The correct answer is:
Al went to the bank to commute his American dollars to euros.
Although usually used as a definition of traveling back and forth regularly between a suburb and a city, in this case, the word commute is used as an exchange for something different, from one currency to another.
Another possibility would be to use as an exchange over one type of payment or investment for another type. As in: “Pensioners can commute their pension for a lump sum.”