How the NZ Buy vs Rent Calculator works: formulas, assumptions & worked example

1. The model in brief

The calculator runs a year-by-year simulation of two versions of you over the length of the mortgage (20 years by default):

The buyer pays a deposit, takes out a repayment mortgage and pays the running costs of owning.
The renter pays rent instead, and invests the money the buyer spent up front (the deposit and one-off purchase costs).

Each year, whichever option costs less that year invests the difference. At the end we compare each side's net worth: what they own minus what they owe. The side with the higher net worth is the one the calculator recommends.

The formulas below are the ones the calculator runs in your browser. Symbols are defined under each formula, and all rates are annual unless stated otherwise.

2. Buying: mortgage and running costs

Monthly mortgage payment

The mortgage is a standard repayment (capital and interest) loan at a fixed rate for the whole term:

M = P × r(1 + r)ⁿ ÷ [(1 + r)ⁿ − 1]

M: monthly payment
P: loan amount: house price minus deposit
r: monthly interest rate: the annual mortgage rate ÷ 12
n: number of payments: term in years × 12

In words: the fixed monthly payment that pays off the loan, with interest, in exactly n payments. For a 0% rate it is simply P ÷ n.

Mortgage still owed

After k years of payments, the balance still owed is the present value of the payments left:

B_k = M × [(1 + r)^m − 1] ÷ [r(1 + r)^m]

B_k: balance owed at the end of year k
m: payments remaining: (term − k) × 12

In words: what it would cost to clear the loan today. It falls to zero at the end of the term.

Running costs and home value

Council Rates and maintenance are percentages of the home's value at the start of each year, so they grow as the home appreciates. Insurance is a fixed yearly amount.

C_t = 12M + (p + c) × V_t−1 + H

V_t = V₀ × (1 + g)^t

C_t: buyer's costs in year t
p: Council Rates rate (% of home value a year)
c: maintenance rate (% of home value a year)
H: home insurance a year
V_t: home value at the end of year t; V₀ is the purchase price
g: home appreciation rate

One-off purchase costs (legal and conveyancing fees, furnishing and moving) aren't charged to the buyer's yearly costs. Instead they count as an opportunity cost: the renter invests the same amount on day one, so it compounds against buying for the whole period.

3. Renting: rent and Council Rates

Rent rises by a fixed percentage each year, starting from the rent you enter (weekly rent is converted to monthly as weekly × 52 ÷ 12):

R_t = 12 × R₀ × (1 + i)^t−1

R_t: renter's costs in year t
R₀: monthly rent today
i: annual rent increase

In New Zealand Council Rates are paid by the property owner, not the tenant, so they're charged to the buyer only.

4. Investing the difference

Each year we work out the gap between the two sides' costs, D_t = C_t − R_t. Whoever pays less invests the difference. The renter's portfolio starts with the deposit plus the one-off purchase costs; the buyer's starts at zero.

I_t = I_t−1 × (1 + a) + max(D_t, 0) × (1 + a/2)

S_t = S_t−1 × (1 + a) + max(−D_t, 0) × (1 + a/2)

I_t: renter's portfolio at the end of year t; I₀ = deposit + purchase costs
S_t: buyer's savings portfolio (only grows in years when owning is cheaper than renting); S₀ = 0
a: investment return rate

Last year's portfolio grows by a full year's return. This year's savings are paid in month by month, so on average each pound or dollar is invested for six months: we credit them with half a year's return, a/2, rather than compounding monthly.

5. Net worth and the crossover year

Buying: W_t = V_t − B_t + S_t

Renting: W_t = I_t

The buyer's net worth is their home equity (the home's value minus the mortgage still owed) plus any savings portfolio. The renter's is their portfolio. The calculator's headline result is the gap between the two at the end of the term.

The crossover year is the first year buying's net worth overtakes renting's. At the start renting counts as ahead: the renter holds the deposit and purchase costs as investments, while the buyer has just taken on the loan. If buying never overtakes, there is no crossover.

6. Worked example with the NZ defaults

Here are the calculator's default NZ inputs run through the formulas above. Open the calculator without changing anything and you'll see the same results. These figures are recalculated whenever the defaults are reviewed.

Step 1: Day one

House price: $750,000
Deposit (10%): $75,000
Loan: $675,000
Monthly payment (5.69% over 20 years): $4,715.97
One-off purchase costs (legal $1,500, furnishing $5,000; no stamp duty in NZ): $6,500
Renter's starting portfolio (deposit + purchase costs): $81,500

Step 2: Year 1 costs

Buying
Mortgage payments (12 × $4,715.97): $56,592
Council Rates (0.5%): $3,750
Maintenance (1%): $7,500
Insurance: $1,200
Total: $69,042

Renting
Rent (12 × $2,448.33): $29,380
Total: $29,380

In year 1 renting is $39,662 cheaper, so the renter invests that difference. With half a year's growth at 7% it adds $41,050 to their portfolio.

Step 3: After 20 years

Buying net worth: $1,354,583
Renting & investing net worth: $1,918,484
Crossover point: none - renting stays ahead for all 20 years.

