Mortgage calculator

The mortgage calculator estimates what a fixed-rate home loan could cost you each month and over its full term. Enter a home price, down payment, interest rate and term, and it produces an estimated principal and interest (P&I) payment, a full amortization schedule, and the total interest you would pay if every payment were made on schedule. Add property tax, homeowner's insurance, HOA dues and private mortgage insurance (PMI) to see an estimated total monthly housing payment rather than the loan payment alone.

It is built for anyone sizing up a purchase: first-time buyers checking whether a price range fits a budget, current owners weighing an additional monthly payment, and people comparing a 15-year term against a 30-year term before talking to a lender. Every figure is an estimate based on the assumptions entered, not a quote; your actual rate, taxes and insurance will come from a lender and your local records. If you are new to the mechanics, start with how mortgage payments work or the plain-language mortgage guide.

The headline figure, labeled Estimated monthly payment, is your estimated total monthly housing payment in the first month of the loan. It is the sum of five parts: the scheduled principal and interest (P&I) payment, estimated PMI if it applies, one twelfth of the annual property tax you entered, one twelfth of the annual homeowner's insurance, and monthly HOA dues. If you leave the add-ons at zero, the headline equals the P&I payment alone.

The breakdown beneath it separates those parts so you can see how much is the loan itself and how much is everything that travels with it. On a $300,000 loan at 6.5 percent over 30 years with no add-ons, the estimated P&I is about $1,896 per month. By contrast, a $405,000 loan on a $450,000 home at the same rate, with $5,400 a year of property tax, $1,800 of insurance, $100 of HOA dues and an estimated PMI charge, comes to approximately $3,429 per month, of which only about $2,560 is P&I.

Below the monthly view, the lifetime totals describe the whole term. Total interest is the sum of every month's interest charge on the schedule; for that $300,000 loan it is roughly $382,600. Total loan cost adds the original principal, total interest and total PMI. Total estimated cost adds the taxes, insurance and HOA dues paid over the months the loan is outstanding. None of these totals include the down payment, closing costs or maintenance, and none are adjusted for inflation.

Two more numbers appear when they are relevant. Loan-to-value (LTV) is the loan amount divided by the home price, which decides whether PMI is estimated. When you add an additional monthly payment, an interest saved figure and a payoff date compare your plan against the same loan with no extra payments. To understand why the split inside the P&I payment moves over time, see principal vs. interest.

This calculator answers "what would this loan cost me?" It is most useful for a handful of decisions:

• Sizing a purchase. Enter a few home prices and down payments to see how the estimated total monthly housing payment moves, including taxes, insurance and PMI rather than P&I alone.
• Choosing a term. Compare a 15-year and a 30-year loan side by side to see the trade between a higher monthly payment and a much lower total interest figure.
• Testing a rate. See what a change of half a percentage point does to the monthly payment and to lifetime interest before you shop.
• Deciding on a down payment. Watch how a larger down payment lowers the loan amount and LTV, and whether it removes the estimated PMI charge. Down payments explained covers the trade-offs.
• Planning extra principal. Add an additional monthly payment and read off the estimated interest saved and the earlier payoff date.

Another tool is better when the question is different. If you already have a mortgage and want to know whether replacing it makes sense, you need a refinance comparison that accounts for closing costs and the months already paid, which this calculator does not do. If the loan has an adjustable rate, an interest-only period or a balloon payment, the fixed-payment formula used here will not describe it. If you want to know how much cash you need at closing, the down payment is only part of the answer; closing costs are out of scope. And if you are deciding between paying down debt and paying down a mortgage, the debt payoff calculator handles the debt side. Try the debt payoff calculator.

Whatever you use it for, treat the output as an estimate based on the assumptions entered. A lender's Loan Estimate, not a calculator, is the document that states your actual terms.

Every number this calculator produces rests on the assumptions below. They are reasonable for a standard fixed-rate loan, but each one is a simplification, and your actual loan will differ in at least a few of them.

