How are index fund fees taken?

How are index fund and ETF fees taken from the platform?

For example I invest into VUSA, which on the Vanguard websites states a 0.07% fee.

Seems like the Community has explained it better. I’ll edit my comment to prevent confusion, but the point stands - no such fees are taken from your account.

The platform/broker in which you have purchased an index fund or ETF, do not pay the index fund / ETF fees. The fees are accrued daily and are included in the NAV(Net Asset Value) of the product, and are paid directly from the product.

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It’s not taken from the platform. That fee is embedded in the movement of the price of the instrument.

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So I can go ahead and add a fund that costs 0.87% and not worry about it?

You do not pay the fees of a fund, they are paid by the fund itself. The OCF is quoted simply to make it clear the underlying ongoing operational fees of the product you bought.