Mortgage P&I vs PITI: why the payment is bigger
The loan formula is only principal and interest. Escrow for tax, insurance, and often PMI is why the debit is larger.
People type a price into a mortgage calculator, see $2,400, and then the Loan Estimate says $3,100. The calculator was not lying. It answered a different question. Banks quote two layers: principal and interest (P&I), and PITI — principal, interest, taxes, and insurance. HOA and PMI can sit next to that.
The formula is only the note
A fixed US mortgage uses the standard amortizing payment: M = P × r(1+r)^n / ((1+r)^n − 1). P is the amount you borrowed, r is the monthly APR, n is the number of months. That M is P&I. It does not know your county tax rate or your insurer.
Takehome’s mortgage page is that formula. Enter loan amount (price minus down payment, plus any financed closing costs), APR, and term in years. You get monthly P&I, total paid, and total interest. That is the number that shrinks if you refinance the rate or shorten the term.
Escrow is why the draft is larger
Most US first-lien loans collect property tax and homeowners insurance in an escrow account. The servicer pays the county and the carrier when bills come due. Your monthly debit is P&I plus 1/12 of those bills, plus a small cushion the rules allow. Tax assessments change. Insurance renewals jump. The escrow analysis once a year can raise or lower the draft even if the note never changed.
If you put less than 20% down, many conventional loans add PMI until you hit the required equity. FHA has its own mortgage insurance structure. VA and some credit-union products differ. None of that is in the P&I formula.
30-year vs 15-year
A 15-year note has a higher monthly P&I and far less interest over the life of the loan. A 30-year note has a lower monthly P&I and more interest if you keep it the whole term. People pick 30-year for cash-flow and then send extra principal when they can. Extra principal is not the same as a 15-year note. You can stop extra payments. You cannot skip a 15-year contractual payment.
Rate matters more than people think on a long term. A half-point on $400,000 over 30 years is a large pile of interest. Use the calculator twice and subtract. That difference is the price of the extra rate, before tax and insurance.
On $350,000, 6.5%, 30 years, this engine prints $2,212.24 a month and $446,406.40 of interest. At 5.75% the same term is $2,042.50 a month and $385,300.00 of interest — $169.74 a month and $61,106.40 less interest. Keep 6.5% and cut the term to 15 years: $3,048.88 a month, $198,798.40 of interest. A cheaper rate and a shorter term are different trades. This page prices one note. The matching guide puts the three side by side.
What “how much house can I afford” actually needs
Affordability is leftover income after PITI, HOA, other debts, and a reserve — not P&I alone. Lenders use debt-to-income rules. You should use a budget. A high P&I with a cheap tax town can still be easier than a cheap note in a high-tax suburb with a brutal HOA.
Run P&I on the mortgage calculator. Then add your county tax estimate and a realistic insurance quote. Compare the sum to take-home from the paycheck calculator or 1099 calculator. The lender’s Loan Estimate still wins for the closing number.
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