How investment fees compound: 0.1% vs. 1% over 30 years

A percentage fee is charged on your whole balance every year, so it compounds against you the same way returns compound for you. In the example below, $100,000 grows 7% a year for 30 years. A 1% annual fee leaves $563,078.79 and a 0.1% fee leaves $738,716.80. The gap is $175,638.01, and almost two-thirds of it opens in the last 10 years.

How much does a 1% fee cost over 30 years?

With $100,000 growing 7% a year, a 1% fee leaves you $198,146.71 (26.03%) below the no-fee balance after 30 years and $175,638.01 below a 0.1% fee.

Example assumptions, for illustration only (not a forecast):

• $100,000 invested once, with nothing added or withdrawn
• a 7% gross return every year
• the fee taken once a year, as a percentage of the balance after that year’s growth
• no taxes, trading costs or inflation adjustment

Each year the balance grows by the return and then loses the fee. After $T$ years:

$$B_T = P\,\big[(1+r)(1-f)\big]^T$$

Here $P$ is the amount invested, $r$ the gross annual return and $f$ the annual fee, both as decimals. The fee in year $t$ is $F_t = f\,(1+r)\,B_{t-1}$: a fixed share of a growing balance.

With a 1% fee, each year multiplies the balance by 1.07 × 0.99 = 1.0593, so the money grows 5.93% a year after fees. With 0.1%, the multiplier is 1.07 × 0.999 = 1.06893. Over 30 years:

• No fee: $100,000 × $1.07^{30}$ = $100,000 × 7.61225504 = $761,225.50
• 0.1% fee: $100,000 × $1.06893^{30}$ = $100,000 × 7.38716802 = $738,716.80
• 1% fee: $100,000 × $1.0593^{30}$ = $100,000 × 5.63078790 = $563,078.79

The 1% account ends $175,638.01 behind the 0.1% account, which is 23.78% less. A fee difference of 0.9 percentage points took nearly a quarter of the final balance.

Why does the gap grow fastest in the last decade?

Because the fee is a percentage of a balance that keeps compounding. Each year the 1% account falls another 0.9% behind the 0.1% account (0.99 ÷ 0.999 = 0.99099), so the gap as a share of the balance climbs steadily. That share applies to a larger balance every year, so the dollar gap accelerates.

Same example, rounded to the dollar:

The gap grew by $16,851 in the first decade, $45,947 in the second and $112,840 in the third. The last decade accounts for 64% of the 30-year gap, and going from 20 to 30 years almost triples it. A fee comparison run over 5 or 10 years understates what the same fee does over a working life.

Are fees paid the same as the money you lose?

No. Fees paid are what the provider collects. What you lose also includes the growth those dollars would have earned if they had stayed invested. In the 1% example:

Each figure is rounded to the cent on its own, so the first two add up to 1¢ more than the third.

Every dollar of fees cost $2.37 of ending balance. Early fees cost the most per dollar: the $1,070 taken in year 1 would have grown to $7,612.26 by year 30 ($1,070 × $1.07^{29}$), while the $5,687.66 taken in year 30 costs only itself. The shortfall is exactly each year’s fee grown at the gross return to the end:

$$\text{shortfall} = \sum_{t=1}^{T} F_t\,(1+r)^{T-t}$$

Account statements can show fees charged to your account, such as an advisory or plan fee, but not a fund’s expense ratio, which is paid out of fund assets. Neither is the shortfall, which answers “how much less will I have?” Between the two fee options here, the 1% account pays $73,642.42 more in fees than the 0.1% account but ends $175,638.01 lower.

What share of your balance does a fee take?

For a single deposit, the share of the no-fee balance you keep is $(1-f)^T$. The return drops out because it multiplies both balances equally. For the same reason, the order of good and bad years doesn’t change the share, as long as the fee is a fixed percentage of the balance and nothing is added or withdrawn.

Share of the no-fee balance lost (single deposit, fee taken once a year):

Regular contributions lower the share, because later deposits are exposed to the fee for fewer years. With $5,000 added at the end of each year for 30 years at 7% gross, starting from nothing:

• No fee: $472,303.93
• 0.1% fee: $463,308.29, which is 1.90% less
• 1% fee: $390,454.29, which is 17.33% less, after $43,387.20 in fees paid

So a 401(k) built up steadily from zero loses a smaller share than the lump-sum table suggests. A rollover or an existing balance behaves like the lump sum.

Which fees compound, and where do you find them?

Any fee charged as a percentage of your balance every year compounds as above. Fees stack, so include every layer that applies:

• Fund expense ratio. A fund’s yearly operating expenses as a percentage of its average net assets, listed in the prospectus fee table. It is paid out of the fund’s assets, so it lowers the value of your shares instead of arriving as a bill.
• Advisory fee. Advisers most often charge a percentage of the assets in your account, commonly billed each quarter. The advisory agreement, Form CRS and the adviser’s Form ADV Part 2A brochure set out the fee.
• Retirement plan fees. A 401(k) can pass plan administration costs to participants on top of the funds’ own expenses. The plan must explain them by the date you can first direct your investments and at least yearly after that, and show at least quarterly what was actually charged to your account. It also lists each fund’s expenses in dollars per $1,000 invested: 0.1% is $1 a year, 1% is $10.
• Flat account fees. Account maintenance fees, which some funds charge only on smaller accounts, and flat monthly subscription fees for advice. They take the same dollars at any balance, so convert them to a percentage of your balance (fee ÷ balance) to compare. The dollars taken still lose the growth they would have earned.
• One-time costs. Commissions, sales loads and redemption fees are charged when you buy or sell. They cut the amount invested or received once but don’t recur on the balance, so they aren’t part of the yearly drag.

