Mortgage Payment PITI Calculator

Purpose and model boundary

Use this calculator to build the whole monthly cost of a fixed-rate home loan rather than the principal and interest alone. It divides the loan payment out of the price and the deposit, then adds property tax, homeowner insurance, association dues and mortgage insurance to reach one monthly figure. That total is the number to set against rent or against a household budget, because a lender collects most of it together.

The part that separates this model from a plain payment formula is that mortgage insurance stops. Insurance is charged only when the loan begins above 80 percent of the purchase price, and it is charged until the repayment schedule brings the balance down to 78 percent of that same original price, at which point it terminates. The calculator reports the month that happens, the insurance actually paid up to that month, and the lower payment that applies for the rest of the term. A model that charges insurance for the whole term overstates the cost of a small deposit, often by thousands of dollars on a thirty-year loan.

The boundary is narrow in specific ways. This is a fixed-rate loan throughout, so no adjustable rate, teaser period or rate reset is represented. Property tax, homeowner insurance and association dues are taken exactly as you enter them and held flat for the whole term: the model does not estimate them from the price, does not reassess the tax after a sale, and does not raise the premium over time. Escrow is not simulated, so there is no cushion, shortfall or annual adjustment, and the monthly tax and insurance figures are one twelfth of what you entered and nothing more.

On the loan side the model assumes every scheduled payment is made and nothing else is paid. Extra payments, recasting, early payoff and refinancing are not represented, and each would move the insurance termination month earlier than the month reported. Termination is measured on the scheduled balance against the original price, so a rise in the home's value does not end the insurance here; that earlier ending is a cancellation a borrower has to request, and a request is not something a calculator can predict. Closing costs, points, origination fees and any up-front insurance premium are excluded, so the total is a monthly payment and not an annual percentage rate. Tax treatment is excluded entirely, and loan types whose insurance does not cancel on the 78 percent rule are outside the model.

Inputs and units

The two optional inputs ship blank on purpose. Blank association dues are read as zero dues. A blank insurance rate means no rate has been quoted, which is a different state from a quoted rate of zero: with a blank rate on a loan above 80 percent of the price the status line says the model cannot price something a lender will charge, while an entered rate of zero is taken at face value.

Entering zero for the price is accepted by the published input rules and then reported as an invalid state by the model, because there is nothing to borrow against. Negative values are refused before any calculation runs.

Governing relationships

Let P be the loan amount, r the monthly interest rate, n the number of scheduled payments, V the home price, PMT the level principal-and-interest payment and B(k) the balance still owed after k payments.

The loan amount is the price less the deposit, and it never goes below zero:

P = max(0, V − Down Payment)

The monthly rate is the annual rate divided by twelve, and the payment count is the term in years multiplied by twelve and rounded to a whole month:

r = Annual Interest Rate / 12, n = round(Loan Term Years × 12)

The level payment is the standard closed form, with a separate branch for a zero rate, which the general form cannot express because it divides by r:

PMT = P × r / (1 − (1 + r)^−n), or PMT = P / n when r is zero

The balance after k payments is also closed form, so the termination month is found exactly rather than by rounding a yearly figure:

B(k) = P(1 + r)^k − PMT((1 + r)^k − 1) / r, or B(k) = P(1 − k / n) when r is zero

Loan to value at the start is the loan over the price, and it is reported as zero when the price is not positive:

LTV = P / V

The three escrow-style costs are simply annualized figures spread evenly:

Monthly Property Tax = Annual Property Tax / 12, Monthly Insurance = Annual Home Insurance / 12, Monthly HOA = Annual HOA Dues / 12

Monthly mortgage insurance is a share of the original loan amount, and it is charged only when a rate has been entered above zero and the loan starts above 80 percent of the price:

Monthly PMI = P × PMI Annual Rate / 12 when PMI Annual Rate > 0 and LTV > 0.8, otherwise zero

The termination month t is the first month at which the scheduled balance has fallen to 78 percent of the original price, searched over the scheduled months only:

t = min{ k : B(k) / V ≤ 0.78 }, and t = 0 when no insurance is charged

Both thresholds are applied as arithmetic. The 80 percent level is where a borrower may request cancellation and the 78 percent level is where insurance terminates on the schedule; the delivered workbook derives both rather than reproducing any published table.

