The Reserve Bank has forecast that the official cash rate will begin rising in the second half of next year and floating rates are the rate most likely to move in line with official cash rate changes.
Ben Kelleher, managing director personal at ANZ NZ, said as New Zealand's largest lender the current housing market continued to concern it because homeownership was getting beyond many.
"New Zealand's fundamental problem is one of supply and demand. Making it more affordable for people to fund new builds is one way we can contribute to increasing supply in the market."
The bank will also offer up to $3000 in cash bank for those borrowers who build a 6+ Homestar rated home.
Homestar is an independent assessment tool used to measure a home that certifies the health, efficiency and sustainability of New Zealand homes.
A 6+ rating and above recognises a house that has been built at or above the current standards set by the New Zealand building code.
The offer is available from July 5.
Borrowers must a have minimum 20 per cent equity or deposit to get the discounted loan as well as an ANZ transaction account with their salary direct credited to it.