How this projection works
Every fund company has a growth calculator. You type in a number, it draws one confident curve, and you close the tab feeling either rich or discouraged. The curve is not a lie, exactly. It is just the least interesting true thing anybody can tell you about your money.
Three things happen between today and the end of your horizon that a single curve leaves out, and all three are computable. Fees get skimmed off the top every year. Inflation quietly shrinks what the ending number buys. And returns arrive unevenly, which means the honest answer was never a number in the first place. It was a range with a middle.
So this calculator does the same compounding math everyone does, then adds those three layers. It runs your deposits month by month at your return minus your fees, deflates the answer into today's money, and puts a band around it from a volatility figure you control. The headline is still one number, because you asked a question and deserve an answer. Everything under it exists to tell you how much to trust that number.
If you want the underlying math on its own, clean and frictionless, the compound interest calculator is the page for that. If you want to know what actually happened rather than what might, the S&P 500 investment calculator runs real annual returns from 1980 forward. This page is the one in between: forward looking, and honest about how little anybody knows about the forward.
The formula
m = (1 + rnet)1/12 − 1
Balance = P(1 + m)N + ∑ Ck(1 + m)N−k
Range = Balance × e±1.2816 · σ√T
Today's money = Balance ÷ (1 + i)Y
P is your starting amount, Ck the deposit made at the end of month k, N the total number of months, and m the monthly rate. Note the exponent on m: a 7% return means your money is 7% bigger after a year, so the monthly rate is the twelfth root, not the twelfth part. σ is annual volatility, T is the dollar-weighted number of years your money is actually in the market, 1.2816 is the z value that brackets the middle 80% of a normal distribution, i is inflation and Y is your horizon in years.
Fees are subtracted from the return rather than billed separately, because that is how they really work. A fund publishes its return after the expense ratio has already been taken out of the assets. You never see the bill. That is precisely why the number is so easy to ignore.
Worked example
$10,000 to start, $500 a month for 30 years, at the default 7% expected return, a 0.20% fund fee, 2.5% inflation and 18% volatility:
The fee leaves 6.8% to compound. You deposit $190,000 over the 30 years and the market adds $445,580, for a median projection of $635,580. Growth first overtakes your own deposits in year 18.
That single number is the middle of a very wide spread. Your money is exposed to the market for 20.8 years on a dollar-weighted average, which at 18% volatility puts 8 outcomes in 10 between $222,086 and $1,818,944. At 2.5% inflation, prices are 2.10 times higher by then, so the median balance buys what $303,008 buys today.
Now price the fee. Run the identical plan in a 1.00% fund instead of a 0.20% one and the median drops to $544,691. That eight tenths of one percent, the difference between a plain index fund and an ordinary managed one, costs $90,888.77. With no fees at all the plan would end at $660,848.85, so the 1.00% fund gives up $116,157.45, or 17.6% of the whole result, to a line item you never see on a statement.
Why a single rate is a fiction
Here is the uncomfortable thing about "7% a year." No market has ever done 7% a year. US stocks have compounded at about 10.0% a year since 1928, and got there through years like 1995 (up 37.2%) and 2008 (down 36.6%). The average is real. The smoothness is invented.
That matters because compounding is multiplicative, so the spread of returns changes where you land, not just how bumpy the trip felt. A projection that reports only the middle path is technically correct and practically useless, in the way that telling a first-time visitor the average January temperature in Chicago is technically correct. It is the variance that decides what you need to pack.
What this page does instead. It treats your ending balance as a spread of possible values centered on the median path. The width comes from three things: how volatile you say the market is, how many years your money is actually exposed, and nothing else. The result is reported as the range that 8 outcomes in 10 fall inside, which is the 10th to the 90th percentile.
The exposure figure is worth a sentence, because it is the part most people get wrong. A lump sum left for 30 years is exposed for the full 30 years. A stream of monthly deposits is not: the money you add in year 29 gets one year of market, not 30. In the worked example the dollar-weighted average is 20.8 years, which is why a contribution plan produces a narrower range than a lump sum of the same final size. Drip feeding really does buy you certainty. It is just not free, because the money you have not deposited yet is not compounding either.
The default volatility, and where it comes from. Using the annual total returns published by Aswath Damodaran at NYU Stern, the standard deviation of US stock returns is 19.4% for 1928 to 2025 and 16.3% for 1980 to 2025. The page defaults to 18%, between the two, because it is projecting a diversified portfolio rather than a pure US stock index, and most real portfolios hold something calmer alongside the stocks. Change it. That is what the box is for.
And the honest limits of the band. The model assumes each year is an independent draw from a bell curve of returns. Real markets are not that tidy in either direction. In the short run they have fatter tails than a bell curve allows, so genuine disasters are more likely than this model says. Over long horizons they have shown some tendency to mean revert, which historically made 30-year outcomes less spread out than independent years would predict. A proper Monte Carlo running thousands of paths would not fix either problem; it would just take longer to be approximately right. The band here is a well-labeled approximation, and the number to take from it is not the edges, it is the width.
