Mortgage Calculator
Estimate your total monthly mortgage payment — principal & interest, property tax, and home insurance — from home price, down payment, interest rate, and loan term.
How It's Calculated
Formula
M_{\text{P\&I}} = P \times \frac{r(1+r)^n}{(1+r)^n - 1}, \quad M_{\text{total}} = M_{\text{P\&I}} + \frac{\text{Tax}_{\text{annual}}}{12} + \frac{\text{Insurance}_{\text{annual}}}{12}This calculator estimates the total monthly payment for a fixed-rate mortgage: principal & interest plus a prorated share of property tax and home insurance. Principal & interest use the standard fixed-rate amortization formula (the same present-value-of-an-annuity formula behind every conventional mortgage amortization schedule) — you finance the home price minus your down payment at a fixed monthly rate over the loan term, and the formula solves for the constant payment that fully pays off that principal by the end of the term. Property tax and home insurance are entered as annual dollar amounts and simply divided by 12 to get their monthly share — this calculator doesn't estimate tax or insurance for you from a ZIP code or a percentage of home value; you supply the annual figures (from a tax bill, an insurance quote, or your own estimate). The result is an estimate for planning purposes only — it is not a loan offer, a rate quote, or an implication of lender approval, and it does not include PMI, HOA dues, closing costs, or discount points.
Worked Examples
Standard 30-year mortgage
- Home price: $400,000, down payment: $80,000 → financed principal = $320,000
- Interest rate: 6.5% annual → periodic (monthly) rate = 6.5% ÷ 100 ÷ 12 = 0.0054167
- Term: 30 years → 360 monthly payments
- Monthly principal & interest = $320,000 × [r(1+r)^360] / [(1+r)^360 − 1] ≈ $2,022.62
- Property tax: $4,800/year → $400.00/month. Insurance: $1,200/year → $100.00/month
- Total estimated monthly payment = $2,022.62 + $400.00 + $100.00 = $2,522.62
15-year mortgage, same home
- Same $320,000 financed principal and 6.5% rate, but 15 years → 180 monthly payments
- A shorter term amortizes the same principal faster, so the fixed monthly principal & interest is higher: ≈ $2,787.54
- Property tax and insurance proration are unaffected by loan term: still $400.00 + $100.00 = $500.00/month
- Total estimated monthly payment ≈ $2,787.54 + $500.00 = $3,287.54
- Because the loan is paid off in half the time, total interest paid over the loan's life is substantially lower than the 30-year case, even though the monthly payment is higher
Frequently Asked Questions
Does this include PMI, HOA fees, or closing costs?
No. This v1 calculator intentionally scopes to principal & interest, property tax, and home insurance only — the core recurring costs every fixed-rate mortgage has. Private mortgage insurance (PMI), HOA dues, closing costs, discount points, and other one-time or lender-specific fees aren't included, since they vary by lender, loan program, and down payment size in ways a jurisdiction-neutral calculator can't assume.
Is the property tax and insurance amount monthly or annual?
Both are ANNUAL dollar amounts — your full-year property tax bill and your full-year homeowners insurance premium. The calculator divides each by 12 to add its monthly share to your total estimated payment; you don't need to do that division yourself before entering a value.
Does this calculator quote me a real interest rate or pre-approve me for a loan?
No. This is a planning estimate only, using an interest rate you enter yourself. It does not pull live market rates, does not connect to any lender, and does not imply pre-approval or eligibility for any loan. Contact a lender directly for an actual rate quote or pre-approval.
What if my down payment is more than my home price?
That's rejected as an invalid input — a down payment equal to or greater than the home price would mean there's no loan to amortize (or a negative one), so the calculator asks you to correct it rather than silently showing a misleading result.
Can I calculate a mortgage with 0% down or 0% interest?
Yes to both. A $0 down payment finances the full home price, which is a valid (if unusual) scenario. A 0% interest rate is handled as an exact special case: the calculator amortizes the principal evenly across the term with no interest component, rather than dividing by zero.
How is the monthly principal & interest payment calculated?
Using the standard fixed-rate loan amortization formula (an ordinary annuity, payments due at the end of each month): a constant monthly payment is solved for such that, after applying that payment every month at the periodic interest rate, the loan balance reaches exactly zero at the final payment. See docs/research/formulas/amortization-payment.md in this project's repository for the full formula derivation and verification.