How the range is calculated

We run your full plan — spending, income, taxes, withdrawals — 1,000 times. Each run lets market returns and inflation move the way they might in real life instead of at one steady average. Everything else stays at your assumptions.

The line on your chart is your plan at steady rates. The range shows how differently the same plan can turn out when those rates bounce around.

In each run, investment returns vary randomly from month to month around the growth rate you chose — stocks swinging about ±15% a year and bonds about ±5%, blended by each account’s stock/bond mix. The average of those swings equals your rate; the swings themselves are the only thing we add.

Stocks and bonds don't move in lockstep, but they aren't independent either: we let their monthly swings move together a little (0.10 on a −1 to 1 scale), so a mixed account is steadier than all-stocks but not as steady as if bonds ignored the stock market.

Runs with weaker returns lean slightly toward higher inflation, and runs with stronger returns toward lower (a link of −0.15 on the same scale) — the hardest stretches for retirees have paired the two. Your rate is still the average across runs.

Each run also gets its own inflation rate, held for that whole run and spread about ±1 percentage point around the rate you assume.

An account’s stock/bond mix is read from its holdings where we can see them; otherwise it is treated as all stocks until you set it. Cash, and accounts with no growth rate entered, don’t swing.

These sizes are fixed, the same for everyone, and not something you can change.

The edges of the range come from the rare good and bad runs, so they need enough runs to settle down. With fewer, the low edge can move noticeably just by chance.

The random numbers start from a fixed starting point for the random draws (a seed). We picked it by checking its results against a much larger reference of 20,000 runs for several sample plans, and kept one whose 1,000-run edges land close to that reference. We recheck it whenever the way the range is drawn changes.

Every good run is matched by an equally bad one, so luck evens out.

Runs come in pairs. The second run of each pair takes every swing of the first and flips it, so a strong month in one is an equally weak month in the other. That keeps the swings centered on your rate and makes the range steadier for the same number of runs.

The shaded band covers the middle 80% of the runs: one run in ten ends below it and one in ten above it, at every point in time.

The thin line inside the shading is the middle of the runs — half end above it, half below. Your plan’s line usually sits a bit above that middle. That’s expected: down years hurt more than up years help.

Because the starting point is fixed, the same plan always draws the same range. A range that shifted every time you looked would be noise, not information.

A scenario uses the same random swings as your plan, so the difference between their ranges comes from the change you made — never from luck.

Instead of random swings, this replays actual yearly US stock and 10-year Treasury returns from 1928 to 2025 (Historical Returns on Stocks, Bonds and Bills — Aswath Damodaran, NYU Stern, checked Sep 24, 2026), with each year's own inflation removed and the inflation rate you chose added back. Your growth rate isn't used here — the years are.

Past sequence from a year: one line, not a band — your plan follows the actual years in order from the year you pick, starting over at 1928 after 2025 if it runs past the end.

Random starting years: Each of the 1,000 runs starts in a randomly chosen year and follows history in order from there, starting over after 2025.

Blocks of past years: Each run stitches together random 5-year stretches of history, keeping each stretch's ups and downs in their real order.

Past returns are not a forecast. Those years happened once; the next ones may look nothing like them.

Source: Historical Returns on Stocks, Bonds and Bills — Aswath Damodaran, NYU Stern, 1928–2025. Real (after-inflation) yearly returns; your own inflation rate is added back.

The simulated setting’s bonds behave like a broad bond fund (about ±5% a year). The past-returns settings use the 10-year Treasury, which swings more. The two settings differ on purpose.

It isn’t a prediction. It shows a range of outcomes under stated assumptions, not what will happen.

It isn’t odds. We don’t turn the range into a percentage chance that your plan works, and the share of runs that end in any place is not the chance it happens to you.

It isn’t a measure of how risky your own investments are. The swings are the same fixed sizes for everyone, blended only by stock/bond mix — not by the particular funds you hold.

Runs that go low aren’t forecasts either: in real life you would see trouble coming years ahead and could adjust income, spending, or timing along the way.

The projections and other figures shown here are hypothetical in nature, do not reflect actual results and are not guarantees of future results. They are built from your inputs, your linked account history and the assumptions shown. Taxes are approximated by a simplified annual estimate you control; the app explains what the tax estimate includes and leaves out. This tool is educational and is not financial, tax, or investment advice.