The margin was similarly slim across most New Zealand cities.
In Auckland, the 33.8 per cent of income to service a mortgage and costs was just 5 per cent more than the 28.5 per cent to pay the average rent, but rates varied between areas of the city. In Auckland City, the report claimed it was more expensive to rent than buy.
A similar report published by interest.co.nz found the amount needed to service a mortgage for a person earning the median income of a 25- to 29-year-old had fallen from 71 per cent four years ago to 44.3 per cent as of February.
ANZ retail managing director Kerri Thompson said seminars for first buyers had been well booked.
"It's become more pronounced in this last year as the interest rates have dropped off. And when we talked to people in the seminars we found that was what they were saying."
ANZ figures also showed rent rises had outstripped rises in house prices in Auckland, where other research last month revealed the average weekly rent for a three-bedroom house had swelled to $550, after climbing $55 in just one month.
Real Estate Institute chief executive Helen O'Sullivan said: "Our BNZ-REINZ indicators are that first-home buyers have reappeared over the last three to six months on the back of a strengthening job market and continued low interest rates."
Buyers who had delayed buying decisions until after the recession were also emerging on the market.
Property Investors Federation national president Andrew King said that while it did appear to be agood time to buy, renting was still generally the cheaper option.
"In some places, especially Auckland, where rents are going up at a very fast rate, it's probably getting more affordable to buy than to rent, for those who want to."
The gap between the cost of renting and buying had been closing, but levels were still not where they should be, he said. "They should be much the same, but they are not, and it still costs a few thousand dollars more to own than to rent.
"And when house prices do start taking off again, and interest rates go up, that margin will only get wider, we'll find it will change around, and it'll become a lot more expensive to buy than to rent."
Property commentator Philip Macalister has seen increased activity at the lower end of the market, with investors vying against first-time buyers.
"If you did want to buy and get onto the property ladder, now is a really good time to be doing it."
While he does not expect interest rates to rise any time soon, he sees no reason for house prices or rent to come down.
"They are still expensive and there are no signs they are going to become more affordable in the future, so we should get used to what we've got now."
A recent global survey found New Zealand had no affordable housing markets, with Auckland's only slightly better than London but less affordable than those in Los Angeles and New York.
Interest.co.nz publisher David Chaston said Auckland buyers particularly had to be financially prepared and realistic over where to buy.
"Our advice has always been don't spend more than 40 per cent of your take-home pay. If you are near that, you are probably in unaffordable territory," he said.
"And unless you have a substantial deposit - we are talking about between 15 and 20 per cent, which is a lot of money in Auckland - you're risking your future financial health."
Owning home adds up for family of five
One of Auckland's newest homeowners is not surprised more people like him are getting out of renting.
After six years of saving, Salvador and Lolita Etraves, both 43, will move into the five-bedroom home they have bought two blocks from the Manurewa house they have been renting.
Mr Etraves said his family of five, who came to Auckland from the Philippines, had been fortunate to be paying just $300 a week renting while putting more than $200 towards their house deposit each week.
For Aucklanders paying more than $400 a week in rent - a figure well below today's average rent of $550 - Mr Etraves believed their cash would be better put towards a mortgage payment if they could raise a deposit.
"My feeling is rents are getting higher and higher ... and are not going to come down."
Mr Etraves, an electrician, and Mrs Etraves, a machinist, decided to buy as interest rates became attractive and their family outgrew their rental.
"The interest is definitely better now than it was not too long before, when we were looking at 9 per cent. The bank also allowed us a 10 per cent deposit, when before it was 20 per cent. It was just the right time for us."
The $41,500 deposit they raised was done with plenty of left-over spending money each week, and Mr Etraves said that spare cash would now go towards the $590 needed each week to service their mortgage.
"People should really be working out a budget or a savings plan if they are paying any more than $400 a week. If they can buy, they should. It's just a matter of getting a cheaper house and finding that deposit."