The FIRE math.

Compounding

Returns earning returns. The curve does almost nothing, then almost everything.

Everyone knows compounding is powerful. Almost nobody internalizes where the power sits. It is not spread evenly across the years; it is stacked violently at the end. That's why the boring middle years feel like failure, and why quitting at year 12 is the single most expensive thing you can do.

The practical consequence: time in the market is not one input among several. It is the input. A 25-year-old saving $200 a month will likely beat a 40-year-old saving $600 a month, and no amount of clever stock-picking closes that gap.

It is the engine under your savings rate is the whole game.

Savings rate

The share of income you don't spend. The only variable that really moves your date.

This is the one that surprises people. Your savings rate does two things at once: it fills the portfolio faster and it shrinks the finish line, because the finish line is a multiple of your spending. Spend less and you need less. It works from both ends, which is why it dominates investment returns.

Starting from zero, at a 5% real return, needing 25× annual expenses:

Read the jump from 10% to 20%: it doesn't halve the wait; it cuts it by 15 years. Note also what's not in that table, your income. A high earner saving 10% retires later than a modest earner saving 50%. The rate is what matters, not the salary.

The honest caveat: this assumes a constant income, a constant real return, and no life. Nobody's path is this smooth. It's a compass, not a schedule.

Worked through in full in your savings rate is the whole game, and in the FIRE tracker.

Your FI number & the 4% rule

The portfolio that pays your expenses without you. Roughly 25 times what you spend in a year.

Invert a withdrawal rate and it stops being an income and becomes a target. Draw 4% and you need 25 times your annual spending. Every FI number you have ever seen is that one multiplication.

The arithmetic is solid. The confidence usually attached to it is not. Run the same 4% draw over thirty years across a plausible range of return and volatility assumptions and survival lands anywhere between 53.2% and 99.0%. That is a spread of 46 points, driven entirely by two numbers nobody can know in advance.

Treat 4% as a planning convention, not a promise, and remember it was calibrated on thirty year retirements. Over fifty years the rate that holds up about as well is 3.0%, which on the same portfolio is $30,000 rather than $40,000.

The full argument, including the one lever that is free: what a million dollars actually pays.

Real vs nominal returns

Nominal is the number on the statement. Real is what it buys.

Inflation is the opponent nobody plans against, because the loss never shows up as a line item. Note the math is division, not subtraction, 7% minus 3% is not quite 4%.

Why the numbers in what a million dollars actually pays are all stated after inflation.

The rule of 72

Divide 72 by the return to get the doubling time. Mental arithmetic, accurate enough.

Useful because it lets you sanity-check a claim in your head, in a conversation, without a spreadsheet.

Close enough to be worth memorizing, and it works in reverse: if someone promises to double your money in three years, they're implying a ~24% annual return. Now you know what to ask them.

Used throughout coast FIRE to check a target without a spreadsheet.

Sequence of returns risk

The order of returns is irrelevant while saving, and brutal once withdrawing.

This is the most under-taught idea in retirement planning. Two people can earn the identical average return over the identical decade and end up in different worlds, purely because of what happened first. Bad years early force you to sell more shares to fund the same spending, and those shares aren't there for the recovery.

The whole subject of the order your returns arrive in.