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I think so far the cost has remained at a minimum of 20k satoshis, I think nothing has changed from this even though the price of bitcoin continues to rise. If we are based on the price in dollar conditions, of course it will be different, but we should see it in BTC so that everything looks the same, nothing is different.
It makes no sense talking about "minimum costs". The fee is calculated in sat/
vbyte. If you say the minimum "cost" is 20k satoshi's, that'll only lead newbies the wrong way.
A one input, 2 output transaction from a native segwit wallet has a size of ~180 bytes, at the moment you should pay at very least >200 sat/vbyte. 200*180 = 36k satoshi's.
And that's for a tiny transaction, and not paying the optimal fee but barely the minimum fee.
If you have bigger transactions (2 or 3 inputs, 2 outputs, non-native segwit wallet) and you want a big chance of getting confirmed in the next 2 or 3 blocks, your fee is rather going to be in the 130k sat range.
But if you talk about the
minimum fee, that's still 0. 0 fee transactions are still theoretically possible, but allmost no nodes will relay them, and allmost no miner will put them into a block he/she is trying to solve...
IIRC, the default minimum relay fee is 1 sat/byte, so for a "small" transaction that's only 200 sat's... Offcourse, at this moment in time, your transaction will not be mined untill the mempool is allmost completely empty (which can take days/weeks/months)