What Is a Mortgage?
A mortgage is a loan secured by real property. The lender puts up the difference between the purchase price and your down payment; you repay that amount with interest in level monthly installments over an agreed term, and the lender keeps a legal claim on the house until the balance is gone. Everything this calculator does follows from that one arrangement.
The loan, in plain terms
Three numbers define a fixed-rate mortgage: how much you borrow, the annual interest rate, and how long you have to repay it. The lender converts those into a single payment that never changes and that lands exactly on zero at the end of the term. That last property is the whole trick. The payment is reverse-engineered from the requirement that nothing be left owing on the final month, which is why it is never a round number.
The security is what separates a mortgage from a personal loan. Because the house backs the debt, the rate is far below what unsecured credit costs; because the house backs the debt, sustained non-payment eventually means losing it. This calculator models the ordinary case — one fixed rate held for the entire term, one payment a month, no penalty for paying early. Adjustable-rate loans, interest-only periods and balloon structures behave differently, and they are covered under Limits.
PITI: what the monthly payment is made of
Lenders use the shorthand PITI — principal, interest, taxes, insurance. The first two repay the loan. The second two are not loan costs at all; they are costs of owning the building, collected alongside the loan payment because most lenders escrow them. The Consumer Financial Protection Bureau describes an escrow account as one the lender sets up to pay property-related expenses, funded from part of each monthly mortgage payment so the annual bills get paid on time.
Here is a real result taken apart — a $420,000 home with 20% down at 6.5% over 30 years, carrying $4,620 of annual property tax and an $1,800 annual insurance premium:
| Component | Per month | Share of payment | Where the figure comes from |
|---|---|---|---|
| Principal & interest | $2,123.75 | 79.9% | A $336,000 loan at 6.5% over 360 months |
| Property tax | $385.00 | 14.5% | $4,620 a year divided by 12 |
| Home insurance | $150.00 | 5.6% | $1,800 a year divided by 12 |
| HOA fees | $0.00 | 0% | Entered as a monthly figure; this house has none |
| Total monthly cost | $2,658.75 | 100% | The number at the top of the result |
A listing advertising $2,124 a month is quoting the first row. The last row is what leaves your account. On a condo the gap is wider: a $300,000 unit with $60,000 down at 6.5% carries $1,516.96 of principal and interest inside a $2,191.96 payment, because a $350 HOA fee and $325 of monthly tax and insurance sit on top of the loan.
Principal, rate, term, and LTV
Four terms carry most of the meaning, and three of them are inputs on this page.
- Principal — what you actually borrow, which is the home price minus the down payment, not the price. A $420,000 house with 20% down is a $336,000 loan.
- Interest rate — the annual nominal rate. The calculator divides it by twelve to get the monthly rate, so 6.5% becomes 0.00541667 per month. This is not the APR, which folds fees into a comparison rate and reads slightly higher on a Loan Estimate.
- Term — the repayment window in years, converted to months. Thirty years is 360 payments; fifteen years is 180.
- Loan-to-value, or LTV — the loan as a share of the price. Twenty percent down is 80% LTV. It is not an input here, but it decides two things the payment cannot show you.
Those two things are private mortgage insurance and the rate itself. The CFPB notes that PMI is generally required on conventional loans when the down payment is under 20 percent, and that it protects the lender rather than the borrower. Lenders also price risk into the rate, so the same borrower is often quoted more at 95% LTV than at 80% — a second cost of a small down payment that no payment formula can predict for you.
How Do You Calculate a Mortgage Payment?
One equation produces the payment. It is the standard amortizing-loan formula, and it is the same arithmetic your lender runs, so a correctly entered calculation matches the principal-and-interest line on a Loan Estimate to the cent.
The mortgage formula, written out
The monthly payment of principal and interest is:
M = P × [ r(1 + r)ⁿ ] ÷ [ (1 + r)ⁿ − 1 ]
- M — the monthly payment of principal and interest
- P — the principal: home price minus down payment
- r — the monthly interest rate: annual rate ÷ 100 ÷ 12
- n — the number of payments: term in years × 12
The bracketed fraction does the work. (1 + r)ⁿ is what one dollar becomes over the full term at the monthly rate, and the ratio converts the lump sum P into the one level payment that extinguishes it in exactly n months. Nothing about it is specific to housing — the same equation prices a car loan or a student loan.
