Mortgage Calculator

Most mortgage calculators show the principal-and-interest payment and stop there. Lenders, by contrast, qualify you on PITI — Principal, Interest, Taxes, and Insurance — because that is the actual cash leaving your account each month. Skip the T and the I and you can underestimate your real housing cost by 25–40%. Principal and Interest (PI) is the amortizing payment from the standard formula. On a $400,000 mortgage at 6.5% over 30 years, PI = $2,528.27/month. This is the only number most online calculators surface. Property Taxes (T) vary enormously by jurisdiction. The Tax Foundation's annual property-tax rankings (taxfoundation.org) show effective rates from 0.27% in Hawaii to 2.33% in New Jersey on owner-occupied housing. The U.S. national median is roughly 1.10% of home value per year. On a $500,000 home in New Jersey, that is $11,650/year, or $971/month — almost as large as the principal portion of the early payments. Even modest 1.10% taxes on a $500,000 home add $458/month. Lenders escrow this and remit to the taxing authority, so it appears in your monthly statement whether you think about it or not. Homeowners Insurance (HOI / I) protects the lender's collateral and your dwelling. The Insurance Information Institute (iii.org) reports the U.S. average annual HOI premium at roughly $1,400 — but Florida, Louisiana, and Oklahoma frequently exceed $4,000 due to hurricane and tornado risk. California earthquake riders, Texas wind/hail riders, and flood insurance (mandatory in FEMA-designated zones via the National Flood Insurance Program) all stack on top. Private Mortgage Insurance (PMI) applies when your loan-to-value ratio (LTV) exceeds 80% — i.e., you put down less than 20%. Conventional PMI rates run 0.30%–1.50% of the loan amount annually, depending on credit score and LTV. On a $400,000 loan at 0.50% PMI, that adds $167/month. Federal law (Homeowners Protection Act of 1998) requires automatic PMI cancellation when the LTV reaches 78% based on the original amortization schedule, and you can request cancellation at 80% with a fresh appraisal. FHA loans use Mortgage Insurance Premium (MIP) instead, which behaves differently — for most FHA loans originated after June 2013, MIP cannot be canceled and remains for the loan's life. Real-world worked example. $500,000 home, $50,000 down (10% LTV = 90%), 6.5% rate, 30-year term. PI = $2,844; property tax @ 1.10% = $458/month; HOI @ $1,400/year = $117/month; PMI @ 0.50% on $450,000 = $188/month. Total PITI = $3,607/month — that is 27% above the $2,844 number you would see on a basic calculator. Plus HOA fees if applicable, which the Community Associations Institute reports at a national average of ~$200–400/month for homes in HOA communities. Educational only. Tax rates and insurance premiums are jurisdiction-specific — consult a local lender, real-estate attorney, or housing counselor for actual numbers.

// PITI breakdown for a $500k home, 10% down
const home = 500000, down = 50000;
const loan = home - down;             // 450000
const rate = 0.065, years = 30;

const r = rate/12, n = years*12;
const PI = loan * r * Math.pow(1+r,n) / (Math.pow(1+r,n) - 1);  // 2844
const tax = home * 0.011 / 12;        //  458 (1.10% effective)
const hoi = 1400 / 12;                //  117 (national avg)
const pmi = loan * 0.005 / 12;        //  188 (0.50%, LTV>80%)