• It is an estimate. Taxes, insurance, PMI rates, HOA dues and interest rates vary by lender, location and time. The figures shown are estimates based on the assumptions entered, and your actual figures will differ.
• The loan is a standard fixed-rate, fully amortizing mortgage with one payment per month. Interest is calculated monthly as the outstanding balance multiplied by the annual rate divided by 12. There is no daily accrual, no leap-year effect and no bi-weekly payment option.
• Each month's interest is rounded to the nearest cent before it is applied, the way a lender statement would show it. Because the scheduled payment is also rounded, the final payment is adjusted by a few cents so the balance ends at exactly zero.
• Property tax and homeowner's insurance are entered as annual amounts and spread evenly across 12 months. They are assumed to stay constant for the life of the loan; in reality they usually rise. HOA dues are entered monthly and are also assumed constant.
• PMI is estimated only when the down payment is less than 20 percent of the price, that is, when loan-to-value (LTV) is above 80 percent. It is calculated as an annual percentage of the original loan amount (0.5 percent by default) divided by 12, and it is assumed to end automatically with the first payment after the scheduled balance reaches 78 percent of the original home price. Real PMI pricing depends on credit score, loan type and lender, and you may be able to request cancellation earlier, at 80 percent LTV. See what PMI is and when it goes away.
• The additional monthly payment is applied every month starting with the first payment and goes entirely to principal. The scheduled payment does not change, because the loan is not re-amortized; it simply ends earlier.
• Total estimated cost adds up every scheduled payment (principal, interest, PMI, taxes, insurance and HOA dues) over the months the loan is outstanding. It excludes the down payment, closing costs, maintenance, utilities, discount points and any tax benefits, and it does not adjust for inflation or the time value of money.
• The payoff date assumes the first payment is made one month after the start date and that every payment is made on time.
• Results are rounded for display. Totals may differ from the sum of the rounded parts by a few cents.

The headline and the breakdown

The large number at the top is the estimated total monthly housing payment for the first month: principal and interest (P&I) plus PMI, taxes, insurance and HOA dues. It is rounded to the nearest whole dollar and always carries the word "estimated" because it depends entirely on the assumptions entered. The breakdown beneath it lists each component to the cent. Components are rounded individually, so they may not sum exactly to the headline; that is expected and is noted under the table.

When PMI applies, a second monthly figure shows the payment after PMI is projected to end. On a $405,000 loan against a $450,000 home at 6.5 percent, for example, the estimated payment with taxes, insurance and dues is approximately $3,429, falling to about $3,260 once the estimated PMI charge of about $169 drops off after roughly 9 years.

The three charts

Payment breakdown is a share view of the first month's payment. It shows how much of what you send each month is P&I and how much is the add-ons. With a small down payment and high taxes, the add-ons can be a quarter or more of the total.

Principal vs. interest over time plots, over the life of the loan, how much of the scheduled P&I payment went to interest and how much to principal. Early on, interest dominates: in month 1 of a $300,000 loan at 6.5 percent, about $1,625 of the $1,896 payment is interest and about $271 is principal. For this loan the principal share does not overtake the interest share until payment 233, more than 19 years in, and the split keeps shifting toward principal through the end of the term. What is amortization? explains why the curve has that shape.

Remaining balance shows the loan balance after each payment. It falls slowly at first and quickly at the end. When you add extra principal, a second line shows the faster payoff, and the gap between the two lines is the balance you no longer owe at that point.

The scenario comparison

The comparison view runs the calculator twice and shows the difference. Four presets are built in: a 15-year term against a 30-year term, a lower or higher rate, a larger or smaller down payment, and an additional monthly payment. Each row shows the base value, the alternative and the delta, and a short sentence summarizes the trade in whole dollars and years and months. Comparing the $300,000 loan at 30 years with the same loan at 15 years, for instance, shows a monthly P&I that is about $717 higher and estimated total interest that is about $212,200 lower.

What "estimated" means here

"Estimated" is not a hedge for its own sake. The calculator knows only what you typed; it does not know your credit profile, your county's tax rate or your lender's PMI table. The arithmetic is exact for the assumptions entered, and every figure is reproducible, but the assumptions are yours. If a lender's Loan Estimate shows a different payment, the difference is almost always in the inputs, not the formula.