One case the equation cannot express is a 0% loan, such as a loan from family, because the denominator collapses to zero. The calculator detects that and falls back to the only sensible answer, the principal spread evenly: a $300,000 loan at 0% over 30 years returns $833.33 a month and $0.00 of total interest.
Step by step
Worked on a $420,000 home with 20% down at 6.5% for 30 years:
- Convert the down payment. The selector is on Percentage, so 20 means 20% of $420,000, which is $84,000. Switch it to Fixed Amount and the same 20 means twenty dollars.
- Subtract it from the price. P = $420,000 − $84,000 = $336,000.
- Find the monthly rate. r = 6.5 ÷ 100 ÷ 12 = 0.00541667.
- Count the payments. n = 30 × 12 = 360.
- Raise the growth factor. (1.00541667)³⁶⁰ = 6.99180.
- Apply the formula. M = 336,000 × (0.00541667 × 6.99180) ÷ (6.99180 − 1) = $2,123.75.
- Add the carrying costs. A 1.1% tax rate on $420,000 is $4,620 a year, so $385.00 a month; $1,800 of insurance ÷ 12 = $150.00; no HOA fee. Total $2,658.75.
Step five is the one people skip when checking a payment by hand, and it is where the arithmetic actually lives. Everything before it is bookkeeping.
Worked example: a $420,000 home with 20% down
Entered exactly as above, the calculator returns this.
- $420,000 home · 20% down · 6.5% · 30 years · $4,620 tax · $1,800 insurance
- $2,658.75 per month
Under that headline the result itemizes what produced it: principal and interest of $2,123.75, property tax of $385.00, home insurance of $150.00, a loan amount of $336,000.00, a down payment of $84,000.00 (20%), and total interest over 30 years of $428,549.48.
Read the last two lines together. You hand over $84,000 at closing and $428,549.48 in interest across the following three decades — $1.28 of interest for every dollar borrowed. The 360 principal-and-interest payments come to $764,549.48 on a loan of $336,000.
How the tax, insurance, and HOA fields behave
Three fields sit below the loan inputs, and each is read the way its label describes. Property tax is a rate: enter the annual percentage your county charges — 1.1 for 1.1% — and the calculator applies it to the home price, then divides by twelve. Home insurance is an annual dollar amount, divided by twelve the same way. The HOA field is already monthly and is added as entered.
The breakdown reports the tax line both ways, the monthly figure and the yearly total it came from, so you can hold it against your real tax bill. On a $420,000 home at 1.1% that reads $385.00 a month out of $4,620.00 a year. If the yearly figure does not resemble your bill, the rate is the thing to check.
Leave all three at zero and the result is principal and interest alone — the figure a listing quotes and the figure a preapproval letter is built around. Fill them in and you get the figure your bank account sees. Where the servicer escrows taxes and insurance, that second number is close to the literal amount debited each month.
Where the money goes: amortization
Every payment is the same size, but what it buys changes every month. Interest is charged on the balance still outstanding, so it is largest at the start and shrinks as the balance falls; whatever the fixed payment does not spend on interest repays principal. The CFPB describes the same mechanic — early in the term you owe more interest because the balance is high, and as principal comes down, more of each payment goes to principal.
On the $336,000 loan at 6.5%, the first payment charges $336,000 × 0.00541667 = $1,820.00 in interest and repays $303.75 of principal. That is 14.3% of the payment doing what most people assume the whole payment does. Twelve payments in, you have retired $3,755.56 of the loan and paid $21,729.43 in interest, leaving a balance of $332,244.44.
The crossover is later than intuition suggests. Principal does not exceed interest within a single payment until month 233 — year 19.4 of a 30-year loan — when $1,063.66 of principal finally beats $1,060.08 of interest. That asymmetry is why the term you choose matters more than almost any other decision on the form, and why the equity you hold in year seven comes mostly from your down payment rather than from your payments.
The same amortization math prices any fixed installment debt, so a car or personal loan runs through our Loan Calculator.
Mortgage Payment Chart
Three reference tables, all produced by this calculator rather than copied from anywhere.
