The woman saw an advert online and rang a call centre in Scotland where a broker convinced her to begin trading on currencies.
The woman changed her mind and decided to get her money out. But was told she needed to make more trades to do so.
Realising she would probably lose more money by continuing to trade the woman pulled out but continued to be hounded by late night calls from the broker.
In the end she had the number blocked and told him she would report him to police if he did not stop calling.
The FMA has also highlighted a second scam case this week as part of a fraud awareness week being run by the Ministry for Business, Innovation and Employment.
A Christchurch man lost $67,000 after he was cold-called by scammers who convinced him to invest in a pharmaceutical company.
He initially said no to the investment after receiving the call from an overseas company but decided to invest after doing some research and believing the company was legitimate.
At the time it did not appear on the FMA's warnings lists and wasn't connected to any scams.
The man became suspicious when the company told him the shares had been sold, and he would receive the funds the following week.
But he never received the money and was told he would need to pay another $21,000 to get the money released. He didn't pay.
Paul Gregory, FMA head of investor capability, said people should hang up on cold callers offering an investment from offshore.
"The best thing investors can do to someone cold-calling offering an investment from offshore is to put down the phone. Ignore that email. If you hand over money and it turns out to be a scam, it's often impossible to get your money back."
Mark Hollingworth, MBIE's consumer protection manager, said scams were a global issue.
"We're seeing scammers use more sophisticated methods as technologies advance to target consumers, as well as fronting scams with well known brand or organisation names to make the scam seem more legitimate."
How to protect yourself
• Find out the company's legal name and do an online search for it.
• Use a licensed provider. In New Zealand the Financial Markets Authority issues licenses to financial service providers. Check the lists here.
• If the business isn't New Zealand based find out who regulates them and check with the regulator that the company is on their lists.
• Check the company isn't on the Financial Markets Authority's warnings list.
• Check the international warning list.
• being extra careful if the company is overseas based as it is often impossible for you to recover your money if an overseas investment turns out to be a scam.