# How the fee of ETF VTI is calculated?

For the ETF VTI, I tried to calculate the fee, but my number doesn't match that \$71.

Here is my calculation: Am I missing anything? The total fee the way I calculated is \$45.57.

The formulas I am using are:

``````Balance: =10000 * POWER(1.09, A2-1)
Fee: =B2*0.0003
``````

Thanks!

• You have only 9 years of growth listed in your chart, not 10. Jan 2, 2020 at 18:04
• @DilipSarwate Thanks. I think I should add another year and calculate the sum of fees starting from year 2, so the sum is \$49.68. Jan 2, 2020 at 18:14
• You forgot to subtract the fee from the balance... you will not get 9% growth on the portion you had to pay out in fees. Doing that, I get fees paid of \$42.52, but the "cost" of the fee is \$58.57. Jan 2, 2020 at 19:21

There might have been an oversight by someone at the company, but I got the number by doing this

`10,000 * POWER(1.09, 10) * 0.0003 * 10 = \$71.02`

Which is incorrect because the fee will have less value early on (as you have shown in your table) but it gets you to the \$71 that they are advertising.

EDIT:

After digging into it some more, Vanguard has cut the VTI expense ratio a few times. Looking at this investopedia article they say that the expense ratio was dropped from 0.05% to 0.04% (and obviously it dropped again from 0.04% to 0.03%). Also in this this blog they say that the overall expense ratio was 0.046%. Doing the same math as you were doing with both of these ratios gives the following

0.04% gives a \$60.77 fee 0.046% gives a \$70.65 fee 0.05% gives a \$70.96 fee (excluding the expense for year 1) So my guess is Vanguard cut their expense ratio but didn't update this comparison of how little their fees were compared to their competitors.

• Ah I see. Thank you. That explained how \$71 is calculated. And I agree with you, the total fees should be less than \$71. Jan 2, 2020 at 18:09