Four inputs do most of the work. The examples below all start from the same base loan: $300,000 borrowed on a $375,000 home at 6.5 percent over 30 years, which has an estimated P&I payment of about $1,896 per month and roughly $382,600 of total interest.

• Term. Shortening the term raises the monthly payment and cuts total interest sharply. The same loan over 15 years is about $2,613 per month (roughly $717, or 38 percent, more) but costs about $170,400 in interest, around $212,200 less. A 20-year term sits between: about $2,237 per month and roughly $236,800 of interest.
• Interest rate. Half a percentage point moves the payment by roughly $100 a month on a loan of this size and total interest by about $35,000. At 6.0 percent the estimate is about $1,799 per month and $347,500 of interest; at 7.0 percent it is about $1,996 and $418,500. The effect is close to linear over a narrow range, so a full point is roughly double that.
• Loan amount, through price or down payment. The payment scales almost proportionally with the amount borrowed. Putting 10 percent down instead of 20 percent on the $375,000 home raises the loan to $337,500 and the P&I payment to about $2,133, and it triggers an estimated PMI charge of about $141 per month for roughly 9 years (about $15,300 in total). At 5 percent down the loan is $356,250, P&I is about $2,252, and estimated PMI runs about $148 per month for roughly 11 years.
• Additional monthly payment. An additional payment does not change the scheduled payment, but it shortens the loan and removes the interest that would have accrued on the balance you retired early. Adding $100 per month saves roughly $61,000 of interest and about 4 years; $250 saves about $120,300 and about 8 years 2 months; $500 saves about $179,800 and about 12 years 6 months. The first dollars matter most, because they retire principal that would otherwise carry interest for decades.

Taxes, insurance and HOA dues change the total monthly housing payment dollar for dollar but do not touch the loan, the schedule or total interest. The PMI rate matters only while LTV is above the removal threshold.

Direction is dependable; magnitude is approximate. The figures above are estimates based on the assumptions entered, and each one is worth re-running with your own numbers. See the extra-principal scenario, or read how mortgage payments work for the mechanics behind the term and rate effects.

1. Comparing the P&I payment with a real housing budget. The loan payment is only part of what you send each month. Leaving taxes, insurance, HOA dues and PMI at zero can understate the estimated total monthly housing payment by several hundred dollars. Enter them, even as rough figures, before judging affordability.

2. Entering the APR instead of the interest rate. A mortgage APR folds certain fees and points into a single percentage, so it is usually higher than the note rate. The calculator's formula uses the interest rate. Entering the APR overstates the payment; entering the rate and then treating the result as a full-cost comparison understates the fees.

3. Assuming the first payments build much equity. In the first month of a $300,000 loan at 6.5 percent, only about $271 of the $1,896 P&I payment reduces the balance. The split shifts slowly. If you plan to sell within a few years, the balance chart is the number to watch, not the payment. Principal vs. interest walks through the schedule.

4. Treating total estimated cost as the cost of the home. That figure includes principal, interest, PMI, taxes, insurance and HOA dues over the loan's life. It leaves out the down payment, closing costs, maintenance and any tax benefits, and it is in today's dollars spread over decades. It is useful for comparing scenarios, not for valuing a purchase.

5. Expecting an extra payment to lower the monthly bill. Additional principal does not re-amortize the loan here. The scheduled payment stays the same and the loan ends sooner; the benefit shows up as interest saved and an earlier payoff date, not as a smaller payment.

6. Reading the PMI estimate as a quote. The default assumes 0.5 percent of the loan per year, ending when the scheduled balance reaches 78 percent of the original price. Your lender's PMI rate depends on credit score and loan type, and you may be able to request cancellation at 80 percent LTV. What is PMI? covers the rules.

7. Forgetting that taxes and insurance rise. The calculator holds both constant for 30 years. A payment that fits comfortably today may not in year ten if assessments and premiums climb, and an escrow account will adjust the monthly amount to match.

8. Entering a down payment larger than the price, or mixing percent and dollars. The two down payment fields are linked; typing 20 in the dollar field produces a $20 down payment and a loan-to-value near 100 percent, complete with an estimated PMI charge. Check the LTV line before trusting the result.

