

Required monthly contribution

To reach a target T in n months from a starting balance P, we solve the annuity-due formula for C: C = (T − P·gⁿ) ÷ (((gⁿ − 1)/(g − 1))·g). If the starting balance alone already exceeds the target, the required contribution is zero.

Time to reach a target

Solved by month-by-month iteration rather than a closed form, so that contribution changes and partial months are handled exactly. If a target is not reached within ninety years we report that rather than showing a misleading figure.

Withdrawal rates and FIRE numbers

A FIRE number is annual spending ÷ withdrawal rate. At 4% that is 25 times spending. Retirement income on the retirement calculator applies a 4% annual withdrawal to the projected pot and divides by twelve.

Coast FIRE discounts the full FIRE number back to today at your expected return over the years remaining until age 65. Lean FIRE uses 70% of your stated spending and Fat FIRE uses double it; both are conventions rather than definitions.

Returns on an existing investment

Total return = (ending value − amount invested) ÷ amount invested. Annualised return, or CAGR, = (ending ÷ starting)^(1/years) − 1. CAGR is the only fair way to compare holdings of different lengths.

What we deliberately do not model

Tax, fees, variable returns, market crashes, currency movements, state and employer pensions, and any country-specific account rule. Each of those is real and material, and each depends on circumstances we cannot see.

The projections are therefore a clean baseline rather than a forecast. Where a factor matters enough to change a decision - fees, inflation, withdrawal rate - we show it explicitly in the insights instead of burying it.

Rates and assumptions

We do not supply default market returns as predictions. The defaults in each calculator are illustrative starting points, and every one of them is editable. Any figure you keep is your assumption, not our forecast.

Frequently asked questions

Where do your default rates come from?

They are illustrative starting points for the calculator, not forecasts. Replace them with figures you are prepared to defend.

Do you account for tax?

No. Tax treatment depends on your country, account type and income, so every projection here is pre-tax.

Why do results differ slightly from other calculators?

Usually because of contribution timing - start of month versus end - or compounding frequency. Both are stated above so you can see exactly what we assume.

Can I check your maths?

Please do. Every formula is written out above, and the calculations run in your browser where you can inspect them.

Last reviewed 2026-09-18.