Start with the same $500,000, the same gross return, and the same 40-year horizon. The only difference between the two paths is the annual cost subtracted before the money compounds: 1.00% on Path A, 0.15% on Path B. Because both paths apply the same gross return and differ only in that annual drag, the entire 40-year gap is determined by the two fee rates and the return assumption. You do not need to trust a projection. You need two spreadsheet columns and one formula per row.
This is not a claim about what any particular advisor charges or what any particular fund charges. The 1% and 0.15% figures are the article’s stated assumptions, chosen because they are easy to compare. The arithmetic below is what those assumptions produce. If your own fee rates differ, substitute them and rerun the same ledger.
The assumptions, stated up front
| Input | Value | Note |
|---|---|---|
| Starting balance | $500,000 | Invested at the start of year 1 |
| Gross annual return | 7.00% nominal | An assumption, not a forecast |
| Path A annual cost | 1.00% | Advisory fee assumption |
| Path B annual cost | 0.15% | Index fund expense ratio assumption |
| Compounding | Annual | Costs deducted once per year |
| Contributions or withdrawals | None | Isolates the fee effect |
| Inflation | 2.50% | Used only to express the gap in today’s dollars |
| Taxes | Ignored | See the note on taxes below |
| Horizon | 40 years | Age 40 to age 80 in the ledger |
The gross return is the return before any fee. Path A nets 6.00% per year (7.00% minus 1.00%). Path B nets 6.85% per year (7.00% minus 0.15%). That 0.85 percentage-point difference is the whole engine of the result.
The mechanics, walked by hand
The formula for each path in each year is:
Ending balance = Beginning balance × (1 + gross return − annual cost)
Year 1, Path A: $500,000 × (1 + 0.07 − 0.01) = $500,000 × 1.06 = $530,000.
Year 1, Path B: $500,000 × (1 + 0.07 − 0.0015) = $500,000 × 1.0685 = $534,250.
After one year the gap is $4,250. That is 0.85% of $500,000, which is exactly what you would expect. The interesting part is what happens when that $4,250 is allowed to compound for 39 more years.
The year-by-year ledger
Balances are end-of-year. The annual gap is Path B minus Path A. The cumulative gap column shows the same difference, so it is identical to the annual gap in this no-contribution model; it is included so the table can be extended if you add contributions later.
| Year | Age | Path A balance (1.00%) | Path B balance (0.15%) | Gap (B − A) |
|---|---|---|---|---|
| 0 | 40 | $500,000 | $500,000 | $0 |
| 1 | 41 | $530,000 | $534,250 | $4,250 |
| 5 | 45 | $669,113 | $691,737 | $22,624 |
| 10 | 50 | $895,424 | $956,979 | $61,555 |
| 20 | 60 | $1,603,568 | $1,831,847 | $228,279 |
| 30 | 70 | $2,871,745 | $3,506,366 | $634,621 |
| 40 | 80 | $5,142,858 | $6,711,354 | $1,568,496 |
At year 40, Path A ends at about $5.14 million and Path B ends at about $6.71 million. The gap is roughly $1.57 million in nominal dollars. If the 7% gross return assumption holds, the gap is seven figures. If it does not, the gap is smaller or larger, but the direction does not change as long as the gross return exceeds both fees.
In today’s dollars, using the 2.5% inflation assumption, divide the nominal gap by 1.025 raised to the 40th power, which is about 2.685. The $1,568,496 nominal gap is about $584,000 in purchasing power at the start. That is the number to hold in your head if you think in today’s prices.
Why the gap is not 1% times 40 years
A common first guess is that a 1% fee costs 1% of $500,000 per year, or $5,000, times 40 years, or $200,000. That understates the cost badly because it ignores compounding on the money that is no longer in the account.
Decompose the $1,568,496 gap into two pieces. The first piece is the simple sum of the annual fee differences applied to the beginning balances. The second piece is the foregone growth on those differences. In a spreadsheet, the clean way to see this is to build a third column: the balance Path B would have if it earned Path B’s net return but paid Path A’s fee. The difference between that column and Path A is the direct fee drag; the difference between Path B and that column is the compounding on the drag. The two pieces together equal the total gap. The compounding piece is the larger of the two over 40 years, which is why the headline cost is not a simple multiplication.