Renting leaves you $563,901 better off after 20 years.

7. Key assumptions and why we chose them

The house price, rent and mortgage rate defaults come from named public sources, listed on the About page. The rest are our estimates. Here's why we chose each one, and how much the 20-year result moves if you change it (all other defaults unchanged).

Estimated default assumptions, the reasoning behind each, and how sensitive the result is to it
Assumption	Default	Why this figure	How much it matters
Investment return	7% a year	A nominal return for a diversified global share portfolio, before fees and tax. That is roughly the long-run return on world shares of about 5% a year above inflation since 1900, plus the 2% midpoint of the Reserve Bank of New Zealand's 1–3% inflation target. It sits below the calculator's 8% "Global Stock Market" preset to leave room for fees. Returns over any single 20-year stretch have varied widely around the average. References: UBS Global Investment Returns Yearbook (Dimson, Marsh & Staunton); Reserve Bank of New Zealand: about monetary policy	At 8%: the result moves $262,980 towards renting.
Home appreciation	3% a year	Roughly the 2% midpoint of the Reserve Bank of New Zealand's 1–3% inflation target plus about 1% a year of real (after-inflation) growth. House prices have risen faster than that over some past decades, but much of that rise came alongside falling interest rates, which can't repeat indefinitely, so we use a deliberately modest figure. References: REINZ monthly property reports and House Price Index; BIS real residential property prices for New Zealand (via FRED)	At 4%: the result moves $237,961 towards buying.
Rent increase	2% a year	Rents are assumed to keep pace with the 2% midpoint of the Reserve Bank of New Zealand's 1–3% inflation target. Recent annual rent growth has often run above this, but over two decades rents are tied to what tenants can afford, which tracks incomes. References: MBIE Tenancy Bond Database, mean weekly rent; Reserve Bank of New Zealand: about monetary policy	At 3%: the result moves $119,036 towards buying.
Maintenance	1% of home value a year Rule of thumb	The widely used "1% of the home's value a year" rule for repairs and upkeep. Older homes typically need more and new builds less. There's no authoritative source for this figure: treat it as a rule of thumb and enter your own if you can.	At 1.5%: the result moves $200,231 towards renting.
Council Rates	0.5% of home value a year Rule of thumb	Rates are set by each council on the property's rateable value, so they vary widely between districts. 0.5% of the home's value a year is a rough stand-in; check your council's rates for the property. There's no authoritative source for this figure: treat it as a rule of thumb and enter your own if you can.	At 0.75%: the result moves $100,116 towards renting.
Home insurance	$1,200 a year Rule of thumb	A typical house insurance premium. NZ premiums have risen quickly, especially in areas with higher natural-hazard risk, so get a quote for your address. It is held flat in cash terms rather than rising with inflation. There's no authoritative source for this figure: treat it as a rule of thumb and enter your own if you can.	At $2,400: the result moves $50,916 towards renting.
Legal fees	$1,500 one-off Rule of thumb	A typical conveyancing quote for a standard purchase, including searches and disbursements. There's no authoritative source for this figure: treat it as a rule of thumb and enter your own if you can.	At $3,000: the result moves $5,805 towards renting.
Furnishing & moving	$5,000 one-off Rule of thumb	An allowance for moving and for furnishing and equipping a home you own, beyond what a renter would need. There's no authoritative source for this figure: treat it as a rule of thumb and enter your own if you can.	At $10,000: the result moves $19,348 towards renting.

"The result" is the gap between buying and renting net worth after 20 years, which is $563,901 in favour of renting with the defaults. The investment return, home appreciation and maintenance assumptions move it most, so they're the ones most worth replacing with your own view.

8. What the model leaves out

The calculator is a deliberately simple model. It leaves out:

Tax on investment returns. The renter's portfolio grows untaxed. In practice most NZ managed funds and KiwiSaver schemes are PIEs taxed each year at your prescribed investor rate (up to 28%), which would lower the renter's result. KiwiSaver withdrawals for a first home and employer contributions aren't modelled either.
Capital gains on the home. The home's gain is treated as tax-free, which is usually right for a main home, as it's excluded from the bright-line test.
Selling costs. The buyer's net worth is the home's full market value minus the mortgage. Selling would cost agent's and legal fees, typically a few percent of the price.
Variable and changing mortgage rates. The rate is fixed for the whole term. In practice most borrowers refix every few years at whatever rates are then.
Year-to-year swings. Returns, house prices and rent grow at constant rates. Real markets are volatile, and the order of good and bad years matters.
Other costs of owning. Mortgage arrangement fees, body corporate levies on units and apartments, and inflation in insurance premiums aren't included.
Discipline. The renter is assumed to invest every dollar of the difference and never dip into it.
Non-financial factors such as security of tenure, flexibility to move, and the freedom to renovate or keep pets.

This is not financial advice. The calculator and this page are general information to help you think the decision through. They don't take account of your personal circumstances. For advice on your situation, speak to a licensed financial advice provider.

Try it with your own numbers

Every default above is editable. Enter your own house price, deposit, rent and assumptions to see which option comes out ahead for you.

Open the calculator