Mortgage payments explained: PITI, PMI, and the math nobody teaches

P  Principal      — pays down the loan balance
I  Interest       — cost of borrowing
T  Taxes          — property taxes (escrowed monthly)
I  Insurance      — homeowner's insurance (escrowed)
+  PMI            — required when down payment is under 20%

A mortgage payment looks like a single line on your bank statement, but it’s actually four or five different things added together — and most homebuyers can’t name all of them. That’s a problem, because some of those components are fixed for the life of the loan, others change every year, and a couple of them disappear entirely if you watch the right number drop below the right threshold.

This guide takes a mortgage payment apart from first principles. We’ll cover where the standard amortization formula comes from, what PITI actually means, the rules that govern PMI (when it’s required, how much it costs, when the bank has to remove it), and the long-tail costs the formulas leave out. A live calculator is embedded so you can plug in your own numbers as we go.

By the end you should be able to look at any mortgage offer and answer four questions cold: what your monthly payment is, how much of the first payment goes to principal, when PMI ends, and roughly what the loan will cost you in total interest.

Part 1: The amortization formula

Every fixed-rate mortgage in the US uses the same formula to compute the monthly principal-and-interest payment. It looks intimidating but expresses something simple: “given a loan amount, an interest rate, and a term, what fixed payment exactly pays off the balance in equal installments?”

M = L × [r(1+r)ⁿ] / [(1+r)ⁿ − 1]

Where:

• M = monthly principal-and-interest payment
• L = loan amount (home price minus down payment)
• r = monthly interest rate (annual rate ÷ 12)
• n = total number of monthly payments (term in years × 12)

The math is a closed-form solution to “what payment makes the present value of n future payments equal to the loan amount, at this discount rate?” If you’ve seen any time-value-of-money formula, this one is the same family.

A worked example: $400,000 loan, 30-year term, 6.5% annual rate.

• r = 0.065 ÷ 12 = 0.005417
• n = 30 × 12 = 360
• (1 + r)ⁿ = (1.005417)³⁶⁰ ≈ 7.0235
• M = 400,000 × (0.005417 × 7.0235) / (7.0235 − 1) ≈ $2,528/month

That $2,528 is your principal-and-interest payment — abbreviated P&I. It’s only one of four pieces of what you actually owe each month.

Part 2: PITI — the full payment

Lenders, real-estate agents, and loan documents talk about PITI:

• Principal (paying down what you borrowed)
• Interest (the cost of borrowing)
• Taxes (property tax, paid to the county)
• Insurance (homeowners insurance, required by the lender)

Principal and interest are the P&I we just computed. Tax and insurance get added on top, almost always collected monthly into an escrow account the lender holds and pays out on your behalf when the bills come due.

Property taxes vary wildly by state and county. In Texas you might pay 2.0–2.5% of home value per year. In California, Proposition 13 caps it at about 1% plus local assessments. Take the annual amount and divide by 12 to get the monthly escrow contribution.

Homeowners insurance is similar: an annual premium (typical range $1,200–$3,500 depending on location, home age, and coverage limits), divided by 12, escrowed monthly.

Two extras that often ride along with PITI but technically aren’t part of the acronym:

• HOA dues — if the property is in a homeowners association, monthly dues go to the HOA directly (not the lender). Common in condos, townhomes, and master-planned communities. Range: $0 to $1,000+/month.
• PMI — private mortgage insurance, required when your down payment is small. We’ll cover this in detail next.

A more complete (but uglier) acronym is PITIA — adding HOA. In practice “PITI” is what you’ll hear, and people just remember to add HOA on top.

Part 3: PMI — the rule everyone gets wrong

If your down payment is less than 20% of the home price, the lender will require private mortgage insurance. PMI is insurance the lender buys (using your money) to protect itself against you defaulting. You pay for it; you get nothing from it.

The trigger is loan-to-value ratio (LTV) — the loan amount divided by the home value, expressed as a percentage:

LTV = Loan Amount / Home Value

If you put 10% down on a $500,000 home, LTV is 90% and PMI is required. If you put 20% down, LTV is 80% — no PMI.

