Questions for guys who have experimented with different apps for currency exchan

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I've been reading about ways to pay a foreign doctor (say you have US dollars and you are trying to pay someone in Euros)

What method would you use to avoid fees with exchange rates and fees associated with sending money to someone in a foreign country?

I asked the bank how do I pay the doctor, they suggested a bunch of different ways (direct debit, wire transfer, bank of america to bank of america at a teller window (probably can't use for sending money to someone foreign?), cashier's check with a $15 fee, and electronic transfer with something about an ABA for electronic transfer. I'm also reading there is something called ACH which seem to be related to money transfer.

But then I go on the internet and google about exchange rates and sending money overseas and there are apps that say they reduce fees compared to doing it yourself, and I'm a bit confused.

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I'm not Australian