Mortgage payment
The monthly figure is not one number: principal and interest amortise, while tax, insurance and HOA ride alongside and never reduce the balance. Set the loan, then watch the balance curve and the interest-to-principal crossover change.
| Component | Per month | What it does |
|---|---|---|
| Principal & interest | $2,101.70 | Amortises the loan to zero by the final month |
| Property tax | $402.50 | 1.15% of value a year, held in escrow |
| Home insurance | $150.00 | $1,800 a year, held in escrow |
| HOA dues | $0.00 | None assumed |
| Total (PITI) | $2,654.20 | What actually leaves your account each month |
Escrow is an estimate. Your servicer re-checks it annually, and a shortfall raises the monthly figure without changing the loan.
L = Price − Down · the balance that actually amortises
PMT = L·i / (1 − (1+i)⁻ⁿ) · i = rate/12, n = years × 12
PITI = PMT + Tax/12 + Ins/12 + HOA · collected monthly, never amortised
B(k) = L(1+i)ᵏ − PMT·((1+i)ᵏ − 1)/i · the curve in the first chart
A clear path from inputs to results.
Work out what a home loan actually costs each month, how every payment splits between interest and principal, and when you will be debt-free. It supports US and UK conventions, escrowed taxes and insurance, PMI, and extra payments, so first-time buyers and refinancers can see the full picture before committing.
How to use
- Enter the home price and your down payment. The loan amount is the difference; in US mode the tool also applies FHA minimum-down checks and flags zero-down requests.
- Set the interest rate (APR) and the term in years. The monthly principal-and-interest payment updates immediately.
- Add annual property tax, hazard insurance, and HOA dues to see the full escrowed monthly payment, plus a PMI rate if your US conventional loan starts above 80% loan-to-value.
- Pick your region: US adds PMI logic and a conforming-limit (jumbo) check, UK switches to pounds and estimates Stamp Duty Land Tax including first-time-buyer relief, and Universal stays currency-neutral.
- Optionally add an extra payment and choose Monthly, Yearly, or Lump Sum to see how much sooner the loan retires and how much interest you save.
- Optionally enable ARM mode with an intro period and a maximum rate cap to preview the payment that applies after the rate resets.
The formula
Reference: Standard annuity-immediate amortization formula (Broverman, Mathematics of Investment and Credit); the APR is taken as a nominal annual rate compounded monthly, the usual US consumer-loan payment convention. Reg Z Appendix J defines the disclosed actuarial APR.
Worked example
First-time buyer, 20% down, 30-year fixed
- Home price $500,000; down payment $100,000; APR 6.5%; term 30 years; property tax $6,000/yr; insurance $1,200/yr; HOA $0; PMI rate 0.5% (not charged at exactly 80% LTV); no extra payments; US region.
- 1
The loan amount is $500,000 − $100,000 = $400,000. The monthly rate is 6.5% ÷ 12 = 0.541667%, and applying the annuity factor 0.00541667 × (1.00541667)^360 ÷ ((1.00541667)^360 − 1) to $400,000 gives a principal-and-interest payment of $2,528.27. Escrow adds $6,000 ÷ 12 = $500.00 of tax and $1,200 ÷ 12 = $100.00 of insurance; at exactly 80% LTV no PMI is charged. In month one, interest is $400,000 × 0.541667% = $2,166.67, so only $2,528.27 − $2,166.67 = $361.60 of the first payment reduces principal. Summing the interest column across all 360 months gives $510,177.20 of total interest.
Monthly payment $3,128.27 ($2,528.27 principal and interest plus $600.00 escrow); total interest $510,177.20 on a $400,000 loan; payoff after 360 months.
Interpreting the result
Budget for the full monthly payment, not just principal and interest: escrow items and PMI sit on top of the loan math. The amortization schedule shows the interest share falling from about 86% of the payment in month one to nearly zero at the end, which is why extra principal paid early in the loan has an outsized effect on total interest and payoff date.
Assumptions & limitations
- Taxes, insurance, and HOA are flat amounts you enter; they are added to the displayed monthly total but do not appear in the amortization schedule, which covers principal, interest, and extra principal only.
- PMI is modeled as a constant monthly premium (your entered rate × loan balance ÷ 12) whenever a US conventional loan starts above 80% LTV; the schedule does not automatically cancel it later.
- Closing costs, origination points, and other transaction fees are not modeled.
- Extra payments go entirely to principal and the required payment stays level; the loan simply ends sooner instead of the payment being recast lower.
- US mode labels a loan jumbo above the tool's built-in conforming limit ($832,750, or $1,249,125 in designated high-cost areas); UK SDLT uses the bands coded in the tool, including first-time-buyer relief on qualifying purchases up to £500,000.
Frequently asked questions
How is the monthly payment calculated?
The engine uses the standard annuity formula M = P·r(1+r)^n ÷ ((1+r)^n − 1), where r is your APR divided by 12 and n is the number of monthly payments. It computes the result with 20-significant-digit decimal arithmetic and rounds to the cent, so a $400,000 loan at 6.5% APR over 30 years comes out to $2,528.27 per month.
When do I pay PMI, and how do I avoid it?
In US mode, PMI is added whenever a conventional loan starts above 80% loan-to-value, charged as your entered annual rate divided by 12 on the loan balance. With 10% down on a $500,000 home, 0.5% on a $450,000 loan is $187.50 per month. Putting 20% down brings LTV to exactly 80%, and the tool charges no PMI.
Why is total interest so much higher than the rate suggests?
The APR is charged on the full outstanding balance every month, and a 30-year term gives interest a long runway. In the worked example the borrower pays $510,177.20 of interest on a $400,000 loan — more than the original principal. Shortening the term or paying extra principal is the direct way to change that ratio.
Does paying an extra $100 a month really help?
On the worked example above it does: adding $100 of principal every month retires the $400,000 loan in 322 months instead of 360 and cuts total interest from $510,177.20 to $446,247.84 — a saving of $63,929.36 and roughly 3.2 years of payments. The effect is largest in the early years, when interest makes up most of each payment.
What is the difference between the US and UK modes?
US mode adds PMI logic, an FHA minimum-down check, and a conforming-limit (jumbo) flag. UK mode switches the currency to pounds and estimates Stamp Duty Land Tax from the tool's built-in bands, including the first-time-buyer relief that exempts the first £300,000 on qualifying purchases up to £500,000 — for example, £20,000 on a standard £600,000 purchase. The core amortization math is identical in both.
Does the calculator recast my payment when I add extra payments?
No. Your required payment stays at the originally computed level and every extra dollar goes straight to principal, so the loan pays off earlier rather than the payment getting smaller. The month-by-month schedule and payoff date update to show the shortened timeline.
Methodology last reviewed 2026-10-19. Results are informational and not financial or engineering advice — see our disclaimer.