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1343
Answer: Much of this answer is developed at length in a teshuva that will appear in Bemareh Habazak IX:10. We will add points that apply to this case.
There are two halachic issues to consider: commerce on Shabbat and amira l’nochri (requesting a non-Jew to do work on Shabbat).
Rashi (Beitza 36b) gives two possible reasons for the prohibition on commerce on Shabbat: it is against the navi’s instructions to refrain from mundane activities; it may bring one to writing. Simple logic dictates that when the Jew’s involvement took place before Shabbat and matters are finished up by others or automatically, the prohibition should not apply. However, Rabbi Akiva Eiger (Shut I:159) extends the prohibition to cases in which the interaction was during the week but it was to take effect on Shabbat. So arguably, regardless of when you arranged it, the payment of your debt (which is also commerce – Rama, Orach Chayim 307:11) on Shabbat is forbidden.
One does not need to be concerned by this opinion for (a combination of) two reasons. 1. It is far from clear that we accept R. Akiva Eiger’s opinion (see opinions in referenced teshuva). After all, even doing full melachot before Shabbat that finish by themselves on Shabbat are permitted. Furthermore, the best answer for R. Akiva Eiger from sources (including Shulchan Aruch, OC 307:4) that a Jew can have a non-Jew acquire something on his behalf on Shabbat is that a transaction finished off by a non-Jew is permitted even if one that finished by itself is forbidden. If so, there would not be a problem in this case.

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We could stop here, but we do not want to imply that there is no other logic for leniency. One should be aware that amira l’nochri is among the most complicated areas of hilchot Shabbat, and people should become accustomed to asking, as there could be more room for leniency or stringency than one might expect.
We should consider whether the bank is working for you when making the transfer. One might be able to look at the transaction between the bank and the credit card company as being done primarily on behalf of the credit card company. They are the ones who initiate the payment on a monthly basis, when the time comes, and they receive the money. Perhaps we should view your instructions to the bank as acquiescing in advance to the payment (albeit if it was not worth your while, you wouldn’t do it). These analyses may differ from case to similar-sounding case.
It is also possible that giving the order during the week to pay on a date that usually falls during the week, is not considered amira l’nochrieven if, down the line, it happens to fall out on Shabbat or Yom Tov. There are several precedents (e.g., Mishna Berura 247:10 and Mishbetzot Zahav, OC 307:2) of the idea that statements that cause the non-Jew’s work on Shabbat may still not be considered direct enough to be amira l’nochri. However, it is very tricky to apply such a concept.
The bottom line is that you can allow these bank transfers arrangement to continue no matter when they fall out.

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