mortgage
Mortgage Payment Calculator
Estimate principal-and-interest mortgage payments from home price, down payment, rate, and term.
mortgage calculator
The Rent vs. Buy Calculator compares two simplified 30-year housing paths. The buying side starts with home price, down payment, fixed-rate mortgage, closing costs, ownership costs, appreciation, selling costs, estimated tax benefit, and opportunity cost on upfront cash. The renting side starts with rent, rent growth, renters insurance, security deposit, renter upfront costs, and opportunity cost on upfront cash.
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Use this calculator when you want to test how stay length, rent growth, home appreciation, property tax, insurance, HOA, maintenance, closing costs, selling costs, and assumed investment return move the modeled rent-versus-buy break-even point. Use Mortgage Payment for principal-and-interest only, House Affordability for income and debt limits, Down Payment for cash-to-close planning, Rent for income-based rent affordability, and lender, tax, insurance, HOA, lease, or legal sources for official figures.
The app calculates downPaymentAmount as homePrice * downPaymentPercent / 100 and loanAmount as max(homePrice - downPaymentAmount, 0). Monthly mortgage payment uses the fixed-payment formula with annualRate / 100 / 12 and loanTermYears * 12. Buying upfront cost equals downPaymentAmount plus homePrice * buyingClosingCostRate / 100. Renting upfront cost equals securityDeposit plus renterUpfrontCost. For each year from 1 through 30, the app adds buying mortgage payments, property tax grown by propertyTaxIncreaseRate, homeowners insurance and HOA grown by costInsuranceIncreaseRate, maintenance as appreciated home value * maintenanceRate / 100, selling costs, opportunity cost on buying upfront cash, then subtracts modeled sale equity and a simplified tax benefit. Renting cost adds rent grown by rentIncreaseRate, renters insurance grown by costInsuranceIncreaseRate, renter upfront cost, and opportunity cost on renter upfront cash, then subtracts the returned security deposit. Break-even is the first year where average monthly buying net cost is less than or equal to average monthly renting net cost.
This formula page covers the app's Rent vs. Buy Calculator: a 30-year comparison of modeled buying and renting costs using entered mortgage, housing-cost, rent-growth, appreciation, tax-rate, sale-equity, and opportunity-cost assumptions. It does not forecast home prices, rent markets, taxes, insurance, repairs, lender approval, or whether buying or renting is right for a specific person.
Down = HP * DPct / 100; Loan = max(0, HP - Down); r = APR / 100 / 12; n = TermY * 12; PMT = r == 0 ? Loan / n : Loan * r / (1 - (1 + r)^(-n)); BuyUp = Down + HP * BuyClosePct / 100; RentUp = Deposit + RentUpCost; TaxRate = min(100, FedRate + StateRate) / 100; BuyAvg_Y = BuyNet_Y / (Y * 12); RentAvg_Y = RentNet_Y / (Y * 12); BreakEven = first Y where BuyAvg_Y <= RentAvg_Y
The calculator first builds the fixed-rate mortgage and upfront costs, then repeats the cost model for each stay length from 1 through 30 years. The displayed year rows are average monthly net costs after modeled sale equity, tax benefit, returned deposit, and opportunity cost are applied.| Symbol | Meaning | How this page uses it |
|---|---|---|
| HP | Home price | The entered purchase price for the buying scenario. |
| DPct | Down payment percent | The entered down payment percentage. |
| Down | Down payment amount | Home price multiplied by down payment percent divided by 100. |
| Loan | Loan amount | Home price minus down payment amount, floored at 0 so the mortgage cannot become negative. |
| APR | Annual mortgage-rate input | The entered annual interest-rate assumption. The app treats it as a fixed annual rate for amortization math, not as a legal APR. |
| r | Monthly mortgage rate | Annual mortgage-rate input divided by 100 and by 12. |
| n | Mortgage payment count | Loan term years multiplied by 12 monthly payments. |
| PMT | Monthly mortgage payment | The fixed principal-and-interest payment before property tax, insurance, HOA, maintenance, and other ownership costs. |
| BuyUp | Buying upfront cost | Down payment amount plus home price multiplied by buying closing-cost rate. |
| RentUp | Renting upfront cost | Security deposit plus the entered renter upfront cost. |
| TaxRate | Simplified combined tax rate | Federal marginal tax-rate input plus state marginal tax-rate input, capped at 100 percent and converted to a decimal. |
