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Are bitcoins with more confirmations more valuable, or does the number of confirmations not add a sort of "time value of money (TVM)"?

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Not really. A 0.2 BTC "bitcoin"† with ten million confirmations has no more value than a 0.2 BTC "bitcoin" with one million confirmations.

The exception might be that a "bitcoin" with less than six confirmations might be regarded as slightly less desirable for up to an hour.

Bitcoin generally meets the fungibility expectations of currencies. Just as banknotes (bills) with serial numbers do. A fresh new banknote is not worth more or less than an old one when you spend it in a shop.

In both cases, there is the case that money that can be traced to crime might be less acceptable - but that has nothing to do with the age of the banknote or of the "bitcoin".

† An unspent transaction output (UTXO).

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    Moreover, the "time value of money" is due to the fact that if you have money earlier, you can invest with it to gain more. Just leaving the money (whether it's fiat or bitcoin) be isn't going to make it increase.
    – Pieter Wuille
    Dec 27, 2022 at 15:04

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