PMI cost is typically 0.5%–1.5% of the loan balance per year, divided by 12 for a monthly charge. On a $450,000 loan at 0.7% PMI, that’s $3,150/year or about $263/month. Stacked on top of P&I, taxes, and insurance, it’s a meaningful chunk of the payment.

When PMI ends — three different rules

Here’s where most homebuyers get confused. PMI doesn’t just go on forever, and there are three different ways it can come off:

Rule 1 — Automatic termination (Homeowners Protection Act of 1998) The lender is required by federal law to terminate PMI when the principal balance reaches 78% of the original home value, on the date your amortization schedule says it will hit that threshold. You don’t have to ask. You don’t have to do anything. It just stops.

Note: 78% of original value, not current value. If your home appreciated, that doesn’t accelerate this trigger.

Rule 2 — Borrower-initiated removal at 80% LTV You can request removal once the balance hits 80% of original value. The lender must comply if you’re current on payments and the property hasn’t lost significant value. This is faster than waiting for the 78% automatic trigger because most schedules cross 80% before they cross 78%.

Rule 3 — Refinance / new appraisal If your home has appreciated significantly, you can pay for a new appraisal and request PMI removal based on current value. If the new appraisal puts the loan below 80% of new value, lender may agree. This is the only way to use appreciation against PMI.

The single most important number for PMI: 78% of original purchase price. The day your principal balance crosses that line, PMI is gone, automatically. On a $500,000 home with 10% down ($450,000 loan, 90% LTV), that means you need to pay the balance down to $390,000 — about 8–10 years into a typical 30-year mortgage at average rates.

Part 4: The amortization schedule

Now the most counterintuitive piece. Even though your payment is fixed each month, the split between principal and interest changes dramatically over the life of the loan.

In month 1 of our $400,000 / 30-year / 6.5% example:

• Total payment: $2,528
• Interest: $400,000 × (0.065/12) = $2,167
• Principal: $2,528 − $2,167 = $361

So 86% of your first payment is interest. Only $361 actually reduces what you owe.

In month 360 (the last payment):

• Total payment: $2,528
• Interest: balance × (0.065/12) ≈ $14
• Principal: ≈ $2,514

99% of the final payment is principal.

The shift happens gradually. The crossover point — when more than half of each payment goes to principal — happens around year 20 on a 30-year mortgage at 6.5%. For the first two-thirds of the loan, you’re mostly paying interest.

This has two practical consequences:

1. Total interest is huge on long mortgages. That $400k loan at 6.5% over 30 years costs $510,178 in interest — more than the loan itself. The same loan over 15 years at the same rate? About $226,773 in interest. Less than half.

2. Extra principal payments early are extremely high-leverage. Paying an extra $200/month from year 1 on the $400k example shaves about 4 years off the loan and saves around $87,000 in interest. The same $200/month starting in year 20 saves only a few thousand. Front-loaded extra principal compounds against the unpaid balance for the longest.

Part 5: Try it on your own numbers

Plug in a real scenario and watch the math react:

Things worth noticing as you adjust inputs:

• Drop the down payment below 20% — PMI appears, monthly payment jumps
• Add $100/month to extra principal — payoff date moves up, interest savings show
• Switch from 30-year to 15-year — monthly P&I roughly doubles, total interest drops by more than half
• Bump the rate by 1% — monthly P&I rises about 10–12% on a 30-year

Part 6: What the formulas don’t tell you

The amortization formula gives you a clean monthly number. But the actual cost of homeownership has several other components that the formula doesn’t see.

Closing costs

Closing on a home costs 2–5% of the purchase price in fees: lender origination, title insurance, appraisal, recording, escrow setup, sometimes points if you bought down the rate. On a $500,000 home that’s $10,000–$25,000 in cash on top of your down payment — and most of it is unrecoverable if you sell within a few years.

Property tax inflation

Your taxes won’t be the same in 10 years. Most counties reassess regularly and tax bills creep up 2–5% per year on average. Plan for this; the escrow line on your statement will rise even if your P&I doesn’t.

