Math for MoneyHow it's calculated
The calculator treats the fee as a reduction of your annual return:
Net return = Return before fees − Annual fee
It then calculates two ending balances with the usual compound growth formula, one at the return before fees and one at the net return. For a single lump sum with no further contributions:
Balance = Initial investment × (1 + annual return)years
The cost of the fee is the difference between the two:
Cost of fees = Balance without fees − Balance after fees
For example, take $10,000 invested for 30 years at 7% before fees, with a 1% annual fee and no further contributions. Without fees: $10,000 × 1.0730 = $76,123. With the fee the net return is 6%: $10,000 × 1.0630 = $57,435. The cost of the fee is $18,688, or 24.5% of the balance without fees.
Monthly contributions are handled the same way in both cases: each one is added at the end of the month and then grows at a monthly rate of (1 + annual return)1/12 − 1. These are the same rules as the default settings of the compound interest calculator, so you can check either balance there.
Subtracting the fee from the return is a simplification. Funds deduct their fee in small amounts throughout the year, as a percentage of the balance at the time. Charging 1% on a balance that has grown by 7% leaves a net return of 5.93% rather than 6%, so the real cost is very slightly higher than shown here.
Why the cost is larger than the fees you pay
The number at the top of the result is not the sum of the fees. It is how much smaller your ending balance is. Each fee leaves your account for good, and so does everything it would have earned in the following years.
In the example above, the first year's fee is about $100. Left in the account at 7% for the remaining 29 years, that single fee would have become about $711. The same thing happens with every later fee, and the fees themselves get larger as the balance grows. That is why the orange part of the chart widens over time.
This also means the number of years matters, not just the fee level. The table uses the example values ($10,000 to start, $500 a month, 7% a year before fees, 1% fee) and changes only the number of years:
| Years | Without fees | Lost to fees | Share lost |
|---|---|---|---|
| 10 | $105,197 | $6,052 | 5.8% |
| 20 | $292,465 | $33,674 | 11.5% |
| 30 | $660,849 | $116,157 | 17.6% |
| 40 | $1,385,516 | $328,820 | 23.7% |
How much difference does the fee level make?
This table keeps the example values ($10,000 to start, $500 a month, 7% a year before fees, 30 years) and changes only the fee. The fee levels are arbitrary steps for illustration, not a description of any particular product. Enter your own fee in the calculator for your real numbers.
| Annual fee | After fees | Lost to fees | Share lost |
|---|---|---|---|
| 0.1% | $648,079 | $12,770 | 1.9% |
| 0.25% | $629,431 | $31,418 | 4.8% |
| 0.5% | $599,657 | $61,192 | 9.3% |
| 1% | $544,691 | $116,157 | 17.6% |
| 1.5% | $495,302 | $165,547 | 25.1% |
| 2% | $450,907 | $209,941 | 31.8% |
Which fees to enter
- Expense ratio. The yearly fee of a mutual fund or ETF, as a percentage of your money in the fund. It is listed in the fund's prospectus or fact sheet.
- Advisory or management fee. A percentage of your balance charged by an adviser or a managed account. It is stated in your agreement and usually shown on your statements.
- Both. If you pay both, add the percentages together.
The calculator does not cover costs that are not a yearly percentage of your balance, such as sales charges, trading commissions, flat account fees or taxes.
Related calculators
- Compound interest calculator: see how a balance and monthly contributions grow, split into contributions and interest.
- FIRE calculator: find how large a portfolio you need to cover your spending and how long it takes to get there.
Frequently asked questions
What is an expense ratio?
An expense ratio is the yearly fee a mutual fund or ETF charges, written as a percentage of the money you have in the fund. It is taken out of the fund's assets automatically, so you never see a bill: the fund's reported return is simply lower by about that amount. You can find it in the fund's prospectus or fact sheet.
Why is the cost of fees larger than the fees I actually pay?
Because every dollar paid in fees also stops growing. The cost shown here is the gap between your ending balance with no fees and your ending balance after fees, so it includes the fees themselves plus all the growth that money would have earned if it had stayed invested. In the example of $10,000 at 7% for 30 years, the first year's fee of about $100 would have grown to about $711 by the end if it had stayed in the account.
How does the calculator apply the fee?
It subtracts the fee from the annual return: net return = return before fees − fee. A 7% return with a 1% fee is calculated as 6% a year. It then runs the same compound growth calculation twice, once at the full return and once at the net return, and compares the two balances. Real funds deduct fees in small amounts throughout the year, so actual results differ slightly.
I pay a fund expense ratio and an advisory fee. What do I enter?
Add them together and enter the total as the annual fee, as long as both are charged as a percentage of your balance. You can then put the fund fee alone in the comparison field to see how much of the cost comes from the advisory fee.
Does a higher fee mean a better return?
A fee is certain and a return is not. This calculator assumes the same return before fees in every case, so the only difference between the balances is the fee. If you expect a more expensive investment to earn more before fees, you can test that by running the calculator twice with different returns and comparing the balances after fees.
Are the results in today's dollars?
Only if you enter a return after inflation. The calculator does not adjust for inflation or taxes on its own. With a return before inflation, the balances are in future dollars. The share of the no-fee balance lost to fees is a percentage, so it stays easy to interpret either way.