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My university has tranfered me money by mistake, and wants me to transfer it back
Confirming whether the payment was an error The simplest method is to confirm manually with the University whether the payment was a mistake and satisfy that between yourselves. If you're concerned it's fraudulant, I recommend calling the University finance office on a phone number you find on their website, or call one of the people you know. Reversing the payment To formally reverse the payment, I'd check your Product Disclosure Statement on your account with the bank. There's almost always a fee involved where a payment is reversed. It's probably easiest to just issue the payment back to the university to an agreed BSB/Account Number.