How the maths works

One engine, every question

All 28 calculators run the same month-by-month simulation, solved for whichever quantity the page is asking about. Growth solves for the ending balance; the savings goal solves for the contribution; the retirement page solves for the time. That is why the tools always agree with each other — feed the output of one into another and the numbers line up exactly.

Rates are annual and effective

When you type 7%, this site means your money is 7% larger after twelve months. To get there it uses a monthly rate of (1 + 0.07)^(1/12) − 1, which is about 0.5654%.

The common shortcut is to divide by twelve, giving 0.5833% a month. Compounded over a year that is 7.23%, not 7% — so a calculator using it is silently running your projection at a higher return than the one you asked for. Over thirty years the difference is thousands.

Contributions land at the end of the month

A standing order set up today makes its first payment at the end of the period, and that payment earns nothing before the month closes. This is what accountants call an ordinary annuity, and it is what actually happens.

Crediting contributions at the start of each period instead hands every single payment an extra month of growth. It makes the tool look better and your plan look easier.

Fees come off the return

A percentage charge applies to your whole balance every year, so it is modelled as a straight deduction from the growth rate: a 7% return with a 1% charge compounds at 6%. This is why the money lost to a fee is several times its headline percentage — each year's charge takes both the money and everything that money would have earned afterwards.

Inflation is reported, not baked in

Projections are shown in future money by default, with the inflation-adjusted figure alongside when you set a rate. Contributions can optionally be raised once a year in line with inflation, the way a pay rise works, rather than smeared across every month.

In the drawdown calculator inflation is not optional: the withdrawal rises every year, because modelling a flat income for thirty years assumes prices stand still.

Three scenarios, never one

Every projection is run at a cautious, middle and optimistic return simultaneously. Not a Monte Carlo simulation — those require assuming a volatility figure and a distribution shape, and produce scientific-looking output resting on inputs nobody labels as guesses. The reasoning is here.

Rounding

Money is shown to whole units and percentages to one decimal. A projection thirty years out reading "412,847.63" communicates a precision that nothing about the underlying problem supports.

What is deliberately not modelled

• Tax, in the investment tools. Rules vary by country, account type and income, so every projection here is gross and you apply your own situation. Tax is modelled in exactly one place — the take-home pay calculator — where every band is statutory, sourced, dated, and refuses to ship unverified.
• The order of returns. The curves are smooth. Real ones are not, and in drawdown the order matters enormously. This is the largest limitation of everything here.
• State and workplace pensions. Entitlements are too country- and career-specific to guess at.
• Currency movement. The currency selector changes the symbol and the formatting. It does not convert between currencies or model exchange-rate effects.
• Anything about whether a plan is wise. That is not an arithmetic question.

Testing

The engine is covered by an automated test suite that checks the rate conversion round-trips exactly, the closed-form solutions agree with the simulation, fees behave identically to an equivalent reduction in return, and empty or negative inputs produce a sensible zero rather than a NaN. If you find a figure that looks wrong, it is worth reporting — see About.