These definitions match how the calculator labels its inputs and outputs. Where a term has a broader meaning in lending, the definition here is the narrower one the calculator actually uses.

Principal

The amount borrowed: the home price minus the down payment. Each month's principal portion is the part of the payment that reduces the balance.

Interest

The lender's charge for the loan, estimated each month as the outstanding balance multiplied by the annual rate divided by 12, rounded to the nearest cent.

Principal and interest (P&I)

The scheduled monthly loan payment, constant for a fixed-rate loan except for the final payment, which is adjusted by a few cents to clear the balance exactly.

Total monthly housing payment

The headline figure: P&I plus estimated PMI, one twelfth of annual property tax, one twelfth of annual homeowner's insurance and monthly HOA dues.

Amortization

The process of paying a loan down to zero through equal scheduled payments, with the interest share falling and the principal share rising over time. The amortization schedule lists every payment.

Term

The number of months over which the loan is scheduled to be repaid. Thirty years is 360 payments; fifteen years is 180.

Interest rate

The annual nominal rate on the note, entered as a percentage such as 6.5. It is not the APR, which also reflects certain fees and points.

Down payment

The cash paid toward the price at purchase. It reduces the loan amount and determines loan-to-value. It is reported separately and is not included in total estimated cost.

Loan-to-value (LTV)

The loan amount divided by the home price, expressed as a percentage. An 80 percent LTV means a 20 percent down payment. The calculator uses LTV to decide whether to estimate PMI.

Private mortgage insurance (PMI)

Insurance that protects the lender when LTV is above 80 percent. The calculator estimates it as an annual percentage of the original loan amount divided by 12, ending when the scheduled balance reaches 78 percent of the original price.

Additional monthly payment

Extra principal paid every month on top of the scheduled P&I payment. It shortens the loan and reduces total interest without changing the scheduled payment.

Escrow

An account a lender may use to collect property tax and insurance with the monthly payment and pay those bills when due. The calculator's tax and insurance add-ons represent the escrow portion of a payment but do not model escrow cushions or annual adjustments.

Total interest

The sum of every month's interest charge over the life of the loan as scheduled.

Total estimated cost

Principal, total interest, total PMI, taxes, insurance and HOA dues added up over the months the loan is outstanding. Excludes the down payment and closing costs.

Payoff date

The month of the final payment, counting the first payment as one month after the loan's start date.

Interest saved

The difference in total interest between the loan with the additional monthly payment you entered and the same loan with none.

For a longer walk through these ideas in context, see the plain-language mortgage guide.

The calculator uses the standard fixed-payment amortization formula, applied month by month in integer cents. Nothing is estimated statistically; every output is the deterministic result of the inputs, and the same inputs always produce the same schedule. The full engine specification is published at /methodology.

Variables

• P: the loan amount, equal to the home price minus the down payment, held in cents.
• rate: the annual interest rate as entered, in percent (6.5 means 6.5 percent).
• r: the monthly rate, rate ÷ 1200. It is used only inside the payment formula and is never rounded or stored.
• n: the term in months (a 30-year loan has n = 360).
• M: the scheduled monthly principal and interest (P&I) payment.
• Bₖ: the balance at the start of month k, with B₁ = P.
• Iₖ, Cₖ: the interest charged and the principal retired in month k.
• E: the additional monthly principal payment, if any.
• LTV: loan-to-value, P ÷ home price × 100.

The scheduled payment

M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)

For P = $300,000, rate 6.5 percent and n = 360, the unrounded payment is $1,896.2041, so M = $1,896.20.

Monthly interest

I_k = round(B_k × rate ÷ 1200)

In month 1 of the example, I₁ = round(300,000 × 6.5 ÷ 1200) = $1,625.00.

Month-by-month steps

For each month k = 1, 2, … while the balance is above zero:

1. Compute interest Iₖ from Bₖ as above.
2. Compute principal Cₖ = M − Iₖ + E.
3. Apply the final-period rule: if k = n, or if Cₖ would exceed Bₖ, set Cₖ = Bₖ so the balance ends at exactly zero.
4. The P&I actually paid that month is Iₖ + Cₖ. This equals M + E in every month except the last.
5. Set Bₖ₊₁ = Bₖ − Cₖ.
6. Add PMI for the month if it applies (see below), plus the monthly tax, insurance and HOA amounts, to get the total housing payment for that month.

