Methodology

The core projection

The deterministic projection advances month by month rather than using a closed-form formula, because month-by-month is the only way to handle contributions that change with age, one-off events, and phases like semi-retirement. Each month it applies growth, then contributions, then checks whether the balance has reached the target.

Two choices matter. Growth uses the twelfth root of the annual rate, not the annual rate divided by twelve; dividing would quietly turn a 5% assumption into 5.12% a year. And returns are real, meaning already net of inflation, so every figure the site reports is in today's purchasing power. Projections run to age 95.

Your target (the FIRE number) is annual spending divided by the withdrawal rate. At 4% that is 25× spending; at 3.5% it is roughly 28.6×. The choice of rate moves the target more than almost any other input, which is why it gets its own tool.

Monte Carlo simulation

Markets do not deliver an average return every year, and the order of returns matters enormously. The simulator runs your plan through many randomised return sequences (1,000 of them, with annual volatility fixed at 15%) and reports the share that still had money at the horizon.

The random number generator is seeded (mulberry32), so the same inputs produce the same fan chart every time. That is a deliberate trade: reproducibility over novelty, because a success rate that jiggles on every reload is impossible to reason about.

A success rate is not a probability of your future. It is the share of simulated futures, under one set of assumptions about volatility and average return, in which the money lasted. Treat 85% as “this plan has meaningful margin”, not as an 85% chance of anything.

Historical backtesting

The backtest replays your plan against approximate US real equity returns from 1900 onward, starting it in every available year and wrapping around at the end of the series. It answers a sharper question than averages can: would this plan have survived the actual past, including the sequences that broke people?

Limitation worth stating plainly: the return series is approximate and US-centric, in the tradition of the Shiller dataset. It is not a substitute for a full historical database, and a UK or European investor's real experience differed. Use it for shape and worst-case intuition, not for precision.

Mortality: the Rich, Broke or Dead view

Most retirement tools quietly assume you live to the horizon. That overstates the risk of running out, because a large share of the scenarios in which your money fails at 92 are scenarios you never reach. The mortality overlay uses a Gompertz–Makeham model calibrated to UK/US unisex life tables, splitting each future year three ways: still invested, alive but out of money, or no longer alive.

For couples the model tracks either-partner-alive survival, which is why a couple's horizon is longer than either individual's.

Withdrawal strategies

• Fixed real, the classic: take the same inflation-adjusted amount every year regardless of markets.
• VPW (variable percentage): take a percentage of the current portfolio, so income falls in bad years and rises in good ones. Never runs out; can pay uncomfortably little.
• Guyton-Klinger guardrails: start with a fixed withdrawal but cut or raise it when the withdrawal rate drifts outside a band. A middle path between the two above.

Other models

• Spending smile (optional Blanchett-style adjustment): 100% of target spending to age 74, 85% from 75–84, 80% from 85. Off by default, because assuming you will spend less is the optimistic choice.
• Debt payoff: monthly interest at APR÷12, minimums applied, surplus directed by strategy, and freed minimums rolled into the next target.
• Mortgage: the loan is amortised twice, with and without the overpayment, and the schedules compared.
• Pension bridge: splits pots into accessible and age-locked, then tests whether the accessible side survives to the unlock age.

Known limitations

These apply across the site and are not hidden in a footnote:

• No tax engine. Contributions and withdrawals are treated as net figures. Tax wrappers change real outcomes materially and are not modelled.
• Currency conversion uses a static table. Multi-currency net worth is converted at approximate fixed rates for display, so cross-currency totals drift from spot.
• Historical data is approximate and US-weighted, as described above.
• No product, platform or fund modelling; no fees are assumed beyond what you enter.
• The AI explainer describes, never advises. It is constrained to explain what your own numbers mean and is explicitly barred from recommending any action.

Corrections

If you find an error in any of this, please say so: hello@firemathlab.com. Models get corrected here rather than defended.