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Understand mortgage payments and the PMI estimate

This is a US fixed-rate mortgage planning model in USD, with monthly interest. It is not a lender quote, financial advice or a decision about PMI cancellation. Changing the interface language does not change the country or currency assumptions.

Enter amounts with the correct units

Enter home price and down payment in USD; the loan is their difference. Enter annual interest as a percentage, term in years, property tax and insurance as annual USD amounts, HOA as a monthly USD amount, and PMI as an annual percentage of the original loan. Enter extra principal as a monthly USD amount. Keep extra payments at 0 for an initial comparison.

The payment formula

For loan principal P, monthly rate r = annual percentage / 1200 and n = years × 12, scheduled principal-and-interest payment M = P × r / (1 − (1 + r)^(-n)). At a 0% rate, M = P / n. Each month interest is opening balance × r; the payment left after interest reduces principal. The engine keeps full numeric precision during calculation and rounds displayed amounts, so a lender that rounds every period can differ slightly.

Reproduce a mortgage example

Set home price to USD 200,000, down payment to USD 20,000, annual rate to 6%, term to 30 years, annual property tax to USD 2,400, annual insurance to USD 1,200, annual PMI to 0.5%, monthly HOA to USD 50 and extra principal to 0.

The loan is USD 180,000. Scheduled principal and interest is USD 1,079.19 per month. Tax is USD 200, insurance USD 100, HOA USD 50 and initial PMI USD 75, giving an initial monthly total of USD 1,504.19.

Verify the first schedule row

In that example, month 1 interest is USD 900.00, principal reduction USD 179.19 and closing balance USD 179,820.81. Expand the schedule and compare these values. The payment column in the loan schedule is principal and interest; it is not the mortgage total including tax, insurance, HOA and PMI. Export the schedule CSV for the separate cost columns.

The PMI stop month is a model rule

The model charges original loan × annual PMI percentage / 1200 while the opening balance is above 80% of the entered home price. In this example it charges USD 75 for 89 months and first shows no PMI in month 90; month 89 closes at about USD 159,975.02. Actual cancellation eligibility and automatic termination are different matters. The CFPB reference explains the conditions; confirm them with your servicer instead of treating this model month as a legal right.

What the estimate does not cover

Tax, insurance and HOA stay constant; the model does not forecast rate changes, closing costs, fees, property value changes or lender-specific rules. It is not an FHA, VA, refinancing or country-specific legal model. An extra payment does not rewrite your required contractual payment. Check inputs and the calculation before relying on the estimate; a disclaimer does not make an incorrect result acceptable.

Sources and references

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