In the example, month 1 retires $271.20 of principal, leaving $299,728.80, and the loan ends after 360 payments with roughly $382,600 of total interest.

Add-ons and PMI

Monthly tax and insurance are the annual amounts divided by 12 and rounded to the nearest cent, computed once. HOA dues are entered monthly. PMI applies when LTV is strictly above 80 percent; the monthly charge is round(P × PMI rate ÷ 1200), with a default annual rate of 0.5 percent. It is charged in any month whose start-of-month balance is strictly above 78 percent of the home price, and it stops with the first payment after the scheduled balance crosses that line.

Rounding policy

Money is held as integer cents throughout. Rounding to cents happens at exactly these points and nowhere else: when dollars are converted to cents on input; when the monthly tax, insurance and PMI amounts are derived; when the scheduled payment M is computed; and when each month's interest is computed. Principal, balances and lifetime totals are plain integer arithmetic on those rounded values and are never rounded again. Rounding uses round-half-up for the non-negative amounts involved.

Because M is rounded once, the balance after n − 1 payments is rarely exactly one payment's worth of principal. The final-period rule absorbs that residue: the last payment is set to whatever clears the remaining balance, so it differs from M by a few cents rather than leaving a tiny balance behind. In the example the final payment is $1,900.91 against a regular payment of $1,896.20; on a $100,000 loan at 4.5 percent it is $502.86 against $506.69; and a zero-rate $1,000 loan over three months pays $333.33, $333.33 and $333.34.

Display rounding

Headline figures such as the estimated monthly payment and total interest are shown to the nearest whole dollar; schedule rows and breakdown items are shown to the cent; LTV to one decimal; durations as years and months derived from the integer month count. Display rounding is applied only at presentation and never fed back into the calculation, which is why displayed components may not sum exactly to a displayed total.

Extra payments and comparisons

When an additional monthly payment is entered, the same inputs are also run with E = 0. Interest saved is the baseline's total interest minus the plan's, and months saved is the difference in the number of payments. Scenario comparisons work the same way: the calculator runs twice with the changed input and reports the difference in each output. For $250 per month on the example loan, the plan finishes after 262 payments instead of 360 and saves about $120,300 of interest. For the reasoning behind the formula, see what amortization is.

The calculator models one thing well: a fixed-rate, fully amortizing loan with level monthly payments. It does not model:

• Adjustable-rate, interest-only, balloon or graduated-payment loans. The payment formula assumes the rate and payment never change.
• Closing costs, discount points, origination fees and prepaid items. Total estimated cost covers the months the loan is outstanding; it does not include the cash needed to close.
• Changes in taxes, insurance, HOA dues or PMI over time. All are held constant; escrow adjustments are not simulated.
• Prepayment penalties. Some loans charge a fee for paying off early. Extra-payment savings shown here assume there is none.
• Bi-weekly payments, lump-sum prepayments, skipped payments or recasting. Extra principal is a fixed monthly amount from the first payment onward.
• Tax effects, opportunity cost and inflation. Lifetime totals are simple sums of nominal dollars.
• Your credit profile. The rate and the PMI rate you enter are inputs; the calculator cannot tell you what a lender will offer.
• Home value changes. LTV is measured against the original price for the whole schedule, so appreciation-based PMI cancellation is not modeled.

Taxes, insurance, PMI, HOA dues and rates vary; results are estimates based on the assumptions entered.

Consult a professional when the decision depends on something the model leaves out. A lender's Loan Estimate is the document that states your actual rate, fees and payment, and it is the right basis for comparing offers. A tax professional can tell you whether mortgage interest or property tax affects your return. A licensed advisor can weigh a larger down payment or extra principal against other uses of the same money; this site does not give that advice. And if you are unsure how the pieces fit, the plain-language mortgage guide is a good place to start.