ebitdang.com · instrument

Compound Lab

The quick number first: a starting sum, a monthly habit, a growth rate. Below it, the full instrument — the years you feed a portfolio and the years it feeds you, across thousands of simulated futures or every market year since 1871. Everything in today's dollars, inflation already taken out.

Quick compound calculator

no simulation — the plain formula, compounded monthly
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Final value
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the full instrument

Same money, plus reality: uncertainty, sequence risk, withdrawal strategies — thousands of simulated futures, or a replay of every market year since 1871.

At retirement
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Plan success
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Spending at 90% success
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Compounding takes over
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median future 10–90% of futures steady-growth path what you deposited sample futures
what this is

One chart, both halves

Most calculators do one half of the job. Compound-interest calculators show money piling up and stop at retirement day; withdrawal calculators start there and ignore how you arrived. This one runs the whole arc — deposits and growth on the left of the divider, spending and (hopefully slow) drawdown on the right — so a change on either side immediately shows its effect on the other.

Every figure is in today's money: returns are real returns, with inflation already subtracted. When the chart says $500,000 at 65, that means the purchasing power of $500,000 now — not a diluted future number. It's the only honest way to show a 40-year plan, and it's why the return assumptions below look lower than the nominal figures funds advertise.

the elbow

The last decade does the heavy lifting

Compounding is famously an exponential curve, but lived from inside it feels like two different regimes. For years the dotted amber line — what you actually deposited — and your balance track each other closely, and saving feels like filling a bucket with a spoon. Then the regimes flip: the marked point on the chart is the crossover — the first year market growth adds more to the pot than your deposits do. From there the portfolio out-earns you at your own game, and the gap only widens.

That geometry has a practical edge: money deposited early is what gets the full runway. Moving your retirement age by two or three years moves the endpoint more than almost any realistic change in monthly saving, because it adds runway to everything already in. Drag the sliders and watch which inputs actually bend the curve.

why a fan, not a line

An average return is not a plan

The dashed line is what every simple calculator shows: the same return every year, forever. Real portfolios don't do that — and for a retiree, when the bad years land matters as much as how many there are. Two retirees can earn identical average returns over 30 years, but the one who hits a crash in the first five years — selling shares every month at depressed prices to eat — can run out of money while the other, living the same returns in reverse order, ends up rich. This is sequence-of-returns risk, and no single line can show it.

So instead of one future, the lab simulates thousands — or, in replay mode, relives every one history offers. Each one draws a random monthly return from your portfolio's distribution and replays your whole plan — deposits, pension, withdrawals. The green band is where 80% of those futures land; the ghost threads are individual futures, including the occasional one that dies on the axis. The plan success tile is simply the share of futures still solvent at your horizon, and the spending at 90% success tile inverts the question: it searches for the highest spending level at which 9 in 10 futures survive.

the assumptions

What the simulation believes

Three building blocks, mixed by your sliders and rebalanced continuously. Defaults are deliberately sober, close to century-scale global real returns rather than the US-only golden run — and you can edit all six numbers in the panel.

building blockreal returnvolatility
Stocks (global, broad)5.0%/yr±16%
Bonds (aggregate)1.5%/yr±7%
Cash, deposits0.2%/yr±1%

Correlations are fixed at 0.1 stocks–bonds, 0.2 bonds–cash, 0 stocks–cash; the blend line under the sliders shows the resulting portfolio return and volatility, including the small diversification bonus. Returns are drawn monthly as lognormal shocks; the fat tails switch swaps in a Student-t distribution (ν=4), which makes crash-like months far more frequent while keeping the same overall volatility. The steady-growth line uses the blend's compound growth rate, so it runs through the middle of the fan by construction.

The replay 1871→ switch abandons the statistical model entirely and asks history directly: your exact plan is started in every year since 1871 and lived through what markets actually did — annual real total returns for the S&P composite and for 10-year US Treasuries, built from Robert Shiller's public long-run dataset (bond returns priced from the yield series; cash held at 0% real). A plan that outlives the record wraps around to 1871, the standard trick among historical-replay calculators. Fewer futures — one per start year — and every year in them actually happened: 1929, 1966, 1973, and the booms in between. Start-year replay is essentially how the famous "4% rule" success rates were computed (on 1926-onward data with different bonds); set spending as a rate and you'll land in the same ballpark here.

the strategies

Fixed vs. flexible spending

Fixed spending is the assumption behind the famous 4% rule (Bengen 1994, the Trinity study 1998): pick a spending level, adjust it for inflation, never deviate. It's the cleanest way to measure a plan, and the harshest way to live one — nobody actually keeps spending through a 50% crash.

Flexible ±10% models what sensible retirees do instead, a simplified version of Guyton–Klinger guardrails: once a year, if withdrawals have drifted to more than 120% of your starting rate (portfolio shrank), cut spending 10%; below 80% (portfolio grew), raise it 10%. Small, rare adjustments — but because the cuts arrive exactly in the bad sequences, they raise survival rates dramatically. The trade is variance in your lifestyle: the hint box under the toggle shows how deep spending dips in the toughest tenth of futures.

the limits

What this can't tell you

  • The parameters are guesses. Nobody knows the next 40 years of returns; the defaults are informed history, not prophecy. Treat the fan as “what this class of assumption implies”, and stress-test with the editor.
  • Markets are wilder than any distribution here. Even the fat-tail mode draws independent months; real crises cluster, trend, and coincide with job loss. Consider the failure rates optimistic floors, not ceilings.
  • Taxes are not modelled. Depending on where you live, capital-gains tax on withdrawals can claim a meaningful slice; read results as pre-tax spending ceilings.
  • Life isn't a constant. Real plans have house purchases, inheritances, career breaks, kids. A constant monthly figure is a deliberate simplification.
  • The currency toggle changes labels, not markets. Returns are the same in every currency here; a real dollar, euro and pound investor lived slightly different histories.
  • Replay mode is US history. The S&P since 1871 is the best long record there is — and also one of the best-performing markets there ever was. The rest of the world's history has been less kind; treat replay success rates as the sunny end of the range.
  • This is an educational instrument, not financial advice. It shows the mechanics of compounding and withdrawal risk; it doesn't know you.