Rent vs. buy: how the simulation works

The rent vs. buy calculator on this site does not apply a formula. It runs a small simulation: one loop over the months you plan to stay, adding up what renting costs and what buying costs, then crediting the buyer with whatever a sale at the end of the horizon would return. This guide walks through that loop exactly as the methodology page describes it, runs it on several horizons and closing-cost entries, and marks where the model stops. Every figure below is computed at build time by the same engine that powers the calculator, from inputs the sentence names.

Why simulate instead of solve

A single formula would have to assume that rent, home value, and loan balance all move together in a tidy way. They do not. Rent steps up once a year. The home's value steps up once a year on a different base. The loan balance falls every month, by an amount that grows as the interest share shrinks. Ownership costs track the appreciating value, so they drift up too. Looping month by month keeps each of those on its own schedule, and every dollar in the two totals can be traced to a specific month.

The renting side, month by month

Renting is the simpler ledger. The simulation starts with the monthly rent you enter and adds it to the renting total every month. At the end of each twelfth month the rent is multiplied by one plus your annual rent-growth percentage. Nothing is credited back: a renter walks away with no asset, so the total cost of renting is the sum of every rent payment. With $2,000 of rent entered and 3% rent growth, a 7-year stay accumulates twelve months at the starting rent, twelve at a rent 3% higher, and so on, for a renting total of $183,899. Set rent growth to 0% and the same stay costs $168,000 — exactly 84 months of unchanged rent.

The buying side, month by month

Buying is tracked as cash out, then cash back. Four things go out:

• the down payment, counted in full at purchase;
• purchase closing costs, if you entered them — as a percent of the price or a dollar amount, treated as cash at purchase and never added to the loan;
• every mortgage payment over the horizon, computed with the standard amortized-loan (PMT) formula at monthly compounding — the same formula the cash-flow guide walks through;
• ownership costs, taken each month as one-twelfth of your annual ownership-cost percentage applied to the home's current value.

Two things change inside the loop. Each month the payment is split into interest (the balance times the monthly rate) and principal (the rest), and the balance falls by the principal portion — the actual amortization schedule, not an approximation. At the end of every twelfth month the home's value is multiplied by one plus the appreciation percentage, which also raises the ownership-cost charge for the following year.

When the horizon ends, the model sells the home at its appreciated value, deducts selling costs as a percent of that sale price, and pays off whatever loan balance the amortization left. What remains is the net sale proceeds, and it is credited against everything paid out: net cost of buying = down payment + purchase closing costs + all mortgage payments + all ownership costs − net sale proceeds. The model then compares the two totals. The lower one is reported as the cheaper option, with the gap shown as the difference; when the two totals are within a dollar of each other it reports a break-even rather than naming a winner.

A sanity check with everything switched off

The cleanest way to see the structure is to remove every moving part. Enter a $350,000 home bought with a $350,000 down payment (so there is no loan), 0% appreciation, 0% ownership costs, 0% selling costs, and a 1-year stay against $2,000 rent with 0% growth. The buyer pays $350,000 on day one, pays nothing monthly, and sells for exactly $350,000 — a net cost of buying of $0. The renter pays $24,000 and gets nothing back. That is the whole machine; everything else in the calculator refines what goes out and how much comes back.

The base example at 7 years

The calculator's own example — $2,000 rent with 3% growth against a $350,000 home with $70,000 down, a 7% mortgage over 30 years, 2% annual ownership costs, 3% appreciation, 6% selling costs, purchase closing costs left blank, and a 7-year stay — gives the engine a $280,000 loan. The PMT formula prices that at $1,862.85 a month. Over 84 months the renter's total comes to $183,899. The buyer pays the $70,000 down, 84 mortgage payments, and ownership costs that start at 2% of $350,000 and drift up with the value; at sale, the appreciated price less 6% selling costs less the remaining balance returns $149,416. The net cost of buying works out to $130,701, so the model reports buying as cheaper by $53,198. That figure is the arithmetic of those exact inputs, not a judgement about whether to buy.

