Read more:
• Reserve Bank cuts Official Cash Rate to 3 per cent - banks follow suit
• Mortgage rates fall below 5 per cent
Interest.co.nz said the rate was available to BNZ customers who had at least 20 per cent equity in their property and who had a BNZ account receiving salary or wages.
Massey University banking expert David Tripe said BNZ's new rate was "probably somewhere near where rates ought to be".
"Rates haven't been coming down to the extent that they ought to as funding costs have fallen.
"I've been saying for some time that there's some scope for fixed rates to come down, because they haven't come down as much as they might have."
Mortgage broker Bruce Patten said BNZ's move was good for consumers.
"I think it's just the beginning of some more to come given the recent rate drops and expectations of further rate drops.
"All I would say to people is 'don't get sucked in by what appears to be good now when it could get even better'.
"The banks are really just trying to lock in and secure their funding with some good rates, I wouldn't necessarily be drawn on what might look good now.
"A few months ago 5.99 looked really, really good and now people are scrambling to get out of them."
Across the ditch, mortgage hunters could get fixed, 5-year rates as low as 4.39, Patten said.
If the OCR dropped to 2 per cent as some economists were predicting it would then fixed mortgage rates could drop down closer to 4 per cent or even sub-four, Patten said.
• Colin Meads first pulled on a black jersey when he was selected for the New Zealand under 21 side which toured Ceylon (now Sri Lanka)
• New Zealand's last polio epidemic broke out.
• On 1 May, in Malaya, Vampires of 14 Squadron carried out the RNZAF's first operational strike mission since the Second World War and the first in jet aircraft.
• Four prisoners were executed in New Zealand prisons in 1955
• NZ cricketers set the unwanted world record at Eden Park when they were dismissed for 26 runs in the second test against England. Only opener Bert Sutcliffe made it into double figures, scoring 11.
• The big-ticket household items in the 50s were washing machines and refrigerators. By 1959 only just 54 per cent of dwellings had the sole or shared use of a refrigerator and 57 per cent had the sole or shared use of a washing machine.