const PITI = PI + tax + hoi + pmi;    // 3607 — 27% > PI alone

An adjustable-rate mortgage (ARM) charges a lower initial rate that resets on a schedule — typically a 5/1, 7/1, or 10/1 ARM where the first number is the fixed-rate period and the second is the reset frequency in years. After the fixed period, the rate equals an index (most ARMs since 2023 use SOFR — Secured Overnight Financing Rate — which replaced LIBOR) plus a margin (typically 2.25%–2.75%). Caps limit how much the rate can move per reset and over the loan's life. Historical 30-year fixed mortgage rates (Freddie Mac PMMS, freddiemac.com/pmms): the 30-year average since the survey began in 1971 is roughly 7.7%. Specific decade averages: 1980s: 12.7%; 1990s: 8.1%; 2000s: 6.5%; 2010s: 4.1%; 2020–2024: 5.8% (with a 2021 low of 2.65% and 2023 high of 7.79%). The 1980s show why ARMs gained popularity — borrowers in 1981 facing 18% fixed rates and a 5/1 ARM at 14% would have benefitted dramatically as Volcker's anti-inflation policy reversed in subsequent years. When ARMs win mathematically: (1) When you will sell or refinance before the fixed period ends. The median U.S. homeowner stays in their home about 13 years per the National Association of Realtors, but among first-time buyers and frequent movers it is 5–7. A 5/1 ARM at 5.5% beats a 30-year fixed at 6.5% by ~$240/month on $400k for the first 5 years — roughly $14,400 saved if you sell on time. (2) When you have high confidence rates will fall. Buyers in late 2023 with 7.5% fixed offers and 5/1 ARMs at 6.5% bet that rates would normalize — a reasonable bet given the historical mean reverts toward 5–6%. When fixed wins: (1) When you intend to stay 15+ years. The 1980s borrower who took a 10% fixed kept that rate while neighbors on ARMs faced 12–18% resets. (2) When your budget cannot absorb a payment increase. Lifetime caps allow a 5% rise from initial — a 5.5% ARM can reset to 10.5%, doubling principal-and-interest. (3) When refinancing back to fixed will likely be expensive (closing costs of 2–5% of loan balance plus appraisal, title, etc.). The 2008 cautionary tale: many ARM borrowers from 2003–2007 took 2/28 or 3/27 ARMs with extremely low teaser rates and were unable to refinance after housing prices collapsed and credit tightened — many lost homes to foreclosure. The Dodd-Frank Act of 2010 banned the most predatory ARM structures, but standard ARMs remain available and reset risk is still real. Decision rule: take an ARM if (years you will keep the loan) < (fixed-period years) + buffer. Otherwise, lock fixed. Educational only — consult a licensed loan officer.

Refinancing replaces your existing mortgage with a new one — usually to lower the rate, change the term, switch from ARM to fixed (or vice versa), or extract equity (cash-out refi). The math question is simple: do the monthly savings exceed the closing costs within the time you plan to keep the loan? Standard refinance closing costs are 2–5% of the new loan amount, per Freddie Mac and CFPB consumer guidance. On a $400,000 refi, that is $8,000–$20,000. Specific line items: lender origination 0.5–1.5%; appraisal $300–700; title insurance 0.3–0.5% of loan; recording fees and transfer taxes (varies by state, sometimes 0.5–1.0%); settlement/escrow $300–800; prepaid interest, taxes, and insurance reserves. Some lenders advertise "no-closing-cost" refinances — the costs are rolled into a slightly higher rate (typically +0.25% to +0.50%), which means you pay through the rate over the loan's life rather than upfront. Break-even formula: closing costs ÷ monthly savings = months to break even. Example: refinancing a $400,000 mortgage from 7.0% to 5.5% on a 30-year term reduces P&I from $2,661 to $2,271 — savings of $390/month. With $9,000 in closing costs, break-even is $9,000 / $390 = 23 months. If you stay in the home longer than 23 months, the refi pays off; shorter, you lose money. The lifetime savings calculation is more nuanced. Cutting the rate from 7.0% to 5.5% over a fresh 30-year term saves $140,400 in interest IF you keep the new loan to maturity ($957,978 total payments vs $817,576). But you also restart amortization — the first years again skew heavily toward interest. If you were already 8 years into the original mortgage, refinancing to a fresh 30-year extends total payoff to 38 years from origination, partially offsetting the rate savings. Refinancing into a 22-year term (matching remaining tenure) preserves the payoff date and captures pure rate savings — many lenders offer custom terms for this reason. Cash-out refinances behave differently. Pulling $50,000 of equity at 5.5% replaces lower-rate primary mortgage debt with new debt at the cash-out's rate. The IRS distinguishes between cash used for "buy, build, or substantially improve" the home (interest deductible, with limits) and cash used for other purposes (interest not deductible) per Tax Cuts and Jobs Act of 2017 and IRS Publication 936. Confirm the tax treatment before assuming a deduction. Rule-of-thumb triggers: refinance when the rate drop is at least 0.75–1.00 percentage points and you will stay 24+ months. With small drops (0.25–0.50 points), break-evens push past 5 years and the calculus rarely justifies the friction. Federal Housing Finance Agency (fhfa.gov) tracks national refi volume and can hint at when rate environments shift. Educational content only — consult a licensed loan officer and tax professional for your specific situation.

// Refi break-even
function refiBreakeven(loan, oldRate, newRate, years, closingCosts) {
  const r0 = oldRate/12, r1 = newRate/12, n = years*12;
  const PI_old = loan * r0 * Math.pow(1+r0,n) / (Math.pow(1+r0,n)-1);
  const PI_new = loan * r1 * Math.pow(1+r1,n) / (Math.pow(1+r1,n)-1);
  const monthlySavings = PI_old - PI_new;
  return { monthlySavings, breakevenMonths: closingCosts / monthlySavings };
}

refiBreakeven(400000, 0.07, 0.055, 30, 9000);
// monthlySavings ≈ 390, breakeven ≈ 23 months