Mortgage Calculator

{{ frequencyLabel }} Housing Payment

{{ currencySymbol }} {{ format(amountFinanced) }} financed {{ formatPercent(loanToValue, 1) }}% LTV {{ currencySymbol }} {{ format(cashToClose) }} cash to close {{ frequencyLabel }} PI {{ currencySymbol }} {{ format(periodicPiPayment) }} {{ frequencyLabel }} escrow {{ currencySymbol }} {{ format(periodicEscrow) }} PMI {{ currencySymbol }} {{ format(firstPeriodPmi) }} Save {{ currencySymbol }} {{ format(comparison.interestSaved) }}

Home price:

Enter purchase price before down payment, such as 425000.

Down payment:

Use percent for LTV scenarios, e.g. 15%, or cash for an exact deposit.

{{ currencySymbol }} %

Interest rate:

Enter annual APR as a percent, such as 6.5; use 0 for a no-interest scenario.

% / yr

Loan term:

Enter whole years and 0-11 extra months, for example 30 yrs and 0 mos.

yrs mos

{{ warning }}

Payment frequency:

Choose Monthly for 12 payments or Biweekly for 26 payments per year.

First payment date:

Use YYYY-MM-DD, normally the first due date after closing.

Interest accrual:

Options: standard amortized, simple daily, or continuous compounding estimate.

Extra principal each payment:

Enter extra cash per payment, such as 150; leave 0 for scheduled payments only.

Lump-sum payment:

Enter the extra amount and payment number, e.g. 5000 at pmt 24; use 0 to skip.

{{ currencySymbol }} at pmt

Closing costs:

Enter lender, title, prepaid, or estimate costs paid at closing, such as 6500.

Property tax:

Use % / yr like 1.10, or switch to annual dollars such as 4675.

% / yr {{ currencySymbol }} / yr

Homeowners insurance:

Enter the yearly premium estimate, such as 1800; use 0 if excluded.

{{ currencySymbol }} / yr

HOA dues:

Enter monthly HOA or condo dues, such as 250; use 0 if none.

{{ currencySymbol }} / mo

PMI rate:

Enter annual PMI factor as a percent, such as 0.55; use 0 when not modeling PMI.

% / yr

PMI ends when LTV reaches:

Choose 80%, 78%, or Never to keep PMI through the full projection.

Metric	Value	Copy
{{ row.label }}	{{ row.display }}

Metric	No acceleration	Current plan	Change	Copy
{{ row.label }}	{{ row.baseDisplay }}	{{ row.currentDisplay }}	{{ row.deltaDisplay }}

Pmt	Date	Total	Principal	Interest	Escrow	PMI	Balance	Equity	Copy
{{ row.idx }}	{{ row.dateLabel }}	{{ row.totalPaymentDisplay }}	{{ row.principalDisplay }}	{{ row.interestDisplay }}	{{ row.escrowDisplay }}	{{ row.pmiDisplay }}	{{ row.balanceDisplay }}	{{ row.equityDisplay }}

Year	Payments	Principal	Interest	Escrow	PMI	Ending balance	Ending equity	Copy
{{ row.year }}	{{ row.totalPaymentDisplay }}	{{ row.principalDisplay }}	{{ row.interestDisplay }}	{{ row.escrowDisplay }}	{{ row.pmiDisplay }}	{{ row.balanceDisplay }}	{{ row.equityDisplay }}

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A mortgage decision is rarely about one monthly number. The loan payment, the cash due at closing, the insurance rules, and the long-term interest cost all pull on the same budget. A buyer can make the first payment look manageable by stretching the loan term or putting less money down, but those choices can raise lifetime interest, trigger mortgage insurance, or leave too little cash for closing and repairs.

The core loan payment is principal plus interest. Principal is the borrowed amount being paid back. Interest is the lender's charge on the remaining balance. A fixed-rate mortgage sets a scheduled payment that pays the loan to zero over the term, but the split changes each period. Early payments are interest-heavy because the balance is still large. Later payments reduce principal faster because less balance remains to charge interest against.

