But her father insisted she got an education. "He said: 'No way. You are going to finish school'."
Mentis went to university and chose a degree in business, majoring in economics and modern history - subjects she loved and excelled in at during high school.
She minored in law - inspired, she says, by contact with the legal fraternity at one of her parents' cafes, which was next to a courthouse.
"It was only a three-year degree but after my first year I thought I have got to get working."
It was through the cafe work that she met a recruiter for Macquarie Bank, who asked her to come in for an interview.
After a whole day doing psychometric testing, she was convinced she wouldn't get the job. "I thought, I'm never going to hear from them again."
But she did, and began full-time work at the bank while finishing her degree by attending university five nights a week.
Mentis says it was an exciting time to be stepping into the world of finance.
"It was 1986 - the beginning of the boom in financial markets."
The financial system had been deregulated in Australia and the economy was opening up for the first time.
She moved to Citibank, where she worked in roles from financial markets, to risk management, venture capital and funds management.
"Every day I would go home and be like 'wow'."
Then she moved into helping distressed businesses get back on their feet. "They were probably the best learning years of my banking career."
Mentis worked under an American chief executive - Jake Williams - who was also an astrophysicist.
"He imparted in us the importance of understanding what had gone on for those businesses. Our job was to get them back on their feet."
But it was not all plain sailing for a woman working in the predominantly male world of finance.
Mentis has vivid memories of one particularly challenging client. She walked into the room for their first meeting and he said: "I'm not having any sheila looking after my money."
Rather than putting her off, it only made Mentis more determined to show him that she could make a difference to his finances.
"He called me 'sheila' for 12 months. After 18 months he was taking me out to lunch and sending me flowers on my birthday."
More importantly, her bank was the first in a syndicate of lenders to be paid out money the client owed.
When Williams moved from Citigroup to Westpac's institutional banking arm, she jumped ship too in late 1995.
She worked to help the bank sort out its syndication and mezzanine debt deals and to set up Westpac's private wealth division, which linked wealthy customers with businesses needing investment.
That was how she came to the attention of National Australia Bank - the Australian parent of BNZ.
NAB had the client's business banking, but Westpac had their private banking and her name kept coming up again and again, Mentis says.
A year of courting by NAB convinced her to switch banks in 2006, when she started as a general manager in specialised investments and moved up the ranks to private banking and business banking, joining the group's executive team in 2014.
Her last role at NAB was chief customer officer, business and private banking - essentially, managing the biggest money earning divisions for the bank or the "jewel in the crown".
Her move to head the BNZ has seen her switch jobs with former BNZ chief Anthony Healy and become the first woman chief executive for the bank.
Mentis says that is a privilege. "I feel huge responsibility as well. I think being a woman just brings a different perspective.
"It's good to have different perspectives on leadership teams and that inclusiveness and diversity is really what makes for good business and good societies."
She says it is also about being a role model for other women who aspire to leadership positions.
But her move to the top has come at a time when banks are facing intense scrutiny from regulators and the public.
Australia's Royal Commission into misconduct in the financial services industry has put the spotlight on some bank practices, and New Zealand regulators have responded by calling for this country's banks to prove they are clean.
"None of us are proud of what we have seen during the Royal Commission," Mentis says.
But she is quick to point to the differences between Australia and New Zealand and says Australia's problems hark back to before the global financial crisis.
Unlike New Zealand, Australia never had a financial sector melt-down or went into a recession.
Instead, its banks were commended for being the top in the world in the strength of their capital and for staying afloat where others collapsed.
Yet, Mentis says, there were people losing their entire life savings through the likes of Storm Financial - a financial advice business which collapsed, leaving investors out of pocket. "It started to break the trust."
And then the aggrieved customers began to go to the politicians.
While the Royal Commission has made headlines this year, she says it is not the first inquiry for the sector- there have been 57 inquiries into financial services in Australia and hundreds of recommendations.
"We were on it. But we didn't move fast enough," she says.
While the BNZ is owned by NAB, she points out that it has a local board. "I am employed by the BNZ's board - they do the hiring and firing."
And she says they are not afraid to put the pressure on.
But despite all that she says the bank can't afford to be complacent, and Mentis admits banks can't get it right all the time.
"BNZ has 1 million customers and carries out 10 million transactions a month. Mistakes will happen but we have got to fix them quickly."
She says there are lessons to be had from Australia, as well as from changes made after inquiries into financial services firms' conduct in Britain and the US.
"Our view is let's take best practice and make it common practice."
Despite the tough environment, Mentis is still brimming with enthusiasm for her job and the role of banks.
"It is such a privilege to be a banker. We are getting invited into the customer's financial world and that is a huge privilege and a huge responsibility."
Historically, New Zealand has often been a stepping stone for Australian banking executives moving up the corporate ladder.
Mentis says she plans to stay long enough to make a difference and leave a legacy, and says she has been in most of her roles for at least five years. "I would love to stay here for as long as possible."
She has come to New Zealand with her husband, leaving their two teenage children behind to finish their university studies.
"We have flown the coop."
She plans to make the most of her time here by seeing the country. "I am going to do every corner of New Zealand and visit every person who works for us."
Angela Mentis
• Job: BNZ chief executive
• Age: 50
• Family: Married with two teenage children
• Qualifications: Bachelor of Business with a major in finance and economics and a sub-major in business law. Graduate Diploma in Applied Finance and Investment from the Securities Institute of Australia.
• Career: Began with Macquarie Bank and has held senior management positions at National Australia Bank, BT Financial Group, Westpac and Citibank.
• Last book read: Shoe Dog (the story of Nike), by Phil Knight
• Last movie watched: The Post
• Last overseas holiday: In 2016 she took her daughter Becky to Italy to celebrate finishing high school