What fees actually cost, in dollars
The reason percentage fees are so easy to shrug at is that the percentage is small and it never arrives as a bill. Nothing is ever debited. The fund simply reports a return that has already had the fee removed, and the money you did not get compounds into money you also do not get, every year, forever.
In the worked example, a 0.20% expense ratio costs $25,268.69 over 30 years. That is on a plan where you deposited $190,000 of your own money. The fee took more than an eighth of your total deposits, and it did so at a rate that sounds like a rounding error.
| Annual cost | What it typically is | Median after 30 years | Given up |
|---|---|---|---|
| 0% | Nothing exists at 0%, but it sets the baseline | $660,849 | nothing |
| 0.20% | A cheap index fund, plus a little | $635,580 | $25,269 |
| 1.00% | An ordinary actively managed fund | $544,691 | $116,157 |
| 1.20% | A 0.20% fund plus a 1% advisor | $524,301 | $136,548 |
The 1.20% row is the common one, and it is worth naming plainly. A 1% fee on assets is the industry standard rate for advice, and on this plan it costs $111,280 on top of whatever the funds charge. Whether that is a good trade depends entirely on what the advisor does for you: tax planning, rebalancing, estate work, and above all talking you out of selling everything in March of a bad year are real services with real value. The point is not that the fee is wrong. The point is that you should know it is a six figure decision before you call it small.
Two things about that table are worth checking against reality. The asset-weighted average expense ratio across all US equity mutual funds was 0.40% in 2025, and index equity ETFs averaged 0.14%, according to the Investment Company Institute. Those numbers are asset weighted, which means they describe where the money sits rather than what the average fund charges. The simple average across active equity funds is closer to 1.10%. Both facts are true at once, and together they tell a hopeful story: expensive funds still exist in large numbers, but most people's money has already left them.
The number your statement shows, and the number you can spend
$635,580 in thirty years is not $635,580. At 2.5% inflation, which is what the US has averaged over the last 30 years, prices roughly double over that stretch. The balance buys what $303,008 buys today.
Neither number is the honest one on its own. The nominal figure is what your account will actually say, and it is what you will pay tax on and withdraw. The real figure is what you can do with it, which is the only thing you actually care about when you are picturing the future. Plan with the real number and check the nominal one, and note that the whole band deflates too: the same worked example's range of $222,086 to $1,818,944 is $105,878 to $867,168 in today's money.
A shortcut you will hear is to subtract inflation from your return and plan entirely in today's dollars. That works, and this page supports it: set the return to your real expectation and inflation to 0. The reason this calculator keeps them separate by default is that people know roughly what returns they expect in the numbers they read about, and quietly forget that those numbers are nominal. Making inflation its own field means you have to look at it.
Contributions do the early work, then hand over
For the first stretch of any plan, the market is not doing much. You are. In the worked example, your $500 a month is the engine for nearly two decades: growth does not overtake cumulative deposits until year 18, and by the end it accounts for 70.1% of the balance.
That crossover year is the single most useful thing on this page for anybody in the first ten years of investing, because it explains why the whole thing feels so slow and so pointless at the start. It is supposed to. You are building the pile that will later do the compounding. The market cannot pay you interest on money you have not deposited yet.
Three things move the crossover earlier, and they are worth ranking. A longer horizon moves it most, which is why starting at 25 rather than 35 is worth more than any fund selection you will ever make. Lower fees move it next: the 1.00% fund pushes the crossover from year 18 to year 21. And raising your contribution with your pay, which the increase field models, moves it later on paper while making you far richer in practice, because you keep feeding the engine. Try 3% a year in that field: the same plan ends at $848,240 instead of $635,580, and the crossover slides to year 20 purely because you deposited more.
What this model does not do
Every projection is a set of assumptions wearing a suit. Here are the ones this page is wearing, stated plainly so you can decide how much to trust the output.
It models a diversified portfolio in aggregate, not a specific fund. There is no fund in here. There is a return, a fee, and a volatility figure. If you are holding three stocks, the volatility of your actual portfolio is far higher than anything in the default and the range this page draws is much too narrow.
It ignores taxes. In a 401(k) or an IRA that is roughly right until you withdraw. In a taxable brokerage account it is not: dividends and realized gains are taxed along the way, which behaves a lot like an extra annual fee. If your money is taxable, adding a point or so to the fee field is a crude but useful way to feel it.
It ignores rebalancing and the sequence of returns. The order of good and bad years does not change the answer here, because we are compounding a median path. That is fine while you are adding money and genuinely dangerous once you start taking it out, when a bad first decade can end a plan that a good first decade would have survived. That risk lives in the withdrawal phase, and the retirement withdrawal calculator is where to go and meet it.
The band understates the extremes. As above: real returns have fatter tails than the lognormal shape used here. Treat the 10th percentile as a bad outcome, not the worst one.
And nothing here is a forecast. It is arithmetic performed on assumptions you supplied. The most valuable thing it can do is not tell you what you will have. It is to show you, in dollars, how much the answer moves when you change one number, and which of those numbers you can actually control. You cannot control the return. You can absolutely control the fee.