Why the horizon matters

Hold every input above fixed and vary only the years to stay:

Three mechanisms are visible in that table. First, the selling cost is charged in full whenever the sale happens, so a 1-year stay pays the same 6% exit as a 15-year stay but has only 12 months of appreciation and principal paydown to offset it — the net sale proceeds after 1 year, $61,714, are less than the $70,000 that went in. Second, at the entered 7% rate the early payments are mostly interest — $1,633.33 of the first $1,862.85 payment — so the balance falls by a small principal share at first and a growing one later. Third, the renter's cost grows with whatever rent growth you enter — at 0% it is flat, as the $168,000 total above shows — while the buyer's payment is fixed, so at the entered 3% the renting total pulls ahead faster the longer the horizon runs. With these inputs the model reports renting as cheaper at 1 and 2 years and buying as cheaper from 3 years on; a different rent, price, rate, or appreciation entry moves that crossover. The engine will not simulate past the loan: ask for a stay longer than the term and it answers "Years to stay cannot exceed the mortgage term."

Purchase closing costs: percent, dollars, or blank

The calculator never assumes purchase closing costs. Leave both fields blank and the engine counts zero cash at purchase beyond the down payment — that is how every row above was run. A percent is multiplied by the home price; a dollar amount is used as given. Either way the figure joins the buying total on day one and is never financed, so the loan, payment, and amortization are unchanged.

Take the base example at a 3-year stay. With closing costs blank, the model reports buying as cheaper by $4,154. Enter 2% of the price and the engine converts it to $7,000 of cash at purchase; the net cost of buying rises to $77,027 against $74,182 for renting, and the cheaper option flips — renting is now cheaper by $2,846. Enter $7,000 as a dollar amount instead and the result is identical, $77,027, because both fields describe the same cash. Enter both at once and the engine refuses rather than guess: "Enter purchase closing costs as either a percent of the price or a dollar amount — not both." At the 7-year stay the same $7,000 entry raises the net cost of buying by exactly that amount, to $137,701, but buying stays cheaper, by $46,198: the same cash weighs less when it is spread across more months of comparison.

Three other inputs the loop is sensitive to

Appreciation. Set it to 0% in the 7-year example and leave everything else alone. The home sells for what it cost, selling costs still come off, and the net sale proceeds fall from $149,416 to $73,787; the net cost of buying becomes $201,692 and the model reports renting as cheaper by $17,793. This is not a forecast — the appreciation input is yours — but it shows how much of a pro-buying result can rest on that one entry.

Mortgage term. Change the term from 30 to 15 years with the same 7-year stay. The payment rises, so more cash goes out each month, but a larger share of each payment is principal, so the balance owed at sale is smaller and the net sale proceeds rise from $149,416 to $220,033. In this example the net cost of buying falls to $115,008. The horizon did not change; the amortization did.

Down payment. Set it equal to the price. There is no loan, no payment, and no balance to retire, so the net sale proceeds are simply the appreciated value less selling costs: $404,629. The net cost of buying comes out at −$991 — a negative number, meaning the sale returned slightly more than the price and the ownership costs together. Read it alongside the omission below: the model gives the $350,000 tied up for 7 years no alternative return at all.

Reading the output

The engine returns these fields: the total cost of renting, the net cost of buying, which is cheaper, the difference between them, the net sale proceeds, the years to stay it was asked to simulate, and the purchase closing costs it actually counted (zero unless you entered them). Compare totals over the same horizon only, and treat the difference as the output of these inputs rather than a margin of safety: the table above shows a 3-year difference of $4,154 that a single closing-cost entry reverses.

What the model leaves out

As the methodology page states, the rent-vs-buy model excludes the opportunity cost of the down payment and any tax treatment of mortgage interest. It also does not model income taxes, PMI, financing points, or market cycles. Rent growth and appreciation are flat annual steps at the rates you enter — there is no year in which they change on their own. None of these omissions is approximated — the model simply has no line for them — so a decisive-looking result can still be missing a cost or a return that matters to you. The output is the shape of a decision under stated assumptions, not its answer. The other guides cover the rental-side models the same way.

Frequently asked questions

Not financial advice: this guide is a general educational explanation of a comparison that excludes income taxes, mortgage-interest deductions, PMI, and the invested-elsewhere value of your down payment. Purchase closing costs are modeled only when you enter them — the calculator does not assume a default, so enter your expected purchase closing costs for a both-ends comparison. Actual costs vary by market. Values are processed locally in your browser and never transmitted. See the methodology page.