Rebates will only be paid when sufficient profit is made. Members will get different amounts calculated on a relationship index which measures the amount of business they do with the bank.
The Cooperative Bank is registered a cooperative company. Everyone who does business with it gets one share, which is not tradable and has no par value. The bank cannot be taken over.
Gascoigne said it was New Zealand's first cooperative bank. The structure existed around the world and bank regulator the Reserve Bank of New Zealand was comfortable with it.
PSIS has come a long way since it was placed in statutory management in 1979 and funds were frozen for several years. It emerged from its problems in 1987 and in 1995 membership opened to all New Zealanders. The name Public Service Investment Society was changed to PSIS Ltd in 1998.
Chief Executive Girol Karacaoglu said the new name would to remove any lingering perceptions that the organisation existed for public servants.
The cooperative model for banks was hugely successful worldwide, including during the global financial crisis, he said.
The bank would stick to personal banking while diversifying from a lending portfolio that is 90 per cent mortgages. It was not signalling a push into commercial lending beyond to small businesses.
The Cooperative Bank wanted to do more insurance business but had no ambitions to operate as a standalone entity in the funds management sector.
It currently has a market share between 0.6 per cent and 0.7 per cent and is aiming to grow faster than its bank peers but is not chasing huge growth.
In July PSIS members voted in favour of amending its trust deed so it could become a bank.
PSIS already offers current accounts, savings accounts, term deposits, insurance, personal loans and home loans.
The new bank gained an upgrade in May to its Standard & Poor's long term credit rating to BBB minus with an outlook of stable.
The 83-year-old institution has more than $1 billion in deposits, which are its main source of funding.
There are now 21 registered banks in New Zealand. The Reserve Bank of New Zealand has developed minimum prudential and governance requirements for non-bank institutions since it was made the sole prudential regulator of the New Zealand financial system.