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Expense ratio calculator and fee impact

A fund fee is charged on your whole balance every year, so it comes off the rate your money compounds at. Start with $10,000, add $300 a month for 30 years at 7 percent before costs, compounded monthly: with no fee you reach $447,156.27, and a 0.65 percent fee leaves $389,198.79.

Ending balance after the fee

$389,198.79

The same money with no fee taken reaches $447,156.27.

What the fee costs
$57,957.49
Cost as a share of the fee-free balance
12.96%
Return left after the fee
6.35%
You paid in
$118,000.00
$
$
%

A fund's published return is already net of its expense ratio. Put the figure before costs here, or put the published one here and set the fee to zero. This rate is applied in twelve monthly slices, so 7 here compounds to 7.23 percent over a year.

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The formula

A=P(1+g−fn)ntA = P\left(1 + \frac{g - f}{n}\right)^{nt}

AA is the ending balance, PP what you start with, gg the return before costs as a decimal, ff the expense ratio as a decimal, nn how many times a year the money compounds, which is twelve on this page, and tt the number of years.

What this calculator works out

Enter what you start with, what you add each month, the return before costs, the fund's expense ratio and how long you hold it. The rate you enter is applied in twelve monthly slices, the same convention the compound interest calculator uses. The calculator runs the same money twice: once at the full return and once at the return minus the fee. It reports both ending balances and the difference between them.

That difference is the point of the page. A fee quoted as a fraction of a percent sounds like a rounding error next to a 7 percent return. Even in the first year it is not one, and charged every year on a balance that keeps growing it stops being anywhere near one.

The fee comes off the rate, not off the gains

An expense ratio is a yearly percentage of the money you hold in the fund, taken out of fund assets rather than billed to you. Because it is charged on the balance and not on the profit, the arithmetic is short: a fee of ff leaves the balance growing at g−fg - f instead of at gg.

A=P(1+g−fn)nt+PMT×(1+g−fn)nt−1g−fnA = P\left(1 + \frac{g - f}{n}\right)^{nt} + PMT \times \frac{\left(1 + \frac{g - f}{n}\right)^{nt} - 1}{\frac{g - f}{n}}

The first term grows what you started with and the second grows what you added. Setting f=0f = 0 gives the fee-free version of the same run, which is what the calculator measures against.

One consequence catches people out. A 0.65 percent fee against a 7 percent return is not taking 0.65 percent of anything you care about. It is taking about 9.3 percent of the return, in every year, including the years the return does not arrive.

Why the gap widens with time

A percentage repeats. Each year the fee removes a slice of a balance larger than last year's, and the money it removed is no longer there to earn anything. Over a long holding period the second effect is the bigger one.

On the worked examples below, 30 years of a 0.65 percent fee leaves about 87 percent of the fee-free balance, so just under 13 percent of the end result has gone. The opening $10,000, exposed to the fee for the whole 30 years, keeps only 82 percent of what it would otherwise have reached. The monthly deposits keep about 88 percent, because none of them has been exposed for the full 30 years and the last one is exposed for a single month. Weighted by what each deposit is worth at the end, they carry roughly 20 years of the fee rather than 30.

So how long you hold the fund matters as much as how large the fee looks, which is what makes a fee that looks negligible expensive. The same mechanism running in your favour is the compound interest calculator.

Weigh the fee against what it buys

A fee is a price, and a price is only bad when what it buys is not worth it. A fund charging more can still leave you ahead, if it earns more than the extra cost after its own trading expenses. What the arithmetic above sets is the size of the hurdle: a fund charging 0.65 percent a year rather than 0.10 percent has to earn 0.55 percentage points a year more before costs, every year, simply to draw level after them.

Two things make that hurdle awkward. The fee is known in advance and the extra return is not, and the fee is charged in the bad years as well as the good ones. That asymmetry, rather than any claim that picking holdings cannot work, is the argument laid out in index funds against active management.

Costs are not the only thing standing between a statement balance and what it will buy. Inflation does the rest, which is the real return calculator.

Worked examples

A 0.65 percent fee held for 30 years

You put $10,000 into a fund, add $300 at the end of every month for 30 years, and the fund earns 7 percent a year before costs, compounded monthly. The expense ratio is 0.65 percent. What do you end with?

  1. Take the fee off the return: 7−0.65=6.357 - 0.65 = 6.35 percent, so the balance compounds at 0.0635 a year.
  2. Find the monthly rate: 0.0635/120.0635/12, which is 0.00529167 to eight decimals, and count the periods: 12×30=36012 \times 30 = 360. Every figure below carries the rate unrounded.
  3. Grow the opening amount: 10000×(1+0.0635/12)360=10000×6.68574310000 \times (1 + 0.0635/12)^{360} = 10000 \times 6.685743, which is $66,857.43.
  4. Grow the deposits: 300×(1+0.0635/12)360−10.0635/12=300×1074.471181300 \times \frac{(1 + 0.0635/12)^{360} - 1}{0.0635/12} = 300 \times 1074.471181, which is $322,341.35.
  5. Add the two parts. Together the $66,857.43 and the $322,341.35 come to $389,198.79, and adding the rounded halves on their own would land a cent low.
  6. Check what you paid in: 10000+300×360=10000 + 300 \times 360 = $118,000.

