Finance · Loans
Estimate a mortgage principal-and-interest payment
Compute the amortizing monthly P&I (12 payments a year) and, if you want, a flat annual insurance amount spread over 12 months. This is not a loan offer. APR is not calculated.
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How the calculator works
The mortgage is treated as a monthly amortizing loan: periodic rate = annual nominal / 12, n = term × 12. P&I follows M = P × r(1+r)^n / ((1+r)^n − 1). Typed insurance is a yearly lump sum divided by 12 and added. It does not decline with remaining principal. Total monthly = P&I + flat monthly insurance.
Formula and method
M = P × r(1+r)^n / ((1+r)^n − 1), with r = rate/12 and n = 12 × years
t is the annual nominal rate as a decimal. M is P&I, excluding insurance.
Assurance mensuelle = assurance annuelle / 12
Arithmetic split of a flat yearly amount. Not a percent of original principal, not a percent of remaining balance.
P&I uses the same amortizing identity as the general loan calculator, locked to monthly payments. US APR under Regulation Z is a disclosure method, not this formula. PMI, MIP, and homeowners insurance are often percent-of-balance or escrowed; the insurance field here is only a constant annual dollar amount. Points, origination, taxes, HOA, and escrow shortages are omitted. The result is not a Loan Estimate and not an offer.
Worked example
$416,000, 6.5%, 30 years, no insurance
Principal $416,000, nominal 6.5%, 30 years, $0 annual insurance.
- r = 0.065 / 12 ≈ 0.0054167, n = 360.
- Monthly P&I ≈ $2,629.40.
- Total P&I paid ≈ $946,585.
- Total interest ≈ $530,585.
- Insurance monthly = $0, so total monthly = P&I.
About $2,629.40 / month P&I, roughly $530,585 interest over the term, excluding fees, taxes, and APR.
Same loan, $1,200 / year flat insurance
Identical, with $1,200 annual insurance.
- P&I unchanged: ≈ $2,629.40.
- Insurance monthly = 1,200 / 12 = $100.
- Total monthly ≈ $2,729.40.
- Interest totals still exclude insurance: insurance is not converted into interest.
$2,629.40 P&I + $100 flat insurance ≈ $2,729.40 / month. This is not declining PMI.
Input notes
- Loan amount
- Mortgage principal. Closing costs belong here only if they are rolled into this balance.
- Annual nominal rate
- Annual note rate. To compare lenders, use each Loan Estimate’s APR; that APR is not computed here.
- Term
- Term in years. Payment count n = term × 12 (rounded). 360 months is 30 years.
- Flat annual insurance
- Dollars per year, then / 12. If your PMI is 0.50% of remaining balance, this field will not reproduce it: type a yearly dollar amount you already estimated, knowing it stays flat.
Assumptions and limits
Assumptions
- Monthly repayment (12 per year), constant nominal rate, level P&I.
- Insurance = dollars per year / 12, independent of remaining balance.
- No points, no escrow for tax, no ARM, no balloon.
- APR is not calculated.
Limits
- Not a loan offer and not a lender simulation.
- PMI/MIP that declines with principal, age-rated life insurance, and lender vs borrower-paid MI are not modeled.
- Fees, title, taxes, HOA, and APR are absent: “cost of credit” here is interest on the amortizing balance only.
- Market rates move; this tool injects none.
How to read the result
P&I is mathematical amortization at the note rate. The insurance line is simply one-twelfth of a yearly lump sum: if your quote falls as the balance falls, the models differ. Total monthly is not APR. To change payment frequency without the insurance line, use the general amortizing-loan calculator.
Common mistakes
Typing a PMI rate (0.50) into the annual-insurance dollar field.
The field wants dollars per year (for example 1,200), not a percent. A remaining-balance rate is not applied.
Comparing this monthly total to a lender’s APR.
APR annualizes finance charges with a regulatory method. Here we add nominal P&I and a flat insurance split. The figures are not interchangeable.
Taking the result as a pre-approval or debt-to-income test.
A lender looks at income, down payment, property, and credit. This tool evaluates none of that.
Comparison
| Item | In this calculator | On a typical US Loan Estimate |
|---|---|---|
| P&I | Yes, note rate / 12 | Yes, from the creditor’s note |
| Insurance | Flat $ / year ÷ 12 only | Often PMI/MIP, HOI, and escrow |
| Fees and points | No | Often in APR and closing costs |
| APR | Not computed | Required disclosure |
Related calculations
- Amortizing loanGet the constant installment from principal, annual nominal rate, and payment frequency. Origination fees, insurance, and APR stay outside the math.
- Compound interestGrow a single principal at a nominal annual rate with a chosen compounding frequency, including continuous compounding. The page also reports the effective annual rate. There are no recurring deposits on this form.
Frequently asked questions
Is this a mortgage offer?
No. It applies the amortizing formula to the numbers you typed.
A US mortgage offer is a Loan Estimate or Closing Disclosure with APR, projected payments, and closing costs. None of that is produced here.
How is insurance handled?
A yearly dollar amount, divided by 12, added to P&I.
If you type 1,200, the tool adds $100 every month from first to last, even when principal has fallen. PMI quoted on remaining balance usually costs more up front and less later. The two approaches are not interchangeable.
Is APR calculated?
No, and the typed rate should not be treated as APR.
APR folds in items this form ignores (points, certain fees, sometimes MI). To compare two lenders, use each disclosure’s APR. Here the rate only builds r = t/12 in the level-payment formula.
Does total interest include insurance?
No. Interest shown is from principal amortization only.
Flat insurance is shown separately. Multiplying $100 by 360 months is a rough sum of this flat model, distinct from interest.
Author and update
Written by Rédaction HexaCalc (editorial team). Content last updated: August 25, 2026. No third-party medical or financial review is claimed.
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A different payment frequency
The general loan calculator uses the same formula with a free payments-per-year count (monthly, quarterly, annual). Still no fees, still no APR.
Calculate a loan with another frequencyEducational mortgage P&I plus an optional flat insurance split. This is a calculator, not financial, tax, or credit advice, and not a loan or investment offer. Lenders and brokers apply their own rounding, fees, insurance, and APR. Check the actual contract and disclosures.
Category: Finance