Montana compound interest calculator

What compounding actually is

Simple interest pays you on what you put in. Compound interest pays you on what you put in plus everything it has already earned, so every period starts from a slightly larger base than the last. That is the entire mechanism. Everything else on this page is arithmetic.

This tool compounds monthly. It takes a starting amount, adds a fixed contribution at the end of each month, and applies one twelfth of the annual return to the whole balance. That matches how most brokerage and deposit balances behave, and it is why the answer here runs a little above an annual compounding formula.

The shortcut worth memorising is the rule of 72: divide 72 by the annual return and you get roughly the number of years for money to double. At 7% that is a little over ten years. At 4% it is eighteen. At 1% it is seventy-two, which is another way of saying money left in a checking account does not double in a working lifetime.

Two things follow from that rule. A return is a lever on time rather than on money: at 7% a balance doubles roughly every ten years, so a forty-year horizon is about four doublings and a twenty-year horizon is two. And the doublings are not equally valuable. The last one moves more money than every earlier one put together, and it only happens if the money is still invested when its turn comes round.

A worked example, using the tool defaults

The defaults are $10,000 to start, $500 added each month, a 7% annual return and 20 years. The tool prints the path as well as the destination:

You paid in $130,000 and finished with about $300,851. Growth is $170,851, or 57% of the final balance. Put another way, more than half the money at the end was never yours to begin with.

A second run, with the return changed

Nothing else on the page moves the answer as far as the return does, so it is worth seeing the range on one set of inputs. Same $10,000 to start, $500 a month, 20 years:

The same $130,000 goes in every time and four different endings come out. Two points of return is worth roughly $68,000 across these 20 years, which is the practical reason to care about a fund charging 1% a year rather than 0.05%. That fee comes out of the growth column, not out of the contributions, and it compounds against you on the same schedule.

The 7% row is worth reading twice. At 3% inflation, $300,851 arriving 20 years from now buys about what $166,574 buys today. The balance is real and the number is nominal, and large figures make the two easy to confuse.

Why does the second half look so different from the first?

Look at the growth column. In the first year it is $919. Between year 15 and year 20 it rises by roughly $84,000, against $30,000 of contributions over the same stretch. Nothing changed in the inputs. The balance simply got large enough that a 7% return on it dwarfs anything a $500 monthly deposit can add.

This is the practical reason the years matter more than the amount. Twenty years at $500 a month beats ten years at $1,000 a month by a wide margin on identical assumptions, even though both put in the same $120,000. The early money is the money that has time to compound, which is also why a delay of five years is expensive in a way that is invisible when you make it.

Does a constant return flatter the result?

Yes, in one specific way, and it is worth being precise about which one.

A fixed return does not overstate the average. If a portfolio genuinely compounds at 7% for 20 years, this is the balance. What the straight line hides is that no portfolio delivers 7% twice in a row. A real 20 years is a scatter: strong years, a flat stretch, one or two badly negative ones. The ending balance depends on the order they arrive in, not only on their average.

While you are still contributing, the order tends to work in your favour. A bad early stretch means each deposit buys more of a cheaper asset, and the recovery applies to a larger holding than you would otherwise have owned. That is the sequence of returns running the helpful way round.

Once contributions stop and withdrawals start, the same effect reverses hard. Selling into a fall permanently removes units that would have recovered, so a bad first decade of retirement does damage a good average later cannot undo. Read the figure this tool prints as the middle of a wide range rather than as the outcome, and treat the withdrawal phase as a separate problem.

What return should you type in?

That depends entirely on where the money is going, and this site takes no view on what you should hold.

• For cash, use the rate you are actually being offered. Compare current rates on high-yield savings accounts and type in the APY rather than a market return.
• For a long-horizon diversified portfolio, some people use a figure near 7% nominal, which is roughly 4% after a 3% inflation assumption. Both numbers are conventions, not promises.
• Whatever you choose, subtract fees. A fund charging 1% a year is a 1% lower return: type 6 instead of 7 and read the difference.

There are two honest ways to use the tool. Enter a nominal return and remember the ending balance is in future dollars, or enter a real return after inflation and read the answer in today's money. Mixing the two is the most common error on this page.

How to check this against your own statement

A projection is worth something only if the inputs match reality, and a statement is the cheapest place to find out that they no longer do.

• Take the balance at the start of the year and the balance today, then subtract the contributions made in between. What is left is growth, and dividing it by the average balance gives a crude return for the period.
• Compare that with the return you typed in. A persistent gap of a point or more usually means fees, cash sitting uninvested, or a mix more conservative than you assumed.
• Check what the contributions actually were rather than what they were supposed to be. A missed month, a pay change or a match that stopped are invisible to the tool and plain on the statement.
• Note whether distributions are reinvested or paid out in cash. Reinvested dividends are part of the compounding modelled here. Cash paid into a spending account is not.

Once a year is enough. The aim is catching the year an assumption quietly stopped being true.

Where the money sits changes what it keeps

The tool projects a return before tax, and the account holding the money decides how much of that return survives to compound again.

• A taxable brokerage or deposit account. Interest is ordinary income in the year it is credited, dividends are taxed as they are paid, and selling at a gain is a taxable event of its own. Each takes a slice out of a balance that would otherwise have kept compounding, so the same 7% is worth less here than in a sheltered account.
• A traditional 401(k) or IRA. Nothing is taxed along the way and the whole withdrawal is taxed as income later.
• A Roth account. Qualified withdrawals are not taxed at all, the one case where the number this tool prints is close to money you can actually spend.

The rules that decide which applies to you sit in our tax section.

The mistakes people make with this projection

• Reading it as a forecast. It is a straight line through a market that does not move in straight lines. The ending figure is what a constant return would have produced, not what any real 20 years produced.
• Ignoring the order of returns. While you are contributing, a bad first decade is survivable and even helpful. Once you start withdrawing, the same sequence of returns in a different order can end very differently. That is why our FIRE number calculator treats the withdrawal phase separately.
• Forgetting tax. In a taxable account, interest is ordinary income in the year it is credited and dividends are taxed as they are paid, so the compounding you actually get is on the after-tax amount.
• Confusing APY with return. A quoted APY already includes compounding. An annual return does not guarantee anything.

Where this projection stops being true

Straight from the tool's own caveats:

• It applies a constant annual return, compounded monthly. Real markets do not deliver the same number twice, and the order of good and bad years matters enormously once you start withdrawing.
• The figures are before inflation. At 3% a year, money loses roughly half its purchasing power over 24 years, so $300,851 in 2046 does not buy what $300,851 buys now.
• The figures are before tax, unless the account is a Roth or otherwise tax-free. Whether that applies to you is the question our Roth vs traditional guide works through.

A checklist before you trust the number

• Decide whether you are working in nominal or real dollars, and use one consistently.
• Subtract fund and platform fees from the return you type in.
• Check the contribution you entered is one you can actually sustain in a bad month.
• Note which account the money is in, and whether growth is taxed on the way out.
• Re-run it with a return two points lower and see whether the plan still works.
• Read how we build these tools before quoting the output anywhere.

Every other tool on the site is listed in the calculator index.