A 0.1% fund held in an account that charges 1% for advice pays both. Together they take about 1.1% a year (1 − 0.999 × 0.99 = 1.099%).

Is a flat fee cheaper than a percentage fee?

It depends on the balance. A flat fee is the same number of dollars at any balance, so as a percentage it is large on small balances and small on big ones. The two cost the same at:

$$\text{break-even balance} = \frac{\text{flat fee per year}}{\text{percentage fee}}$$

For example, $120 a year ($10 a month) against 0.25% of assets breaks even at $120 ÷ 0.0025 = $48,000.

Balances grow, so compare over the whole horizon, not only at today’s balance. Over 30 years at 7% with no deposits, fees taken at the end of each year, rounded to the dollar:

Starting from $5,000, the flat fee takes 29.78% of the no-fee result and the percentage fee 7.23%. Starting from $30,000, the 0.25% fee is under $120 for the first 7 years and over it from year 8, the first year the balance it is charged on ($50,650) is above the $48,000 break-even. The flat-fee account still only pulls ahead in year 15, because it paid more in the early years. Regular deposits get a small account past the break-even sooner.

Why do fee calculators give different answers?

Mostly because they apply the fee differently. With the same $100,000, 7% and 30 years and a 1% fee:

Subtracting the fee from the return is a shortcut that skips the fee on that year’s growth (1.07 × 0.99 is 1.0593, not 1.06). Here it overstates the balance by $11,270.33.

The SEC’s own illustration uses $100,000 growing 4% a year for 20 years, with fees of 0.25%, 0.50% and 1.00% ending at roughly $208,000, $198,000 and $179,000. Taking the fee from the balance reproduces those figures: $208,413, $198,211 and $179,213. Subtracting it from the return gives $180,611 for the 1% case.

Tools also differ on the return. “7% compounded monthly” (7% ÷ 12 each month) grows $100,000 to $811,649.75 in 30 years before fees, not $761,225.50.

How do you compare two funds or accounts?

1. Total the ongoing percentage fees for each option: the expense ratio plus any advisory, wrap or plan fee charged on assets.
2. Convert flat fees to a percentage of your balance (fee ÷ balance), at today’s balance and at the balance you expect later.
3. Use the same gross return and horizon for both. The share table above, or the calculators below, then give the gap.
4. Work out the extra return the costlier option needs just to tie. Solve $(1+g_B)(1-f_B) = (1+g_A)(1-f_A)$ for $g_B$. For a 1% option to match a 0.1% option earning 7%, it must earn 1.07 × 0.999 ÷ 0.99 − 1 = 7.97% gross, 0.97 percentage points more every year.
5. Check share classes and loads. The same fund can come in share classes with different expense ratios and sales charges. FINRA’s Fund Analyzer lets you look up and compare a specific fund’s costs.

Cost is one factor, not the whole decision. An advisory fee may pay for planning, tax help or help sticking to a plan. The arithmetic shows what those services cost, not what they are worth to you.

Try it

• Investment fee calculator: enter a starting balance of 100,000, an annual contribution of 0, a gross annual return of 7% and 30 years invested. Set Scenario A to a 0.1% annual fee with a $0 flat fee, Scenario B to 1% with a $0 flat fee, and take fees once a year. You should see $761,225.50 with no fee, $738,716.80 for A and $563,078.79 for B, with fees paid of $9,914.80 and $83,557.22. For the flat-fee comparison, start at 30,000 with Scenario A at 0% plus a $120 flat fee and Scenario B at 0.25% with a $0 flat fee: A should end at $217,032.36 and B at $211,846.71.
• Compound interest calculator: check the after-fee growth rates directly. With an initial deposit of 100,000, no contributions, annual compounding and 30 years, an annual interest rate of 6.893% gives $738,716.80 and 5.93% gives $563,078.79. For the contribution example, set the initial deposit to 0 and add a $5,000 yearly contribution at the end of each period: 5.93% gives $390,454.29 and 6.893% gives $463,308.29.
• Retirement savings calculator: to see fees in your own projection, enter the return after fees, $(1+r)(1-f)-1$, as the expected annual return. For example, use 5.93% instead of 7% for a 1% fee, then run it again at the lower-fee rate and compare.

What this model leaves out

• Varying returns. Actual returns change from year to year. For a single deposit, the share lost to a percentage fee is the same for any sequence of returns. Once you add deposits or take withdrawals, the order of returns changes the dollar cost.
• Taxes and inflation. All figures are nominal and before tax.
• Costs outside the fee table. Brokerage commissions and other charges from the firm holding your account don’t appear in a fund’s fee table, and ETFs can carry transaction costs the prospectus doesn’t list.
• Changing fees. Expense ratios change, and some charges vary with the amount invested. Rerun the numbers with the fee you expect at each balance.
• What the fee buys. The model counts cost, not value.

These figures are educational estimates, not investment advice.