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Mortgage Calculator (Monthly Payment with Taxes, Insurance and HOA)

Principal & interest = P × r × (1 + r)^n / ((1 + r)^n − 1) · Monthly total = P&I + property tax ÷ 12 + insurance ÷ 12 + HOA

M=P r (1+r)n(1+r)n−1M = \dfrac{P\,r\,(1+r)^n}{(1+r)^n - 1}

Worked example

A $350,000 mortgage at 6.5% over 30 years (360 months): the monthly rate is 6.5 ÷ 12 = 0.5417%, (1 + r)^360 = 6.99, and the principal-and-interest payment comes to about $2,212. Over the full term that is roughly $796,406 in payments, of which $446,406 — 56% — is interest. That interest exceeds the amount borrowed, which is why the term and extra principal payments matter as much as the rate.

Where this can give the wrong answer

A 0% rate is accepted and falls back to principal ÷ term, the straight-line split — useful for 0% promotional financing, not a division-by-zero bug.

Formula last checked against OpenStax, Contemporary Mathematics §6.8 'The Basics of Loans' and §6.12 'Renting and Homeownership' (level-payment formula); Consumer Financial Protection Bureau, Loan Estimate explainer (consumerfinance.gov) — 'Projected payments' made up of principal and interest, mortgage insurance and estimated escrow for property taxes and homeowner's insurance on 2 October 2026.

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