Retirement Math: How Much Is Enough, and How Long Will It Take

“How much do I need to retire?” has a real answer — not a vibe, an equation. Actually two equations, because the question has two honest framings. This module works both, in today’s money, and ends with the most underrated formula in personal finance: the one that maps your savings rate to your years of work remaining.

Frame 1: the expenses view — your number is 25× spending

The classic result comes from William Bengen’s 1994 paper and the 1998 Trinity study: historically, a retiree with a diversified portfolio (50–75% stocks) who withdrew 4% of the starting balance in year one, then adjusted that amount for inflation, survived every 30-year period in over a century of US market history (the 75/25 portfolio succeeded in 98% of historical windows).

Invert 4% and you get the rule’s famous form:

Spending of $40,000 a month → $480,000 a year → a target of $12 million (all in today’s pesos — we’ll handle inflation properly below). Notice it’s spending, not income, that sets the bar: every peso you don’t need each month cuts the target by 300.

Is 4% still right? The honest answer is “roughly, with error bars.” Morningstar’s 2025 State of Retirement Income put the safe starting rate at 3.9% for 2026 (it was 3.7% a year earlier) using forward-looking return estimates, while Bengen himself — with a broader asset mix — now argues for about 4.7%. Treat 3.5–4% as prudent, 5% as optimistic, and remember the rule assumes you never adapt spending — real retirees do, which buys slack.

Frame 2: the income view — replacing your paycheck

Pension systems and financial planners talk in replacement rates: what fraction of your pre-retirement income keeps your lifestyle? T. Rowe Price uses 75% as a starting point (you stop saving, stop paying payroll deductions, spend a bit less), with expert estimates ranging 55–80%. Fidelity’s milestone ladder makes the same idea concrete: to retire at 67 on savings that replace ~45% of income (a public pension covering the rest), hold 1× your salary by 30, 3× by 40, 6× by 50, 8× by 60, 10× by 67 — powered by saving 15% of gross income throughout.

The two frames are the same equation wearing different clothes: pick a retirement income, divide by the withdrawal rate, get a portfolio. The expenses view is more honest (you spend expenses, not income), but the income view is the language your AFORE speaks — which brings us to the uncomfortable local number.

Nominal vs. real: always compute in today’s money

Every number so far is in today’s money, and the way to keep it that way is to separate the two returns that get conflated in every retirement conversation. The nominal return is what your statement shows — the headline percentage your investments earn. The real return is what’s left after inflation, i.e. the growth in what your money can actually buy. The conversion (the Fisher equation) is:

A 9% nominal return with 4% inflation is a 4.8% real return — not 5%, and definitely not 9%. Over 126 years of data, the UBS Global Investment Returns Yearbook puts US equities at 6.6% per year real and world equities at ~5% real — which is why a ~5% real return (roughly 9% nominal at Mexican inflation) is the standard planning assumption for a diversified stock portfolio, and why I use it below. If you project at 10% nominal and forget the conversion, inflation quietly eats a third of your “plan” and the target that looked reachable isn’t.

The formula: savings rate → years of work

Here’s the engine. If you save a fraction $s$ of income, invest at real return $r$, and need $25\times$ your spending (which is $(1-s)$ of income), the years $t$ to reach the target from zero satisfy a clean closed form:

At $r = 5\%$ real, this produces the table that Mr. Money Mustache made famous:

Read it twice, because it’s the most important table in this track. Your savings rate is the only variable that appears on both sides of the ledger — saving more simultaneously builds the portfolio faster and shrinks the lifestyle the portfolio must fund. That’s why going from 10% to 25% doesn’t shave a few years off; it shaves nineteen. A raise you save entirely moves this number; a raise you spend entirely doesn’t move it at all.

The second half: your money doesn’t stop working when you do

Here’s the part most retirement explainers skip. Reaching your number isn’t the end of compounding — the portfolio keeps generating returns all through retirement. What changes is which portfolio: once you depend on the money for groceries, you can’t hold 90% equities through a 40% drawdown, so you shift toward bonds, CETES, and short-duration instruments. Safer means lower: think ~6.5% nominal, which at 4% inflation is only about 2.4% real — versus the ~5% real you earned while accumulating.

That one lower number defines the two ways to live off a portfolio:

Living off interest alone. You spend only the real return and never touch the principal. A $12M portfolio earning 2.4% real pays about $288,000 a year ($24,000 a month) forever, in today’s purchasing power, and your heirs get the full $12M. The catch is visible immediately: interest alone covers your desired spending only if your withdrawal rate is no higher than the retirement-phase real return — and 4% > 2.4%.

Eating capital (what the 4% rule actually assumes). You spend your desired amount $E$ while the remaining balance keeps earning $r$. The capital declines, but far more slowly than “savings ÷ spending” suggests, because every peso not yet spent is still compounding. Starting from portfolio $T$, the money runs out after

Run the module’s example through it: a $12M target, spending $480,000 a year, earning 2.4% real in retirement. Interest covers $288,000 of the $480,000; you eat capital for the rest — and the formula says the money lasts about 39 years, with roughly $3.7M still left after 30 years (today’s money). Without any post-retirement return, $12M ÷ $480,000 would last just 25 years. That’s the 4% rule seen from the inside: a withdrawal rate above the safe real return is planned capital consumption, engineered to run out slower than you do — and it’s exactly why the Trinity study tests 30-year windows rather than eternity.

Try it live

The full lifecycle in one calculator: it computes your number, the years to reach it at your savings rate, and then the second half — what interest alone would pay you at the safer retirement return, how many years the money lasts at your desired spending, and how much capital is left along the way. The chart now shows both halves: the climb to your number, then the two retirement paths (living off interest vs. eating capital).

Next: where the long-term savings actually go — Module 6: ETFs and index investing.

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