The totals follow from these:

Total Monthly Payment = PMT + Monthly Property Tax + Monthly Insurance + Monthly HOA + Monthly PMI

Payment After PMI Ends = Total Monthly Payment − Monthly PMI

PMI Total Cost = Monthly PMI × t

Total Interest Paid = PMT × n − P

Calculation sequence

1. Check the entered values against the published input rules. A value outside its stated range is refused and nothing is calculated.
2. Calculate the loan amount as the price less the deposit, floored at zero.
3. Calculate the monthly rate and the whole number of scheduled payments.
4. Calculate the level principal-and-interest payment, taking the zero-rate branch when the rate is zero.
5. Calculate loan to value at the start from the loan amount and the price.
6. Read the optional inputs, treating a blank association due as zero dues and a blank insurance rate as no rate entered.
7. Divide the annual property tax, the annual homeowner insurance and the association dues by twelve.
8. Calculate the monthly mortgage insurance, which is zero unless a rate above zero was entered and loan to value at the start is above 80 percent.
9. Build the month-by-month balance from the closed form and take the first month at which it has fallen to 78 percent of the original price. That is the termination month, and it is zero when no insurance is charged.
10. Add the five active parts into the total monthly payment, subtract the insurance to get the payment that applies afterwards, multiply the monthly insurance by the termination month to get the insurance actually paid, and calculate interest over the full term as the total of all payments less the amount borrowed.
11. Build the year-by-year balance and cumulative interest series for the first chart and the payment split for the second.
12. Evaluate the status conditions below in order. The first condition that is true is the one returned.

Outputs and interpretation

Three outputs carry the answer. Total Monthly Payment is everything added together and is the figure to compare against rent or against your budget, not the principal and interest alone. PMI Total Cost is every mortgage-insurance payment added up from the first month to the month it terminates, which is the real price of a smaller deposit and the number most tools do not show. PMI End Month is the first month in which the balance has fallen to 78 percent of the original price, and it reads zero when no insurance is charged at all.

The two charts read the same outputs. The first plots the balance still owed and the interest paid to date, year by year across the term, which shows how slowly principal moves in the early years of a long loan. The second splits the current monthly payment into its parts, so you can see how much of the total is the loan and how much is tax, insurance, dues and mortgage insurance.

Validation and status logic

The calculator evaluates these conditions in the order shown, and the first one that is true is the status returned. Later conditions are not tested once an earlier one matches, so the order is the precedence. The last row is the fallthrough that applies when nothing above it has matched.

The last CHECK row carries a value in angle brackets. The calculator substitutes the termination month there, so what you read on the page is a whole number of months rather than the placeholder. The delivered example scenarios record three concrete forms of it:

• CHECK: mortgage insurance is charged until month 34, when the balance reaches 78% of the original price and it terminates
• CHECK: mortgage insurance is charged until month 103, when the balance reaches 78% of the original price and it terminates
• CHECK: mortgage insurance is charged until month 129, when the balance reaches 78% of the original price and it terminates

The delivered test cases record three status strings verbatim: OK, NOT VALID: there is no purchase price to borrow against, and CHECK: the loan is above 80% of the price, where a lender normally requires mortgage insurance, and no rate has been entered for it. No test case records a substituted termination month, so the three forms above come from the delivered example scenarios rather than from the test corpus.

Three of the conditions describe states the published input rules already refuse, so you will not reach them from the page: a down payment below zero, an interest rate below zero, and a term below one year are all rejected at entry. They remain in the model because the delivered workbook is also used directly, where nothing stops a value being typed into a cell.

Note that the two CHECK rows are not faults. The first says the model cannot price something a lender will probably charge. The second is the model telling you when the insurance stops, which is the whole point of the tool.

Assumptions and limitations

• The loan is a fully amortizing fixed-rate loan with equal monthly payments and no balloon. An adjustable rate, an interest-only period or a balloon payment would all give a different answer.
• Every scheduled payment is made, on time, and nothing extra is paid. Extra payments, recasting and early payoff all move the insurance termination month earlier than the month reported.
• Property tax, homeowner insurance and association dues are held flat in nominal dollars for the whole term. In practice all three tend to rise, and a tax reassessment after a sale can move the tax sharply in the first year.
• Escrow is not simulated. There is no cushion, no shortfall and no annual adjustment, so the monthly tax and insurance figures are exactly one twelfth of what you entered.
• Mortgage insurance is a fixed annual percentage of the original loan amount, charged monthly. An up-front premium, a single-premium policy, or lender-paid insurance priced into the rate are all outside the model.
• Termination is measured against the original purchase price on the scheduled balance. Appreciation does not shorten it here, and a borrower-requested cancellation at 80 percent, which a lender may refuse or condition on an appraisal, is not modeled.
• Loan types whose insurance does not cancel on this rule are not covered. Several government-backed programs charge insurance for the life of the loan or on different terms.
• The number of payments is the term in years multiplied by twelve and rounded to a whole month, so a fractional year is rounded before anything else is calculated.
• Closing costs, points, origination fees, prepaid items and all tax treatment are excluded. The total shown is a monthly payment, not an annual percentage rate.
• All figures are nominal. Nothing is adjusted for inflation.

