I’ve heard that there is a problem with interest from bank accounts over Rosh Hashanah and Shabbos before/after Yom Tov, as interest is calculated daily and there is no havloah in this case.
What should I do in practice? I have interest-bearing bank accounts in Israel and abroad, but neither has any facility for returning the interest paid over Shabbos/Yom Tov.
As you said there is a problem with receiving profits on Shabbos or Yom Tov, however this is only an issue when Yom Tov is adjacent to Shabbos or when on Rosh Hashana, when the two days are considered like one long day. However on a regular two day Yom Tov, R’ Moshe says that since one of the two days is surely not Yom Tov, although we observe it, however for this halacha we can be meikel, and there is no problem with using the interest that was accrued during those days.
When there is a problem, R’ Moshe says that the money should be given to tzedakah discreetly, in a way that the donor will not get any recognition for it, and therefore essentially is not benefiting from the money at all.
Igros Moshe O”H 4-59, Beer Moshe vol 5:100-1