Mortgage cost components and where they affect the decision
Component	Where it shows up	Planning effect
Down payment	Cash before the loan starts	Reduces the financed balance and loan-to-value ratio
Closing costs	Cash to close	Raises upfront cash need even when the loan balance is unchanged
Principal and interest	Scheduled mortgage payment	Determines amortization, payoff timing, and most lifetime borrowing cost
Tax, insurance, HOA, and PMI	Total housing payment	Raises monthly cash flow, but usually does not reduce the mortgage balance
Extra principal	After the scheduled payment	Reduces the balance early, which can shorten payoff and cut later interest

Loan-to-value, often shortened to LTV, is the loan balance divided by the home's value. LTV matters because a conventional mortgage with less than 20% down often carries private mortgage insurance, or PMI. The borrower pays that cost, but it protects the lender if the loan defaults. PMI rules can depend on the loan type, payment history, original value, investor rules, and servicer process, so an 80% or 78% LTV estimate is a planning milestone rather than a promise that a charge will disappear automatically on the next statement.

Diagram showing cash to close, scheduled principal and interest, recurring housing costs, and extra principal reducing the loan balance over time.

The mortgage payment also has to be separated from the cost of owning the home. Property tax and homeowners insurance may be collected through escrow, but they are not interest and they do not pay the loan down. HOA dues, flood insurance, maintenance, utilities, and future tax reassessments can change affordability even when the mortgage note itself is fixed. A clean principal-and-interest quote is useful only after the surrounding housing costs are visible too.

A mortgage estimate is strongest when it is used to compare scenarios with the same assumptions. Changing the rate, term, payment frequency, down payment, first payment date, or PMI rule changes the answer for a real reason. The numbers still remain planning estimates. Lender disclosures, escrow analyses, tax bills, insurance renewals, and servicing rules are the documents that control the final obligation.

How to Use This Tool:

Enter the loan structure first, then add ownership costs and acceleration choices only after the base payment looks plausible.

Set Home price, Down payment, Interest rate, and Loan term. Check Amount financed, Loan-to-value, and Principal and interest payment before adding optional costs.
Use Closing costs when you want Cash to close to include lender, title, prepaid, or other closing estimates. These costs increase upfront cash in this model, not the financed balance.
Add Property tax, Homeowners insurance, HOA dues, and PMI rate to estimate the opening housing payment. Use percent mode for property tax when you want the estimate tied to the entered home price.
Keep Payment frequency, First payment date, and Interest accrual the same when comparing scenarios. Switching from monthly to biweekly or changing the first date changes the schedule length and some interest rows.
Model payoff acceleration with Extra principal each payment or Lump-sum payment. The Acceleration Comparison tab then compares the current plan with the same loan and no extra principal.
If a warning appears, fix that issue before relying on the tables. A non-positive home price, zero-month term, down payment that covers the whole price, missing PMI on a high-LTV scenario, or interest charge larger than the scheduled payment can make the projection incomplete.

After the snapshot agrees with the scenario you intended, use Amortization Schedule for payment-by-payment detail, Loan-Year Summary for annual totals, and the two chart tabs to inspect balance, equity, and cost mix over time.

Interpreting Results:

Read Principal and interest payment as the clean loan formula and Initial housing payment as the first-period cash-flow estimate after escrow, PMI, and recurring extra principal are added. A lender quote that lists only principal and interest can feel lower than the payment you actually need to budget for.

Cash to close is the down payment plus the entered closing costs. It does not include moving, repairs, reserves, or future maintenance.
Total interest, Total paid, and Projected payoff date show the long-run cost of the loan structure better than the first payment alone.
Total PMI and the PMI end date are estimates based on the selected LTV stop rule. Check lender disclosures and servicer requirements before assuming PMI will stop exactly on that date.
Acceleration Comparison is most useful when only the extra principal fields changed. If you also changed rate, term, date, or escrow assumptions, the savings comparison no longer isolates the extra-payment effect.
Equity uses the entered home price as a static value. It does not forecast market appreciation, depreciation, selling costs, or refinance value.

A lower opening payment is not automatically the better choice. Verify the warning banner, cash to close, lifetime interest, PMI estimate, and first-year principal before comparing offers or deciding how much house the budget can carry.

