How the math works

The calculator answers one question: after your planned stay, which path leaves you with more money — buying a home, or renting a similar one and investing the difference? It simulates both paths month by month, then "cashes out" both sides at the end, with all exit costs and taxes paid. The engine is open source and covered by 37 automated tests, including ten verification scenarios derived by hand with closed-form math, independently of the code.

The core principle: symmetric opportunity cost

Money not spent on housing doesn't vanish — it gets invested. Each month we compute both sides' total housing cost. If owning costs more (the usual case early on), the renter invests the difference. If renting costs more (common after rents have grown for a decade, after the mortgage is paid off, or in cash purchases), the buyer invests the surplus instead. Both portfolios grow at the same rate and both are taxed the same way at the end. Most calculators only credit the renter's side; that asymmetry quietly biases results, and it's the single most common flaw we found when auditing other tools.

The renter's portfolio starts with what the buyer spent upfront (down payment + closing costs, minus the renter's own security deposit). If the deposit somehow exceeds the buyer's upfront cash, the buyer's portfolio is seeded with the difference instead — the comparison is symmetric in both directions.

The buyer's monthly cost

• Mortgage payment — standard amortization: monthly rate r = annual/12; payment = L·r(1+r)ⁿ/((1+r)ⁿ−1) on loan L over n months. Payments stop when the loan is paid off (if your stay outlasts the term, later years have no payment). A 0% rate divides principal evenly; a 100% down payment means no loan at all.
• Property tax — year 1 charges exactly your stated rate on the purchase price; the bill then grows at your property-tax growth rate each year.
• Homeowner's insurance and HOA — grow with general inflation each year.
• Maintenance — your maintenance percentage applied to the home's value at the start of each year (1%/year is the common rule of thumb).
• PMI — with under 20% down, PMI (your annual rate on the original loan) is charged in any month that begins with the balance above 80% of the original purchase price, then stops permanently. That's the federally guaranteed automatic-termination schedule; borrowers can often cancel earlier by request once appreciation lifts equity, so our treatment is slightly conservative toward buying.
• Minus tax savings — see taxes below; spread across the year's months.

The renter's monthly cost

Rent plus renter's insurance. Rent steps up once per year at your rent-growth rate (lease renewals); renter's insurance grows with inflation. The security deposit is locked up at move-in and returned without interest at the end — its cost is the investment growth it missed.

Growth conventions

• Home value compounds monthly at (1+a)^1/12, so each year-end value matches your stated annual appreciation exactly.
• Investments compound monthly at (return − fund fees)/12, with contributions added at month-end. The return you enter is total return, dividends included — entering price growth and dividends separately double-counts (a flaw we found in several tools, including the previous version of this one).
• Rent and recurring bills step annually, as they do in real life.

Taxes (US model, 2026 rules)

While owning: if you choose to itemize, the deductible amount is mortgage interest (capped pro-rata using the IRS average-balance method when the loan exceeds the $750,000 acquisition-debt cap) plus property tax (capped by the $40,400 SALT limit for 2026). Only the excess over your standard deduction ($16,100 single / $32,200 married for 2026) produces a benefit, valued at your marginal rate. This is why mortgage tax breaks help far less than commonly believed: for most buyers since 2018, the standard deduction already beats itemizing, and the calculator defaults to that.

At the end: the home sale pays selling costs, then capital-gains tax at your rate on any gain beyond the Section 121 exclusion ($250,000 single / $500,000 married); gain is the net sale proceeds minus the purchase price. Both investment portfolios pay capital-gains tax on growth above contributed basis — we track every contribution, so the basis is exact. The renter also gets the security deposit back.

The verdict, break-even, and tipping point

• Net worth series — for every year we compute both sides' liquidate-now value with the exact same exit math as the final year. The chart, the table, and the headline all use this one consistent basis.
• Break-even year — the first year buying pulls ahead and stays ahead through your horizon; temporary crossovers don't count.
• Tipping-point rent — a binary search for the rent at which both paths tie at your horizon. Above it, buying wins; below it, renting wins.
• Tie band — verdicts within 1% of the larger side are called a tie, because no model is that precise.
• Sensitivity table — we re-run the full simulation with each key assumption (appreciation, investment return, rent growth, mortgage rate) moved ±1 point and flag any that flips the verdict.

Default assumptions (July 2026)

Input	Default	Why
Mortgage rate	6.5%	~30-yr fixed average, mid-2026
Home appreciation	3%/yr	long-run US nominal average, cooled 2026 market
Rent growth	2.5%/yr	national rent indices, 2025–26 trend
Investment return	7%/yr total	conservative nominal total-return expectation
Property tax	1.1%/yr	US effective-rate median
Home insurance	$2,500/yr	2026 premium levels
Maintenance	1% of value/yr	standard industry rule of thumb
Closing / selling costs	3% / 6%	typical buyer costs; commissions + transfer at sale
PMI	0.6%/yr	typical conventional-loan range (0.3–1.1%)
Stay length	10 years	median US owner tenure ≈ 12 years; 30-year defaults overstate buying
Inflation	2.5%/yr	drives insurance/HOA growth

Every default is editable, and shared links preserve your exact inputs.

Known simplifications

We prefer honest simplifications to false precision. The ones that matter:

• Returns and appreciation are steady averages — no volatility, crashes, or sequence-of-returns risk. Real outcomes vary around these paths.
• Investment taxes are settled once at the end (no annual dividend-tax drag; in tax-advantaged accounts the end-tax can also be set to 0).
• No refinancing, no extra principal payments, no rent control, no moving costs on the rent side.
• State/local income taxes, transfer taxes, and non-US tax systems aren't modeled — set taxes to 0 for a clean pre-tax comparison anywhere.
• The "renter invests the difference" assumption requires discipline real renters don't always have — we model the math, you know your behavior.

Check our work

The engine ships with tests for every rule above — amortization against standard tables, hand-enumerable zero-rate scenarios, PMI cancellation timing, the $750k cap math, Section 121, and full 10-year composite scenarios derived independently with closed-form formulas. The code is open source at github.com/jnyst1985/buyvsrent. Found an error? Report it — verified corrections get credited here.