why discount collaterized swaps with EONIA?

the collateral at every moment must coincide with value mark-to-market of swap

let’s take as a example simple swap with just one cashflow , which pays 100 euros at time T [it has no variable leg]

at time T swap’s value is 100 euros
so collateral value is also 100
at time T-1 (previous day) how much collateral we have to put?
if collateral is in EUR and grows with overnight EONIA rate
we must put 100 euros (=value of cashflow) decounted with EONIA rate
but as collateral coincides with MTM of derivative the cashflow must be discounted with the same rate

another example

if swap is in EUR but the collateral is in USD we still have to discount the derivative with OIS rate (usd fed funds)

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