Monthly principal and interest per $100,000 borrowed
Scale a row to your own loan: a $336,000 loan is 3.36 times the figures shown. Principal and interest only — tax, insurance and HOA come on top.
| Interest rate | 15-year | 20-year | 30-year | Total interest, 30-year |
|---|---|---|---|---|
| 5.0% | $790.79 | $659.96 | $536.82 | $93,255.78 |
| 5.5% | $817.08 | $687.89 | $567.79 | $104,404.04 |
| 6.0% | $843.86 | $716.43 | $599.55 | $115,838.19 |
| 6.5% | $871.11 | $745.57 | $632.07 | $127,544.49 |
| 7.0% | $898.83 | $775.30 | $665.30 | $139,508.90 |
| 7.5% | $927.01 | $805.59 | $699.21 | $151,717.22 |
| 8.0% | $955.65 | $836.44 | $733.76 | $164,155.25 |
Check the scaling against the worked example: 3.36 × $632.07 = $2,123.76, one cent above the calculator's $2,123.75, because the table row is rounded before it is multiplied. That is the accuracy any per-$100,000 chart can offer, including this one.
What half a point of rate costs
Each extra half point adds roughly $31 to $35 a month per $100,000 on a 30-year loan, and the step widens as rates climb: $30.97 moving from 5.0% to 5.5%, $32.52 from 6.0% to 6.5%, $34.55 from 7.5% to 8.0%.
On the $336,000 example that compounds into real money. Dropping from 6.5% to 6.0% takes the payment from $2,123.75 to $2,014.49 — $109.26 a month — and cuts total interest by $39,333.16. Going the other way, to 7.0%, costs $111.67 a month and $40,200.42 over the term. Half a point is worth more than most buyers assume, and more than most of them negotiate for.
Where a 30-year loan stands at each five-year mark
The same $336,000 loan at 6.5%, tracked in five-year steps. The calculator reports the payment and the lifetime interest; the columns below apply that payment month by month.
| After | Balance remaining | Principal repaid | Interest paid to date | Share of loan repaid |
|---|---|---|---|---|
| 5 years | $314,532.88 | $21,467.12 | $105,957.80 | 6.4% |
| 10 years | $284,847.78 | $51,152.22 | $203,697.61 | 15.2% |
| 15 years | $243,798.71 | $92,201.29 | $290,073.46 | 27.4% |
| 20 years | $187,035.35 | $148,964.65 | $360,735.00 | 44.3% |
| 25 years | $108,541.98 | $227,458.02 | $409,666.55 | 67.7% |
| 30 years | $0.00 | $336,000.00 | $428,549.48 | 100% |
Halfway through in calendar time you have repaid 27.4% of what you borrowed and paid $290,073.46 in interest — 67.7% of all the interest the loan will ever charge. The last five years reverse it completely: $108,541.98 of balance disappears while only $18,882.93 of interest accrues.
How to Read Your Result
The result opens with one number and then takes it apart. Each line answers a different question, and the one at the bottom is usually the one worth arguing about.
The top line is not the line lenders advertise
The figure at the top is everything you entered, added together. Directly beneath it, principal and interest is broken out on its own — that is the loan payment, and it is the number quoted in listings, rate tables and preapproval letters. On the worked example the difference is $535.00 a month, or 20.1% of the payment. On the condo, where a $350 HOA fee lands on top of $325 of monthly tax and insurance, non-loan costs are 30.8% of the $2,191.96 total and the HOA fee alone is 16.0%.
If you are weighing a house against a condo, or one county against another, compare the top line. Two homes with identical loan payments can differ by several hundred dollars a month once tax bills and association fees are counted.
Total interest is the number that changes minds
The last line of the result is the lifetime interest, and it reframes decisions the payment cannot. At 6.5% over 30 years, $336,000 borrowed costs $428,549.48 in interest, which is $1.28 of interest for every dollar lent. The same loan at 5.0% costs $313,339.44; at 8.0% it costs $551,561.63. A three-point spread swings the lifetime cost by $238,222.19 without changing a single thing about the house.
The figure assumes you hold the loan for its full term, which many borrowers do not. Sell or refinance in year seven and you pay only the interest accrued to that point, which the milestone table above puts at well under a third of the total. Treat the lifetime number as the price of the loan as written, not as a forecast of your life.
Checking the payment against your income
Lenders have traditionally capped housing costs near 28% of gross monthly income. Applied to the worked example, $2,658.75 ÷ 0.28 implies $9,495.54 a month before tax — about $113,946 a year — for this payment alone to sit inside the guideline. That is a convention, not a rule of law: the CFPB says only that different loan products and lenders set different debt-to-income limits, and underwriting also weighs your other debts, your credit profile and your reserves.
To run the question from the other end — what purchase price your income supports under the 28/36 rule — use our Home Affordability Calculator.
