Retirement and FIRE

All three scenarios use today’s purchasing power and one input currency. Enter an effective real annual return, with inflation already removed. Saving: contributions at month-end, constant monthly return equivalent to the annual rate. Starting 1000 plus monthly 100 at 0% gives 2200 after one year. Starting balance plus future deposits is not your historical cost basis.

FIRE target = annual spending / chosen withdrawal rate. The first target month is found within 100 years; existing wealth may already cover it. A negative-return saving plan can approach a ceiling without reaching it; this is not reported as achieved. The chosen withdrawal rate is an assumption, not a validated safe rate or retirement guarantee.

Drawdown: take the requested amount at the start of each year, capped by available money, then apply the annual return. Real spending growth is extra growth beyond inflation. The graph begins at today’s wealth. The ledger preserves requested and paid withdrawals and shortfalls even after exhaustion. Example: 1000, withdrawal 100 and 10% return gives 990 then 979. Total shortfalls show the unfunded spending over the selected period.

Limits: amounts 0–10¹²; returns above −100% through 100%; saving in whole months up to 1200, drawdown in whole years up to 100. Years representing whole months may differ only within numerical rounding tolerance. Extremely small/large nonzero amounts use scientific notation; nonrepresentable values are rejected rather than reported as exhaustion. No taxes, fees, variable returns or sequence-of-returns risk. Deterministic scenarios, not forecasts.

Context: Investor.gov: managing lifetime income.