Financial independence, retire early (FIRE) sounds like a lifestyle, but at its core it is arithmetic. Three formulas answer most of the questions: how much you need, how much you can safely withdraw, and how quickly your savings rate changes the timeline. This guide walks through them with examples, drawn from the Personal Finance Minimalist Cheatsheet, which covers the math across three pages.

The Rule of 25: your target number

The Rule of 25 estimates how much you need invested to cover your living costs without a paycheck:

Target = 25 × annual expenses

If you spend $40,000 a year, your target is $1,000,000. This is the inverse of the 4 percent rule, explained next.

The 4 percent safe withdrawal rate

The 4 percent rule comes from the Trinity Study, which examined historical US stock and bond returns. It suggested that withdrawing 4 percent of a portfolio in the first year, then adjusting for inflation each year, historically lasted 30 years in most periods studied. Using the example above, 4 percent of $1,000,000 is $40,000 in year one.

Treat this as a planning guide, not a guarantee. Future returns, inflation and taxes may differ from the past, and some people choose lower rates for longer retirements.

Savings rate and time to independence

The higher your savings rate, the sooner you reach your target. The cheatsheet compares timelines at savings rates of 10, 25, 50 and 70 percent. The pattern is consistent: the gap between 50 and 70 percent saved is much larger than the gap between 10 and 25 percent, because a larger share of income reduces expenses and increases the amount invested.

The FIRE sheet also describes four common archetypes: Lean (lower spending), Fat (higher spending), Barista (part-time income alongside investments) and Coast (enough saved to let compound growth cover future needs).

Compound growth in one formula

A = P(1 + r/n)^(nt)

Here P is the principal, r the annual rate, n the number of compounding periods per year, t the years, and A the final amount. The Rule of 72 is a faster mental check: divide 72 by the annual return to estimate the years needed to double. At 8 percent, money roughly doubles in nine years.

Budgeting systems: choose the one you will follow

  • 50/30/20: allocate 50 percent of take-home pay to needs, 30 percent to wants and 20 percent to saving or debt repayment.
  • Zero-based budgeting: give every dollar a job until income minus planned spending equals zero.
  • Pay yourself first: move savings out automatically on payday, then spend what remains.
  • Envelope system: allocate cash or digital categories in advance and stop spending when a category runs out.

The cheatsheet matches personality types with systems. Minimalists often do well with pay yourself first, while people who overspend may prefer envelopes.

What drives your credit score

FICO Score 8 weighs five factors. Payment history carries the most weight, followed by credit utilization (the share of available credit you use), length of credit history, credit mix and new credit. Paying on time and keeping balances low relative to limits matter most for most people.

Credit building and repair have pitfalls, and not every tactic is appropriate for every situation. Check official sources such as your credit reports before acting.

This article is educational and not personal financial advice. Consider talking to a licensed advisor about your situation.

For the full formulas and worksheets, see the Personal Finance Minimalist Cheatsheet. Related: the finance formulas every student should know.