When the result asks you to check something
Four conditions return an instruction instead of a number:
- Enter the home price — the price is blank, zero or negative.
- Enter the interest rate — the rate is missing or negative. Zero is legitimate and is handled separately.
- Enter the loan term in years — the term is blank, zero or negative.
- The down payment covers the whole price — a 100% down payment, or a cash figure at or above the price, leaves nothing to finance.
One mistake is harder to catch because it returns a plausible number. If the selector reads Fixed Amount and you type 20 meaning twenty percent, the calculator honors the field exactly: a $20 down payment on a $420,000 house, a loan of $419,980.00 and a payment of $2,654.56. Next to the correct $2,123.75 it looks like an ordinary result. The defense is the breakdown — the down payment line prints the dollar figure it used, and appends the percentage only when you chose Percentage.
How to Lower the Payment
Three levers move the number, and they do not cost the same. Every row below is the worked example with exactly one input changed, run through this calculator.
| Change | Monthly P&I | Vs. $2,123.75 | Total interest | Vs. $428,549.48 |
|---|---|---|---|---|
| Baseline: $336,000 loan, 6.5%, 30 years | $2,123.75 | — | $428,549.48 | — |
| Rate half a point lower (6.0%) | $2,014.49 | −$109.26 | $389,216.32 | −$39,333.16 |
| Rate half a point higher (7.0%) | $2,235.42 | +$111.67 | $468,749.90 | +$40,200.42 |
| 15-year term instead of 30 | $2,926.92 | +$803.17 | $190,845.73 | −$237,703.75 |
| 10% down instead of 20% ($378,000 loan) | $2,389.22 | +$265.47 | $482,118.17 | +$53,568.69 |
| 5% down instead of 20% ($399,000 loan) | $2,521.95 | +$398.20 | $508,902.51 | +$80,353.03 |
The rows deliberately point in different directions. Shortening the term is the only change that raises the monthly payment while cutting the total cost: $803.17 more a month buys back $237,703.75 of interest. Notice too that the 15-year payment is 1.38 times the 30-year payment rather than double, because so much less interest accrues on a balance that falls twice as fast.
A larger down payment cuts the payment and the interest together, and at 20% it also clears private mortgage insurance. The CFPB's rule here is worth knowing precisely: you may ask the servicer to cancel PMI on the date the balance is scheduled to fall to 80% of the home's original value, and the servicer must terminate it automatically at 78%. Below 20% down, that premium is paid on top of every figure in the table.
The rate is the largest lever and the one you control least, which is the practical argument for collecting more than one Loan Estimate. On this loan, half a point separates $2,123.75 from $2,014.49 — a difference no amount of budgeting produces on its own.
If rates have moved since you closed, test whether a new loan earns back its own closing costs with our Refinance Calculator.
Limits: Where This Calculator Stops
This is a payment model, not a loan quote. Seven things it does not do:
- No private mortgage insurance. There is no PMI field. The 5%-down row above shows $2,521.95, and the real payment is that plus a premium the calculator never adds — on a conventional loan below 20% down, that premium is normally unavoidable.
- No closing costs, points or fees. Origination charges, discount points, title work and prepaid items are settled at closing and never surface in a monthly figure. Lenders are compared on the Loan Estimate, where those live, not on the payment alone.
- Fixed rate only. The math assumes one rate for the whole term. An adjustable-rate loan follows this only until its first reset, after which the payment is recomputed on the new rate and the remaining balance.
- Taxes and insurance are frozen. Whatever you type is spread evenly across every year of the term. Assessments get revised and premiums get repriced, so a 30-year projection built from today's figures understates the later years.
- No extra payments, biweekly schedules or recasts. Every projection assumes exactly one scheduled payment a month for the full term, so the interest totals are an upper bound for anyone who pays ahead.
- Total interest is pre-tax. The $428,549.48 is a gross figure. Interest on up to $750,000 of home acquisition debt ($375,000 if married filing separately, for debt secured after December 15, 2017) may be deductible, but only if you itemize on Schedule A — see IRS Publication 936. The calculator assumes nothing about your tax return.
- It is not a rate quote. No market rate is supplied here; the rate is yours to enter, and the result is only as current as that number.
Rounding is the last small caveat. Payments are reported to the cent, and applying the reported payment for all 360 months lands within a cent of zero — which is also why a lender's schedule usually adjusts the final payment by a few cents.