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.

Inflation

The rate at which money loses purchasing power. The reason a nominal return is not a return.

A portfolio returning 7% while prices rise 3% has grown your ability to buy things by roughly 4%. The first number is what statements show. The second is what happened.

Over long horizons the difference dominates. It is also why cash is the wrong tool for anything but near-term money: a savings account paying less than inflation is a guaranteed loss of purchasing power, stated in a way that looks like a gain.

Everything on this site that projects forward is stated in real terms for this reason. When we say 5% expected return, we mean after inflation, and a nominal figure would have to be meaningfully higher to say the same thing.

Why every projection here is stated after inflation: what a million dollars actually pays.

Basis point

One hundredth of a percentage point. The unit finance uses when a percent is too blunt.

A hundred basis points is one percent. Twenty-five is a quarter of a percent. The unit exists because differences that sound trivial as percentages are not trivial at all once compounded.

A fee difference of 150 basis points sounds like rounding. Over 30 years it costs 35.8% of everything the portfolio earned.

When you see a number quoted in basis points, someone is trying to make it sound small. Convert it and decide for yourself.

The clearest example: what investment fees really cost.

Opportunity cost

What you gave up by choosing this instead of the next best thing. The cost that never appears on a statement.

Every dollar has an alternative use, and the real cost of any decision is the best option you did not take. It is the most consistently ignored number in personal finance because nothing bills you for it.

It is why holding a large cash pile is expensive despite paying interest, why a down payment is not free money just because it becomes equity, and why paying off a low-rate mortgage early is a real decision rather than an obvious one.

Whenever an option looks costless, the cost is usually opportunity cost, and it is usually the largest number in the comparison.

Applied to the largest purchase most people make: buying a house is a trade.