Restrictions and non-computing states

Every required input must be present: the price, the deposit, the interest rate, the term, the annual property tax and the annual homeowner insurance. The two optional inputs, association dues and the mortgage-insurance rate, may be left blank.

Values outside their published ranges are refused before anything is calculated. The price, the deposit, the interest rate, the annual property tax, the annual homeowner insurance and the association dues must all be zero or more. The term must be between 1 and 40 years. The mortgage-insurance rate must be between 0% and 100%.

Inside those ranges the model still refuses states it cannot answer, and it says so on the status line rather than returning a number. A price of zero leaves nothing to borrow against. A deposit equal to or greater than the price leaves no loan to compute. In both cases the loan amount, the principal-and-interest payment and the interest over the term are reported as zero, while the monthly tax, insurance and dues are still shown, because those costs do not depend on a loan existing. Treat the total monthly payment in a NOT VALID state as arithmetic on the parts that remain, not as an answer to your question.

Mortgage insurance is not charged at exactly 80 percent loan to value, only above it. A deposit of exactly one fifth of the price therefore produces no insurance, no termination month and no insurance total, which is the shipped example state.

Errors and warnings

Three different things can go wrong, and they are worth keeping apart.

A rejected entry happens before any calculation. A value outside its published range, or a required input left empty, is refused at the page and no figures are produced. It is a statement about the value you typed, not about your mortgage. Correct the field and the calculator runs.

A NOT VALID or CHECK status is the model's own finding, produced by a calculation that ran to completion. NOT VALID means the inputs do not describe a mortgage this model can answer, and the numbers alongside it should not be read as a result. CHECK means the answer computed and is worth reading, but something deserves attention: either the loan is above 80 percent of the price with no insurance rate entered, so a real cost is missing from the total, or insurance is being charged and the status is telling you the month it stops.

A connection or calculation-service failure is neither of those. The calculation service could not be reached or could not complete, so no result exists for the values you entered. That is an availability problem, never a finding about your mortgage, and it never means zero. If a figure is missing, re-run rather than reading a blank as a result.

The cost categories this calculator adds together are the ones the Consumer Financial Protection Bureau describes in What costs come with taking out a mortgage?, which separates principal and interest from property taxes, homeowners insurance and mortgage insurance, and notes that condominium or association dues are usually paid separately from the mortgage payment itself.

The two mortgage-insurance thresholds used here are the published cancellation rule. The CFPB's When can I remove private mortgage insurance (PMI) from my loan? states that a borrower may request cancellation when the principal balance is scheduled to fall to 80 percent of the original value of the home, and that the servicer must terminate the insurance automatically on the date the principal balance is scheduled to reach 78 percent of that original value, provided payments are current. This calculator reports the automatic 78 percent month, which is the later and more conservative of the two. The underlying statute is the Homeowners Protection Act, 12 U.S.C. 4902, Termination of private mortgage insurance.

For when mortgage insurance is required at all, the CFPB's What is private mortgage insurance? explains that it is typically required on a conventional loan with a down payment of less than 20 percent of the purchase price, and that premiums may be charged monthly, up front, or as a combination. This calculator models the monthly form only, at the annual rate you enter.

The interest rate input is the note rate, not the annual percentage rate. The CFPB's What is the difference between a mortgage interest rate and an APR? describes the interest rate as the yearly cost of borrowing the money, excluding fees, while the annual percentage rate also folds in points, broker fees and other charges paid to get the loan.

Property tax and homeowners insurance are shown here as one twelfth of the annual amounts you enter. In practice a lender usually collects them through an escrow account, and the CFPB's What is an escrow or impound account? notes that the escrow portion of a payment is adjusted each year because taxes and premiums change. This calculator does not model that adjustment.

Deductibility of mortgage interest is outside this model. The rules, limits and worksheets are in the Internal Revenue Service's Publication 936, Home Mortgage Interest Deduction.

The level-payment formula, the closed-form remaining balance and the arithmetic that locates the 78 percent month are standard financial mathematics. They are not taken from any of the sources above; they are documented and independently checked in the audit delivered with the workbook, which is available with the download.

These sources give consumer and statutory context. They do not supply this calculator's inputs and they do not certify its result. This calculator is informational and is not financial, tax, mortgage, insurance or real-estate advice, and it is not a lender disclosure or an escrow analysis. Confirm the payment components, the insurance rate and the cancellation terms with your lender before acting on any figure here.