Why not just compare my mortgage payment to my rent?

Because a payment and rent are not the same kind of dollar. Part of a mortgage payment buys equity you keep, while interest, taxes, insurance, and maintenance are gone for good, just like rent. A fair comparison nets out the equity you build, adds appreciation and selling costs, and credits the renter for investing the cash they did not spend. Two paths can have identical monthly outflows and still leave you with very different net worth years later.

What discount or investment-return rate should I use?

Use a rate that reflects where the renter would realistically park the surplus cash. A broadly diversified stock-and-bond portfolio has historically returned somewhere in the mid-single digits after inflation, but the future is not guaranteed. A common approach is to test a conservative rate and an optimistic rate and see whether the decision flips. If buying only wins when investment returns are very low, that is useful to know. See the methodology for the exact rate assumptions the calculator uses.

Does the math include the opportunity cost of my down payment?

Yes. The down payment and closing costs are real money the buyer ties up in the home. The renter keeps that lump sum and invests it, so the model grows it at the assumed return for the whole horizon. Ignoring this opportunity cost is one of the most common mistakes in rent-versus-buy comparisons. The opportunity cost guide walks through why this single number often decides the answer.

Is home appreciation guaranteed in this model?

No. Appreciation is an assumption you choose, not a promise. Home prices can rise, stall, or fall over any given period, and selling costs eat into whatever gain there is. Treat the appreciation input as a scenario to test, not a forecast. A sensible habit is to check whether buying still wins when appreciation is modest, so your decision does not depend on an optimistic guess.

How the Rent vs Buy Math Works

Why payment-vs-rent is the wrong comparison

The most common way people compare renting and buying is to line up the monthly mortgage payment against the monthly rent. It feels intuitive, but it quietly compares two different kinds of dollar.

Rent is pure expense. It buys you a place to live and nothing else. A mortgage payment is a mix. Part of it pays down principal, which turns into equity you keep. The rest, interest plus property taxes, insurance, and maintenance, is money that leaves and never comes back, exactly like rent.

So a 2,400 dollar mortgage payment is not 2,400 dollars of cost. And a renter who pays less each month is sitting on extra cash that can be invested. A payment-vs-rent comparison ignores both effects. To get an honest answer you have to follow every dollar to the end of your time horizon and see who is actually richer. That is what an invest-the-difference rent vs buy calculator does.

Step 1: both sides spend the same money

The cornerstone of a fair model is simple: the buyer and the renter have the same budget. Whatever cash one side does not spend on housing, the other side has available to invest. This is the "invest the difference" idea.

The buyer puts a large lump sum into the home up front: the down payment plus closing costs. The renter does not. So in the model the renter immediately invests that same lump sum. Each month, whichever side has the lower total housing cost invests the surplus. If buying costs more in a given month, the buyer invests nothing extra and the renter invests the gap. If renting costs more later because rent has risen, the buyer starts investing the gap instead.

Step 2: the buy side (equity, appreciation, costs)

For the buyer, net worth at the end of the horizon comes from what the home is worth minus what is still owed and minus the cost of selling it.

Equity from paying down the loan. Each mortgage payment chips away at the principal. Early on most of the payment is interest, so equity builds slowly; later it speeds up. You can see this pattern in an amortization schedule.
Appreciation (or depreciation). If the home rises in value, that gain belongs to the buyer. If it falls, the loss does too. Appreciation is an assumption, not a guarantee.
Ongoing carrying costs. Property taxes, homeowners insurance, maintenance, and any HOA dues are real expenses that reduce how much the buyer can invest. The mortgage calculator helps you estimate the principal-and-interest piece.
Selling costs at the end. When the home is sold, agent commissions and other transaction fees come out of the proceeds. The closing and selling costs guide explains why this matters.

The buyer's ending net worth is the projected home value, minus the remaining loan balance, minus selling costs, plus any side investments they were able to make in months when buying was cheaper than renting.

Step 3: the rent side (invest the difference)

The renter's net worth is just one account: the investment portfolio. It starts with the lump sum the buyer spent on the down payment and closing costs, then grows two ways.

The up-front lump sum compounds. Because the renter never tied up cash in a down payment, that money earns the assumed investment return for the entire horizon. This is the opportunity cost of the down payment, and it is often the single biggest factor in the result.
Monthly surplus gets added. In any month where renting costs less than owning, the difference is invested too, and it compounds from then on.

Rent itself usually rises over time. The model applies an annual rent-growth assumption, so the renter's housing cost climbs year after year, which shrinks the monthly surplus and can eventually flip it so the buyer is the one investing extra.

Step 4: compare net worth and find break-even

Now both sides are measured the same way: total net worth at the end of the horizon. Subtract one from the other and you have a clean answer for that horizon. The model also walks year by year and reports the break-even horizon, the point where the buyer's net worth first overtakes the renter's.

Because the result depends entirely on the assumptions, it is worth running your own numbers in the rent vs buy calculator and reading the methodology, which lays out the exact formulas and a fully worked example.

The levers that move the answer

A handful of inputs do most of the work. Understanding them tells you when buying tends to win and when renting does.

How long you stay (the horizon)

Time is the buyer's best friend. Up-front buying and selling costs are spread over more years, and equity has longer to build. Short stays usually favor renting because there is not enough time to recover transaction costs.

Appreciation versus investment-return spread

What really matters is not appreciation alone but how it compares to what the renter's invested cash could earn. If a diversified portfolio is expected to out-earn home-price growth, the renter's invested down payment is a powerful advantage. If appreciation is expected to exceed investment returns, buying pulls ahead faster.

Rent growth

Faster rent growth helps the buyer. A mortgage principal-and-interest payment is fixed, while rent tends to climb. The quicker rent rises, the sooner the renter loses their monthly cost advantage.

Costs on both sides

Property taxes, insurance, maintenance, closing costs, and selling commissions all drag on the buyer. Higher costs push the break-even year further out. The down payment calculator and closing cost estimator help you pin down these inputs before you compare.

None of these levers settle the question on their own. The point of the math is to hold them all together honestly so you can see which path leaves you better off over the time you actually plan to stay. This is general information, not personalized advice, so treat the output as a starting point for your own planning.