To get 2.7%, I did 1-(99.91%)^30. Is that not correct?

I'm not sure - but even if that is mathematically correct....

Hot tip: you may want to avoid pompously flying in with a "This is bad math" if you don't actually know that the math is incorrect. Having nothing to offer on what the

*correct* math might be, and then shifting the goalposts to an unrelated point is pretty cheesy too.

There are two slightly different ways to apply an expense ratio to a rate-of-return. dandarc's method applies the ER to the amount at the beginning of the period, while another option

as used by this calculator applies the ER to the amount at the end of the period. When your rate-of-return is positive, the second method results in a slightly lower figure than the first, since the expense ratio applies to a larger number.

X=investment, R=rate-of-return, E=expense ratio, Y=years

Method 1: X*(1+R-E)^Y = $1000*(1+0.08-0.0008)^30 = $9841.43

Method 2: X*((1+R)*(1-E))^Y = $1000*((1+0.08)*(1-0.0008))^30 = $9823.93

The "advantage" to Method 2 is that when comparing the effects of two different ERs, the rate-of-return becomes a non-factor. The equation to find "percentage decrease in final value due to a higher expense ratio" simplifies to:

Eh=high expense ratio, El=low expense ratio

1-((1-Eh)/(1-El))^Y = 1-((1-0.0017)/(1-0.0008))^30 = 2.667165%

Philociraptor did 1-(1-Eh-El)^Y = 1-(1-(0.0017-0.0008))^30 = 2.665059184%

I'm not sure what the derivation is for that equation, or why the result is freakishly-close-but-not-the-same, so I'm in no position to declare it either "bad math" or "good math".

Anyway, it would be interesting to see Vanguard research on people who intentionally made the switch from an all-in-one fund to individual funds for the reduced expense ratios, to see whether the cost advantage actually materialized in their returns, or if lack-of-trading/increased-trading eliminated the theoretical advantage.