There are several varieties, fixed rate mortgages exist for 10-30 year terms.

Adjustable rate mortgages also exist and commonly with a lower starting interest rate, but they are often a trap for people with low incomes who suddenly cannot afford their home because of interest rates outside their control.

And some mortgages have a cliff, so that you're paying mostly just interest and very little principle. Then at the end of the term you basically have to pay the entire principle at once.

So you can do it either way. A fixed rate is vastly less risky, I'm surprised that an adjustable rate is the default in NZ. In the time I've had a home rates have varied from like <3% to 7%.