Rent or buy, compared as wealth at a chosen horizon

What this comparison actually measures

The owner’s path ends in a sale. The property grows at the appreciation rate you supply, the selling costs at the horizon take their share of whatever it is then worth, and the mortgage balance still outstanding on the schedule is repaid out of the proceeds. What remains is the owner’s wealth: not the value of the house, but the money a sale would actually release.

The renter’s path ends in a portfolio. The cash a purchase would have consumed — deposit and settlement costs together — is invested instead, at an opportunity-cost rate you choose. So is the monthly difference between what owning costs and what renting costs, contributed month after month across the horizon. The sum of the two at the horizon is the renter’s wealth. Note what that assumes about behaviour: a renter who spends the difference rather than investing it has not lived this path at all, and the comparison silently credits them with a discipline most people do not have.

The answer is a difference, and its sign is the part that gets read. Positive means the owner finishes ahead; negative means the renter does. But the sign is produced by forecasts you entered, not by anything the calculation knows about property or markets — which makes the right use of this page adversarial rather than confirmatory. Move one assumption at a time and find out how far the sign survives. An answer that flips under a small, defensible change of rate was never an answer.

The horizon does the heaviest lifting. Early in a schedule the balance has barely begun to amortise and the selling cost still takes its full share of the value, so most of what appreciation produced is consumed on the way out. Short horizons flatter renting for that structural reason and not as an artefact, which is why the same purchase can be a poor decision over a handful of years and a sound one over a decade with nothing else changed.

Two rates stand against each other, and neither is knowable. Appreciation drives the owner’s side; the opportunity-cost rate drives the renter’s. Each is a forecast, they are usually correlated in ways this model does not represent, and a modest move in either can reverse the result. The opportunity-cost rate is required outright, with no placeholder — the calculation will not choose the most decisive assumption on your behalf.

A great deal is deliberately absent. No tax of any kind: no relief on mortgage interest, no exclusion or charge on a gain, nothing on the return the renter earns. Rent is level for the whole horizon and so is the cost of owning, so neither rent rises nor a tax or insurance escalation appears. Moving costs, transaction costs at purchase beyond the outlay you enter, refinancing and any change of circumstance are outside it. So is everything non-financial — security of tenure, freedom to move, control over the property, the cost of a landlord selling underneath you. That last category is frequently the real reason a household chooses, and this calculation is entirely silent about it.

When this calculation is used

• Testing whether a purchase you are already inclined to make survives its own assumptions.
• Finding the horizon at which buying stops losing, by moving the horizon and watching the sign.
• Seeing what an honest opportunity-cost rate does to a decision that felt purely about a home.
• Stress-testing a plan against a flat or falling market rather than a rising one.
• Framing the conversation in figures you own, before an agent or a lender frames it for you.

Worked example

The pack’s declared vectors are three purchases at ordinary scale on long fixed schedules. Two of them carry a substantial monthly ownership premium over rent at horizons of a few years; the third pairs a much smaller monthly premium with the longest horizon of the three and the fastest appreciation.

Two of the three come out negative — the renter ahead — and one comes out positive. The two negative vectors carry the same monthly premium as each other, and the shorter-horizon one shows the wider gap: at that horizon the selling cost and a barely amortised balance consume most of what appreciation produced. The positive vector finishes ahead despite carrying the highest opportunity-cost rate of the three, because its monthly premium over rent is small, its horizon the longest and its appreciation the fastest — three assumptions pulling the same way. Which is the honest summary of this instrument: the answer belongs to the assumptions, not to the tenure.

No figure is stored on this page; the certified engine computes each on mount. The pack declares a refusal when the horizon runs past the mortgage term, and a warning for the case where owning costs less each month than renting — which makes the renter’s invested premium negative and changes how the comparison should be read. None of the declared vectors trips that warning; in all three, owning costs more per month than renting.

What each input represents

Assumptions and limits

• Rent is level for the whole horizon, and so is the monthly cost of owning; neither is escalated for inflation, rent reviews or rising taxes and insurance.
• The renter invests the entire initial outlay and every month’s difference, at one constant rate, without interruption, charges or tax — an assumption about behaviour as much as about markets.
• Appreciation compounds annually at a single rate, and the selling cost is a share of the value at the horizon.
• The mortgage is fixed for the term and paid exactly to schedule; the balance at the horizon is the closed-form scheduled one, with no overpayment, no arrears and no refinancing.
• No tax appears anywhere — not on the mortgage interest, not on the gain from the sale, not on the renter’s return — and every one of those differs by place and by circumstance.
• Moving costs, purchase transaction costs beyond the initial outlay entered, and the non-financial value of either tenure are all outside the model.
• Every figure is nominal money of the day in one currency: nothing is discounted or inflation-adjusted, so the two wealth figures are comparable to each other but not to today’s prices.

What the guards protect against

• A horizon longer than the mortgage term is refused rather than approximated. Past full repayment the closed-form balance the owner’s side depends on stops describing the loan, and the declared refusal vector pins that behaviour in place.
• Rent, the monthly ownership cost, the home price, the loan, the term and the horizon must all be greater than nothing — the comparison needs two live paths and a real date to compare them at.
• The opportunity-cost rate is required with no placeholder, which is a design choice rather than an oversight: a default there would quietly decide the sign of most answers.
• Appreciation may be negative within its bounds, so a falling market is representable rather than excluded. The rates and shares are otherwise bounded to plausible spans and refused beyond them, because a result outside those ranges would not describe any market anyone is buying in.

Provenance

Wealth-at-horizon comparison of ownership and tenancy under an explicit opportunity-cost rate

Owner wealth as the appreciated value at the horizon, net of selling costs and of the closed-form scheduled mortgage balance; renter wealth as the future value of the initial cash outlay plus the future value of the monthly ownership premium invested as an ordinary annuity; the reported answer is the difference between them.

Educational reference, not financial or housing advice, and not a recommendation to buy, sell or rent. The result is only as good as the assumptions supplied: appreciation, the opportunity-cost rate, the horizon and the monthly costs are all forecasts the reader owns, no tax of any kind is modelled, and no figure is defaulted from any jurisdiction. A different but equally defensible set of assumptions can reverse the sign of the answer, so treat the comparison as a way of testing a decision rather than as a verdict on one, and take advice that accounts for your own circumstances before acting. The signed pack carries its own citation, which displays from the verified leaf once the calculator loads; the page reports the verification state of the release it mounted rather than asserting one.