What PITI means and how this calculator builds it
A mortgage payment in the United States is usually quoted as PITI: principal, interest, taxes, and insurance. Principal and interest are the loan repayment itself. Taxes and insurance are typically collected monthly by the servicer into an escrow account and paid out annually on your behalf. This calculator computes all four, adds private mortgage insurance and homeowners association dues where they apply, and reports the total.
The principal and interest portion uses the standard amortization formula: payment = L * i * (1 + i)^n / ((1 + i)^n - 1), where L is the loan amount, i is the annual rate divided by 12, and n is the term in months. The loan amount is the home price minus the down payment, which you can enter either as a dollar figure or as a percentage of the price using the unit toggle.
The other components are straightforward conversions. Annual property tax divided by 12, annual homeowners insurance divided by 12, and the HOA figure you enter, which is already monthly. These are added to principal and interest to give the monthly total shown at the top of the result.
Worked example: a 400,000 home with 20 percent down
Using the defaults of a 400,000 home price, an 80,000 down payment, a 30 year term at 6.5 percent, 3,600 in annual property tax, and 1,500 in annual homeowners insurance, the loan amount is 320,000. The monthly rate is 0.065 / 12 = 0.00541667 and n is 360, giving principal and interest of 2,022.62.
Property tax adds 3,600 / 12 = 300.00 and insurance adds 1,500 / 12 = 125.00. There is no HOA fee in this example and no PMI, because the 80,000 down payment is exactly 20 percent of the price. The monthly total is therefore 2,022.62 + 300.00 + 125.00 = 2,447.62. Over the full 360 months, interest alone comes to 408,142.36, which is more than the amount borrowed.
Change the down payment to 40,000, or 10 percent, and two things happen. The loan rises to 360,000, so principal and interest rise to 2,275.44. PMI now applies at the rate you enter, 0.5 percent of the loan per year by default, which is 360,000 * 0.005 / 12 = 150.00 a month. The monthly total becomes 2,850.44, and the smaller down payment has increased the payment by over 400 a month.
How PMI is calculated and when it stops
Private mortgage insurance protects the lender, not the borrower, and is generally required on conventional loans when the down payment is under 20 percent. This calculator applies PMI whenever the down payment ratio is below 0.20, computing it as the loan amount times the annual PMI rate divided by 12. The rate stays fixed on the original loan amount for as long as PMI applies, which matches how most monthly PMI is billed.
PMI does not run for the life of the loan. Under the Homeowners Protection Act, a lender must automatically terminate borrower paid PMI on most conventional loans once the balance reaches 78 percent of the original home value. The calculator finds that month by stepping through the amortization schedule until the balance falls to 0.78 times the price you entered, then reports the date. On the 10 percent down example, that happens in month 109, a little over nine years in.
Because PMI ends, the total cost figure does not bill it for the full term. The calculator adds principal, interest, tax, insurance, and HOA across all months, then adds PMI only for the months it actually applies. That is a meaningful distinction: at 150 a month, the difference between billing PMI for 109 months and for 360 months is over 37,000.
What this calculator leaves out
Closing costs are not included. Origination fees, title insurance, appraisal, recording fees, and prepaid escrow deposits commonly run two to five percent of the loan and are paid at settlement rather than monthly, so they never appear in the payment figure. Discount points, which buy down the rate, are also outside the model; if you pay points, enter the bought down rate and account for the cost separately.
Income tax treatment is excluded. The mortgage interest deduction and the state and local tax deduction can change the effective cost of owning, but they depend on your filing status, whether you itemize, and current limits, so no general figure would be accurate. The tool reports pre tax cash flow only.
Several other real costs are outside the scope: maintenance and repairs, utilities, flood or earthquake coverage sold separately from the standard policy, special assessments levied by an HOA, and any increase in property tax after a reassessment. Property tax and insurance are entered as fixed annual figures and held constant for the entire term, but in practice both tend to rise year over year. Treat the monthly total as a first year estimate rather than a fixed obligation.
The mistake people make when budgeting a mortgage
The most frequent mistake is budgeting against principal and interest and being surprised by the escrow. On the default example, principal and interest are 2,022.62 but the actual monthly obligation is 2,447.62, a difference of 21 percent. Rate quote sites and listing pages very often show only the principal and interest figure, so the gap is easy to miss until the first statement arrives.
The second mistake is assuming the escrow portion is fixed. Servicers run an annual escrow analysis, and if taxes or insurance rose, the monthly payment rises and a shortage may be billed. Payment increases of one to two hundred dollars a year on a fixed rate mortgage are ordinary and catch people who expected a fixed rate to mean a fixed payment.
The third is treating the maximum a lender approves as the amount to borrow. Approval is based on documented income and debts, not on the rest of your spending. The home affordability calculator on this site works the other direction, starting from income and a target debt to income ratio, which is a more useful frame for deciding what to look at.