Technical Details:

Fixed-rate amortization solves one scheduled principal-and-interest payment from three quantities: starting loan principal, periodic interest rate, and number of payment periods. If every scheduled payment is made and no extra principal is added, the balance reaches zero at the end of the term. Interest is recalculated from the remaining balance each period, so early payments devote more dollars to interest and later payments devote more dollars to principal.

The annual rate entered here is treated as the nominal annual borrowing rate for the payment formula. That differs from a regulatory annual percentage rate disclosure when lender fees or points are folded into the APR. For fair scenario comparisons, keep the same rate basis, payment frequency, first payment date, and accrual method across runs.

Formula Core:

The scheduled payment formula sets the base principal-and-interest amount. The interest line then shows how each schedule row charges interest under the selected accrual method.

\begin{array}{lll} P & = & \frac{L \times r}{1 - {(1 + r)}^{- n}} \\ I_{t} & = & B_{t - 1} \times q_{t} \\ q_{t}^{standard} & = & \frac{APR}{m} \\ q_{t}^{daily} & = & \frac{APR}{365.25} \times d_{t} \\ q_{t}^{continuous} & = & e^{\frac{APR \times d_{t}}{365.25}} - 1 \end{array}

Mortgage formula variables
Symbol	Meaning	Visible field or result
`L`	Starting loan principal after down payment	Amount financed
`r`	Periodic rate used to solve the scheduled payment	Interest rate, Payment frequency, and Interest accrual
`n`	Original number of payment periods	Loan term converted to monthly or biweekly periods
`B_t-1`	Balance before the current payment	Previous row's Balance
`d_t`	Days between the prior payment date and current payment date	Derived from First payment date and Payment frequency
`m`	Payments per year	`12` for monthly or `26` for biweekly

For a $361,250 financed balance, 6.50% annual rate, 30-year term, and monthly standard amortization, r = 0.065 / 12 and n = 360. Substituting those values into the payment formula gives a principal-and-interest payment of about $2,283.35 before escrow, PMI, HOA dues, or extra principal.

Escrow-style costs are allocated per payment period. Annual property tax, annual homeowners insurance, and annualized HOA dues are divided by 12 for monthly schedules or 26 for biweekly schedules. PMI is estimated from the remaining balance each period when the entered PMI rate is positive and the balance is still above the selected LTV stop threshold. Setting the PMI stop rule to Never in this estimate keeps PMI in the schedule through payoff.

Line diagram showing the mortgage balance falling, equity rising, and milestone markers for 80 percent LTV, half balance, and payoff.

Mortgage calculation boundaries and warnings
Condition	Result behavior	Interpretation
Down payment equals or exceeds Home price	No amortization schedule is built	No balance remains to finance
Loan term is less than 1 month	No valid payment horizon is available	The model needs at least one payment period
Loan-to-value is above 80% and PMI rate is 0	A warning flags missing mortgage insurance	The opening housing payment may be too low for a high-LTV conventional loan
Loan term is longer than 360 months	A lifetime-interest warning appears	The lower first payment can hide a much larger total interest cost
Scheduled payment does not cover accrued interest	The schedule stops and warns	Negative amortization would make the payoff projection unreliable
Extra principal exceeds the remaining balance after scheduled principal	The extra amount is capped in the final row	The balance does not go below zero

Responsible Use Note:

Use the output as an educational planning estimate, not as financial advice, a lender quote, or a substitute for a Loan Estimate or Closing Disclosure. The calculator compares scenarios from the numbers you enter, but actual obligations can differ because of lender fees, points, escrow cushions, tax reassessments, insurance renewal changes, loan program rules, and servicing policy.

The calculations run in your browser. Treat copied rows, downloaded tables, chart images, JSON exports, and shared URLs as financial information because they can reveal the purchase price, loan balance, rate, payment, and payoff assumptions you entered.