Maintenance

A common rule of thumb: budget 1% of home value per year for maintenance. On a $500,000 home, that’s $5,000/year, or about $417/month — a real cost that doesn’t appear in any mortgage calculator. Some years it’s $0; one year a roof needs replacement and it’s $30,000. Average it out.

Opportunity cost vs. renting + investing

The buy-vs-rent decision isn’t “which monthly payment is lower.” It’s “which option puts more dollars into appreciating assets over the same time horizon, after accounting for all costs?” In high-cost-of-living areas with modest appreciation, renting and investing the difference often wins. In moderate-cost areas with higher appreciation and stable employment, buying often wins. The mortgage calculator alone can’t answer this — it’s a separate analysis.

Life-event risk

A 30-year mortgage assumes 30 years of stable employment, no relocation, no divorce, no major health event, no upgrade-the-house impulse. The average US homeowner moves every 13 years — half of those 30 years of math never happen for the median buyer. Selling earlier means closing costs, agent fees (5–6%), and possibly losing money if the local market dipped. The longer you plan to stay, the more buying makes sense.

Refinance optionality

Mortgage rates move. If you lock at 6.5% and rates drop to 4.5% three years later, you can refinance and reset the math. This is real optionality but it costs $3,000–$8,000 in fees and doesn’t always pay off — break-even is usually 18–36 months in the new loan.

Part 7: How to actually evaluate a mortgage offer

Five numbers to memorize before signing anything:

1. Total monthly PITI + HOA + PMI — what hits your bank account each month, including everything
2. Your debt-to-income ratio (DTI) — total monthly debt payments / gross monthly income. Lenders cap at 43–50%; banks consider you safest below 36%. If your PITI alone pushes you above 30% of gross income, you’re stretching
3. Total interest over the loan — the calculator computes this. On a 30-year, expect it to be larger than the loan principal at typical rates. This is the lifetime cost of borrowing, full stop
4. Date PMI ends (if applicable) — the month when your balance crosses 78% of original price. Mark it on your calendar; the lender is supposed to drop PMI automatically but errors happen, and one phone call at 80% can save months
5. Break-even on rate-buy-down points — if the lender offers to lower your rate by 0.25% for $4,000 in points, divide $4,000 by the monthly P&I savings. If break-even is past your expected stay, points aren’t worth it

Part 8: Putting it together

A mortgage payment is a closed-form formula multiplied by a balance, plus a county tax bill divided by 12, plus an insurance premium divided by 12, plus (if your down payment was small) a percentage of the balance until you cross a federal-law threshold, plus (if there’s an HOA) whatever they decide.

That’s the whole thing. Most of the complexity comes from how those four components evolve: P&I stays fixed, taxes and insurance creep up, PMI eventually drops to zero, HOA varies on the association’s whim. The amortization schedule shifts the principal/interest split each month, gradually at first, then quickly in the final third of the loan.

You don’t need to memorize the amortization formula — the mortgage calculator on the previous page handles it. You do need to know:

• What’s in PITI and what’s not
• The 80% / 78% LTV thresholds for PMI
• That the first decade of payments is mostly interest
• That extra principal early is far more powerful than extra principal late
• That the formula’s monthly number is a floor — closing costs, maintenance, and tax inflation push the real cost meaningfully higher

If you take one thing: a mortgage is the largest financial product most people will ever buy, and the marketing language around it (“low monthly payment!”, “no PMI with 10% down on jumbo!”) routinely obscures the underlying math. The math is simple. Run the numbers yourself.

Related reading:

• True cost of owning a car: what your $30,000 vehicle actually costs over 10 years — the other big purchase, same hidden-cost decomposition.
• Compound interest: the most misunderstood formula in finance — the math engine behind amortization (and behind the case for paying down vs investing the spread).
• Net worth: the only financial number that really matters — where home equity sits on the household balance sheet, and what counts.

This guide is educational, not financial advice. Mortgage products vary by lender, state, and individual circumstances. The math here is universal; the products and rules wrapping it are not. Consult a licensed mortgage broker or financial planner before signing.