| BuyRec_Y | Buying recurring cost through year Y | Mortgage payments while the loan is active plus modeled property tax, homeowners insurance, HOA, and maintenance through the selected stay length. |
| RentRec_Y | Renting recurring cost through year Y | Rent and renter's insurance through the selected stay length after applying the entered growth assumptions. |
| TaxBenefit_Y | Simplified tax benefit | Annual mortgage interest plus property tax, multiplied by the simplified combined tax rate. This is a planning shortcut, not an actual tax-return result. |
| Value_Y | Home value at sale | Home price grown by the entered home-value appreciation rate for Y years. |
| Bal_Y | Remaining loan balance | The amortized loan balance after Y years, or 0 once the modeled loan term has ended. |
| Equity_Y | Sale equity | Home value at sale minus remaining loan balance. |
| SellCost_Y | Selling cost | Home value at sale multiplied by the entered selling closing-cost rate. |
| BuyOpp_Y | Buying opportunity cost | Buying upfront cost multiplied by the assumed investment-growth factor minus the upfront cost. |
| RentOpp_Y | Renting opportunity cost | Renting upfront cost multiplied by the assumed investment-growth factor minus the upfront cost. |
| BuyNet_Y | Buying net cost | Buying upfront cost plus buying recurring costs plus selling cost, minus sale equity and simplified tax benefit, plus buying opportunity cost. |
| RentNet_Y | Renting net cost | Renting upfront cost plus renting recurring costs, minus the returned security deposit, plus renting opportunity cost. |
| BuyAvg_Y | Average monthly buying cost | Buying net cost divided by the selected stay length in months. |
| RentAvg_Y | Average monthly renting cost | Renting net cost divided by the selected stay length in months. |
| BreakEven | Break-even year | The first year from 1 through 30 where average monthly buying cost is less than or equal to average monthly renting cost. |
These examples use the app's package fixtures so the formula page matches the production calculator instead of a generic rent-versus-buy worksheet.
The examples show how sensitive the result is to entered stay length, appreciation, rent growth, tax-rate, sale-cost, and opportunity-cost assumptions. They do not show whether buying or renting is personally suitable.
Geographic scope: works globally. The math is currency-agnostic, so enter amounts in your own currency; local taxes, fees, and product rules are not included.
It simulates both paths for 30 years - every buying cost (mortgage, taxes, insurance, HOA, maintenance, buying and selling closing costs, offset by appreciation and equity) against every renting cost (rent with annual increases, renter's insurance, deposit, offset by investment returns on the money not spent on buying). It then reports the average monthly net cost of each path at years 1, 5, 10, and 30, plus the break-even year.
The first year where buying's average monthly net cost drops to or below renting's - effectively, how long you must stay for buying to win under your assumptions. Short stays favor renting because buying's upfront costs (down payment, closing costs) and selling costs need years of equity growth to amortize. If your realistic horizon is shorter than the break-even year, the model says rent.
Home appreciation, rent growth, and the investment return on un-spent cash are the big three - small changes to any of them move the break-even year materially, which is why they are explicit inputs rather than hidden constants. The takeaway in the worked example demonstrates this sensitivity deliberately. Run pessimistic and optimistic sets and treat the spread, not one number, as the answer.
This calculator is an original implementation based on the app's documented rent-versus-buy formulas, app-specific assumptions, deterministic fixtures, edge cases, rounding policy tests, and internal validation. It is not copied from a single source.
Outputs are checked with deterministic fixtures, edge cases, rounding policy tests, and internal validation artifacts. The result remains an educational estimate, not a homebuying recommendation, rent recommendation, lender quote, approval, tax answer, legal answer, insurance estimate, investment forecast, or personalised advice.
Formula version 2026.05.22-generic-rent-vs-buy. The version marks the calculation logic and validation fixture set used for this estimate.
Results are educational estimates, not advice. Read the full disclaimer.
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