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Gordon Layton, from Bundaberg, Queensland, was trying to electronically send AU $71,400 (£38,200) to a company that moved an old house on to his block of land, but he got the details wrong.
The cash was transferred from his ING account into an incorrect ANZ account on 14 June.
Speaking to A Current Affair, the 88-year-old - who had a stroke on his birthday - said: "Well obviously I wasn't pleased.
"In fact, I was really p****d off that this guy had taken the opportunity to say 'well I'm not giving it back, b****r you.'"
He added: "It made me angry, but I try not to get uptight. It's bad for my blood pressure."
Gordon contacted the banks to ask for the payment to be blocked, but it was too late.
To make matters worse, the house moving company is now threatening legal action to get the money they are owed.
Gordon's daughter Jacqui Morrison-White said: "It's a sickening feeling when you realise $71,400 of your father's money is gone.
"Within three hours of that transfer we knew he'd made a mistake.
"However, I had faith that given that we'd come across the problem so quickly, and we've notified both the banks so promptly, that we would be fine."
She continued: "It's become evident that the ANZ did try to get the money back.
"The funds had already been moved out that day and they had to ask the unintended recipient's permission to get the money back. Of course, he said no.
"Two great big banks earn a tonne of money every year for their stakeholders. Little old pensioner makes a mistake and they've thrown their arms in the air and said 'we can't help you'. I think that's wrong."
ANZ said it is working with police to try and recover the funds.
A spokesperson said: "ANZ does not publicly comment on any specific customer details, however we are aware of this matter and have been working with both our customer and relevant law enforcement on a regular basis to try and recover the funds for Mr Layton and assist the police with their enquiries.
"When a bank notifies ANZ of a mistaken payment, we trace the funds and endeavour to recover them from the unintended recipient.
"As this is now a police matter, we won't make any further comment."
In a statement, an ING spokesperson said: "Unfortunately Mr Layton paid the money to the wrong person who has an account at ANZ. When we were alerted to Mr Layton's mistake we sent a recall request to ANZ but they were unable to return the funds to Mr Layton's ING account."
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