Worked Examples:

A 30-year purchase with escrow and PMI

Set Home price to $425,000, Down payment to 15%, Interest rate to 6.50%, Loan term to 30 years, monthly payments, and First payment date to June 1, 2026. With 1.10% property tax, $1,800 homeowners insurance, and 0.55% PMI, Amount financed is $361,250.00, Principal and interest payment is $2,283.35, and Initial housing payment is $2,988.50. The first Amortization Schedule row shows $1,956.77 of interest and $326.57 of principal, which is normal for an early fixed-rate payment.

Recurring extra principal plus one lump sum

Keep the same loan and date, then enter $200 in Extra principal each payment and $5,000 in Lump-sum payment at payment 24. Acceleration Comparison moves the projected payoff from May 1, 2056 to August 1, 2049, trimming 81 payments. Total interest drops by about $124,330.49 and Total PMI drops by about $4,330.30 because the earlier principal reduction lowers later balances.

A small down-payment change crosses the PMI boundary

With the same $425,000 purchase and a 20% down payment, Loan-to-value starts at exactly 80.0%, so First-payment PMI is $0.00 when the stop rule is 80%. Change the down payment to 19.5% and leave the 0.55% PMI rate in place. First-payment PMI becomes about $156.81 and Total PMI becomes about $1,094.65. The mortgage payment changed only slightly, but the insurance estimate changed because the starting balance moved above the LTV threshold.

When results disappear

Enter a Down payment that equals the Home price, or set Loan term to 0 years and 0 months. The warning banner explains the invalid setup, and Payment Snapshot, Amortization Schedule, and chart tabs clear because there is no positive loan balance or payment horizon. Restore a positive Amount financed and at least one month of term before reading the payoff estimate.

FAQ:

Why is Initial housing payment higher than Principal and interest payment?

Principal and interest payment is the loan formula. Initial housing payment also includes Escrow per payment, First-payment PMI, and any recurring extra principal, so it is closer to the first-period cash-flow estimate.

Does biweekly always save money?

Not by itself in every comparison. Biweekly mode uses 26 payments per year and changes the payment count, escrow allocation, and schedule dates. Compare it against monthly only after using the same loan amount, rate, first payment date, accrual method, and extra-principal assumptions.

Why did PMI not stop at the exact date I expected?

The PMI estimate follows the selected PMI ends when LTV reaches rule and the schedule balance. Real cancellation can depend on original value, loan type, payment history, appraisals, investor rules, and servicer process, so use the estimate as a planning marker.

Why did Acceleration Comparison say there was no acceleration?

The comparison needs Extra principal each payment or Lump-sum payment to be above zero. If both fields are zero, the current plan and no-acceleration plan are the same loan path.

What does Simple daily accrual change?

Simple daily accrual recalculates each row's interest from the actual day count between payment dates. In this calculator, the scheduled payment is still seeded from the average yearly rate. Continuous compounding estimate changes the seeded periodic rate and the row-by-row interest factor.

Are my mortgage numbers sent anywhere?

The mortgage calculations run in your browser. Shared links with filled-in values and exported CSV, DOCX, chart image, or JSON files can still expose your scenario to anyone who receives them.

Glossary:

Amortization: The process of paying a loan down over repeated scheduled payments.
Principal: The borrowed balance that remains to be repaid.
Loan-to-value (LTV): The loan balance divided by the home's value, expressed as a percentage.
Escrow: Money collected with the mortgage payment for costs such as property tax and homeowners insurance.
Private mortgage insurance (PMI): Mortgage insurance that may apply to some high-LTV conventional loans and is estimated here from the remaining balance.
Cash to close: The upfront down payment plus the entered closing costs in this calculator.
Extra principal: Money paid beyond the scheduled principal-and-interest payment that directly reduces the loan balance.

References:

How do mortgage lenders calculate monthly payments?, Consumer Financial Protection Bureau, updated December 18, 2024.
On a mortgage, what's the difference between my principal and interest payment and my total monthly payment?, Consumer Financial Protection Bureau, updated August 30, 2023.
When can I remove private mortgage insurance (PMI) from my loan?, Consumer Financial Protection Bureau, updated June 30, 2025.
Figure out how much you want to spend, Consumer Financial Protection Bureau, updated February 18, 2026.