You end with $389,198.79. You paid in $118,000, so $271,198.79 of that balance is growth rather than money you supplied.

The same money with no fee taken

Run the identical $10,000 and $300 a month for 30 years at the full 7 percent compounded monthly, with nothing deducted. What is the fee-free balance?

  1. The balance now compounds at 0.07, so the monthly rate is 0.07/120.07/12, again carried unrounded.
  2. (1+0.07/12)360=8.116497(1 + 0.07/12)^{360} = 8.116497, against 6.685743 once the fee was taken.
  3. Grow the opening amount and the deposits at that rate and add them: the balance is $447,156.27.
  4. Subtract what you paid in: $447,156.27 minus $118,000.

With no fee the balance is $447,156.27, of which $329,156.27 is growth. That is the figure the 0.65 percent run is measured against, and the fee has cost just under 13 percent of it.

The same question at 0.10 percent

Keep everything else the same and move to a fund charging 0.10 percent instead of 0.65 percent. What does the cheaper fund end with?

  1. The return left after the fee is 7−0.10=6.907 - 0.10 = 6.90 percent, so the monthly rate is 0.069/12=0.005750.069/12 = 0.00575.
  2. 1.00575360=7.8779801.00575^{360} = 7.877980, between the 6.685743 of the expensive fund and the 8.116497 of the fee-free run.
  3. Grow the opening $10,000 and the $300 monthly deposits at that rate: the balance reaches $437,630.90.
  4. Set it beside the other two: $447,156.27 with no fee at all, and $389,198.79 at 0.65 percent.

The cheaper fund ends at $437,630.90, of which $319,630.90 is growth. It gives up about 2.1 percent of the fee-free balance where the 0.65 percent fund gives up nearly 13 percent, so roughly a sixth as much. A difference of 0.55 percentage points in the quoted fee is doing all of that.

The mistake that costs the most

Judging a fee against one year of return instead of against a lifetime of balances.

Next to a 7 percent return, 0.65 percent reads as a rounding error. It is not a share of the return, though. It is a share of everything you hold, charged again every year, in the losing years as well. In year one alone it is already about 9.3 percent of the return.

The rough test takes one line: multiply the fee by the number of years you expect to hold the fund. At 0.65 percent for 30 years that is about 19.5 percent, and the true figure for a sum left alone the whole time is 17.6 percent, slightly less because the fee is charged on a balance the fee itself has shrunk. Money added later has been exposed for less time, which is why the blended figure on the run above is just under 13 percent rather than 17.6 percent. None of those numbers is a rounding error.

Common questions

Is a fund's published return already after the expense ratio?

Yes. A reported total return is net of the expense ratio, so subtracting the fee from a published figure charges it twice. Enter a return before costs here, or enter a published net return and set the fee to zero. What the ratio does not cover is a sales charge, the commission your broker takes, the gap between bid and ask on an exchange traded fund, or the tax due on distributions.

When is the fee actually taken?

A slice comes out of fund assets each day the fund is valued, so no bill ever arrives and the price you see is already net of it. This calculator does the same thing once a month, by reducing the rate the balance grows at. A fee charged on the balance at the start of a period takes exactly that share of it, so subtracting the fee from the rate is the arithmetic rather than a shortcut. Take the same yearly fee daily instead of monthly, holding the return where it is, and a 30 year balance moves by well under a tenth of a percent, which is the sense in which the monthly step here is close enough.

Does 7 percent here mean the same thing as a fund's annualised return?

Not quite, and the difference is worth a minute. The figure you type is a yearly rate this calculator applies in twelve monthly slices, so 7 percent entered here compounds to 7.23 percent over a year. A fund's reported annualised return is already the whole year, with the compounding inside it. A fund that reported 7 percent a year therefore corresponds to about 6.78 percent typed here, not 7. Type 7 anyway and both 30 year balances on this page land close to 5 percent high, which leaves the share the fee takes almost unchanged but overstates every dollar figure. The APR against APY calculator converts between the two.

Is the cheaper fund always the better one?

No. What you keep is the return after every cost, and a fund charging more can leave you ahead if it earns more than the difference. The fee is simply the part known in advance, and it is charged whatever happens, which makes it the first thing to check rather than the only thing. In the United States a fund has to state its expense ratio in its prospectus, and a fund sold elsewhere often prints the same idea as an ongoing charges figure.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.