Sensitivity to the return assumption
The dollar gap scales with the gross return. Rerun the same ledger with all other assumptions fixed and only the gross return changed:
| Gross return | Path A net | Path B net | 40-year gap |
|---|---|---|---|
| 5.00% | 4.00% | 4.85% | $1,003,000 |
| 7.00% | 6.00% | 6.85% | $1,568,496 |
| 9.00% | 8.00% | 8.85% | $2,441,000 |
These are rounded to the nearest thousand because the point is the direction, not the last digit. At a 5% gross return the gap is about $1.0 million; at 9% it is about $2.4 million. Quoting a single gap number without the return assumption attached is misleading. The assumption is part of the answer.
What the fee buys
Whether a 1% advisory fee is worth paying is a separate question from its arithmetic cost. The ledger above quantifies the cost. It does not tell you whether the advice prevents a behavioral mistake larger than the fee. That is a question you have to answer with your own evidence: have you sold at the bottom, chased a hot fund, or abandoned a plan during a drawdown? If the answer is yes and an advisor would have stopped you, the fee may be cheaper than the mistake. If the answer is no, the arithmetic is the arithmetic.
The same logic applies to the 0.15% expense ratio. A low expense ratio leaves more of a fund’s earnings with the investor, and those costs are deducted from the fund’s total value on a regular basis rather than paid out of the original investment, as Vanguard’s ETF education page describes. That is a factual statement about how expense ratios work. It is not a claim that any specific fund charges 0.15%, and it is not a claim that a low-cost fund is the right choice for every investor.
A note on taxes
The ledger ignores taxes. That is a deliberate simplification, not a claim that taxes do not matter. Advisory fees, fund distributions, and capital gains can each be taxed differently depending on the account type and the investor’s situation. If you want to model taxes, add a tax column to the spreadsheet and apply your own rates to the relevant cash flows. The fee comparison itself does not require a tax assumption, and adding one would make the arithmetic harder to check without changing the direction of the result.
The spreadsheet recipe
You can rebuild every number above in a few minutes. Set up columns A through F:
- A1: 500000 (starting balance)
- B1: 0.07 (gross return)
- C1: 0.01 (Path A cost)
- D1: 0.0015 (Path B cost)
- E1: 0.025 (inflation)
Then in row 2, put the year number in A2 and the formulas:
- B2: =$A$1*(1+$B$1-$C$1) — Path A balance after year 1
- C2: =$A$1*(1+$B$1-$D$1) — Path B balance after year 1
- D2: =C2-B2 — the gap
For row 3 and below, replace $A$1 with the previous row’s balance:
- B3: =B2*(1+$B$1-$C$1)
- C3: =C2*(1+$B$1-$D$1)
- D3: =C3-B3
Copy those three formulas down to row 41. Row 41 is year 40. The value in D41 is the nominal gap. To express it in today’s dollars, divide by (1+$E$1)^40. If your spreadsheet returns a different number from the table above, check that you are using annual compounding and that the fee is subtracted before the return is applied, not after.
What to do with the number
The ledger does not tell you to fire your advisor or to buy a particular fund. It tells you what the fee difference costs under a stated set of assumptions. If the 7% return assumption holds, the gap is six figures in today’s dollars and seven figures in nominal dollars. If it does not, the gap is smaller, but it does not disappear. The useful move is to put your own fee rates and your own return assumption into the spreadsheet and look at the number. Then decide whether what the fee buys is worth what the ledger says it costs.
For a related look at how small, consistent contributions interact with the same compounding mechanics, see What a Ten-Dollar Weekly Bump Actually Does to Your Retirement Number. The arithmetic is the same; only the input changes.
FAQ
Is the 1% fee the same as a 1% expense ratio? Not necessarily. An advisory fee is typically charged on the account balance, while an expense ratio is deducted from the fund’s assets. The ledger treats both as an annual percentage subtracted before compounding, which is the right comparison for this question. The actual mechanics and disclosure requirements can differ, so read the fee documents for your own account.
Why does the gap grow faster in later years? Because the fee difference is applied to a larger balance each year, and the foregone growth on earlier fee differences compounds. The gap is small in year 1 and large in year 40 for the same reason a small contribution becomes a large balance over time.
What if I add contributions? The fee drag applies to the whole balance, including new contributions. Adding contributions will increase the dollar gap, not reduce it, as long as the gross return exceeds both fees. You can model this by adding a contribution column and applying the same formula to the new balance each year.
Does inflation change the comparison? No. Inflation changes how you express the gap, not the gap itself. The nominal gap is the same regardless of the inflation assumption. The real gap is smaller because future dollars buy less.
What if the gross return is lower than both fees? Then both paths lose money, and the lower-fee path loses less. The direction of the comparison does not reverse. The ledger assumes a positive gross return because that is the scenario most readers are planning for, but the formula works for any return.