Mortgage Calculator
Calculate your monthly principal & interest payment, full PITI (taxes and insurance), total interest cost, and year-by-year amortization schedule. Works for 15- and 30-year fixed-rate mortgages.
A mortgage payment consists of principal and interest (P&I) calculated by the standard amortization formula, plus taxes, insurance, and HOA (collectively PITI). The formula is M = P × [r(1+r)^n] / [(1+r)^n − 1], where P is the loan principal, r is the monthly rate (annual rate ÷ 12), and n is the total number of payments. This is a closed-form mathematical identity requiring no external data refresh.
PMI (private mortgage insurance) is required by most conventional lenders when the loan-to-value ratio exceeds 80% (down payment less than 20%); typical cost 0.3–1.5% of the loan balance per year per Fannie Mae/Freddie Mac pricing grids. The OBBB §70108 permanently extended the $750,000 acquisition-debt cap on deductible mortgage interest.
Worked example:$450,000 home, 20% down ($90,000), 6.5% rate, 30-year term. P = $360,000; r = 0.5417%; n = 360. Monthly P&I = $2,275.44. Add $450 taxes + $150 insurance = total PITI $2,875.44/month. Total interest over 30 years: $459,158.
How to use this calculator
- Enter home price and down payment (amount or percent).
- Enter your interest rate and loan term (15 or 30 years most common).
- Optionally add property taxes, insurance, HOA, and PMI for the full PITI estimate.
- Use the extra monthly payment field to see payoff acceleration and interest savings.
Formula and assumptions
The monthly P&I uses the standard amortization formula (closed-form, no source-data refresh needed). PITI adds escrowed costs. PMI rate range from Fannie Mae/Freddie Mac historical pricing grids.
M = P × [r(1+r)^n] / [(1+r)^n − 1] where: P = loan principal r = annual rate / 12 n = loanTermYears × 12 PITI = M + (annualPropertyTax / 12) + (annualInsurance / 12) + HOA + PMI LTV = principal / homePrice
- Fixed-rate mortgage
- Rate stays constant throughout term
- Monthly compounding
- Standard US mortgage convention
- Extra payments
- Applied fully to principal each month
- PMI removal
- Not modeled — adjust manually when LTV < 80%
- Mortgage interest cap
- $750,000 acquisition debt per OBBB §70108
Worked example
$400,000 home, 20% down ($80,000), 7.0% rate, 30-year term
First five years amortization (sample)
Early mortgage payments go overwhelmingly to interest because interest accrues on the full remaining balance. Each month the interest portion shrinks slightly as the balance falls — this is called negative amortization in reverse. The table below uses the worked-example loan ($360,000, 6.5%, 30-year, monthly P&I $2,275.44).
| Year | Beginning balance | Total paid | Principal paid | Interest paid | Ending balance |
|---|---|---|---|---|---|
| 1 | $360,000 | $27,305 | $4,268 | $23,037 | $355,732 |
| 2 | $355,732 | $27,305 | $4,551 | $22,754 | $351,181 |
| 3 | $351,181 | $27,305 | $4,852 | $22,453 | $346,329 |
| 4 | $346,329 | $27,305 | $5,173 | $22,132 | $341,156 |
| 5 | $341,156 | $27,305 | $5,514 | $21,791 | $335,642 |
After 5 years of payments ($136,525 total paid), only $24,358 has reduced the loan balance — 82% of early payments go toward interest. This is why early extra-principal payments have an outsized payoff over the life of the loan.
Limitations
- Assumes fixed-rate mortgage — ARM or interest-only loans behave differently.
- PMI cancellation at 80% LTV is not automatically modeled (see Homeowners Protection Act, 12 U.S.C. §4902).
- Does not include closing costs, origination fees, or points.
- Property tax and insurance amounts will change over time.
- Educational estimate only — contact a licensed lender for actual rates.
Frequently asked questions
Your monthly mortgage P&I is calculated with M = P[r(1+r)^n] / [(1+r)^n−1]. A $320,000 loan at 7% for 30 years yields $2,129/month with $446,608 in total interest. Adding property tax, insurance, HOA, and PMI gives your full PITI payment.
Recent updates
- May 2026Added first-5-year amortization table and leadAnswerBlock with BLUF definition.
- Feb 2026OBBB §70108 permanently extended the $750K acquisition-debt cap; PMI deduction made permanent. Calculator notes updated.
- Nov 2025Default rate updated to reflect Freddie Mac Primary Mortgage Market Survey (PMMS) 30-year national average.