Explanation
How a fixed-rate mortgage payment works
You borrow the home price minus your down payment. A fixed-rate mortgage repays that loan with the same monthly principal and interest payment for the whole term, usually 30 or 15 years. Early payments are mostly interest because the balance is large; as the balance falls, more of each payment goes to principal. Many lenders also collect property tax and home insurance with the payment, and some homes have HOA dues, so the amount you actually pay each month is higher than principal and interest alone.
P = home price − down payment; M = P × i / (1 − (1 + i)^−N); i = R/1200; N = 12 × years; when R = 0, M = P/N
| P | loan amount: home price minus down payment (USD) |
|---|---|
| i | monthly rate as a decimal fraction; R is the annual interest rate in percent and i = R/1200 |
| N | number of monthly payments, 12 for each year of the term (months) |
| M | monthly principal and interest before rounding to the cent (USD) |
Your total monthly payment
Total monthly payment = M + property tax ÷ 12 + home insurance ÷ 12 + HOA dues. Property tax and insurance are usually quoted per year, so each is divided by 12 and rounded to the cent. HOA dues are already monthly. Leave any of them blank if they do not apply or you pay them separately.
Example: $320,000 at 6.5% for 30 years
| Home price | $400,000 |
|---|---|
| Down payment | $80,000 |
| Interest rate | 6.5 |
| Loan term | 30 |
| Property tax | $0 |
| Home insurance | $0 |
| HOA dues | $0 |
| Result | $2,022.62 |
Loan amount: $400,000 home price − $80,000 down payment = $320,000.
Borrowing $320,000 at 6.5% a year for 30 years means 360 monthly payments of $2,022.62 for principal and interest.
Rounding each month to the cent leaves a small difference, so the last payment is $2,020.06.
Adding up the schedule, you repay $728,140.64 in total, of which $408,140.64 is interest.
A $400,000 home with $80,000 (20%) down leaves a $320,000 loan. At 6.5% for 30 years, principal and interest come to $2,022.62 a month, and about $408,000 of the total repaid is interest.
Example: adding tax, insurance and HOA
| Home price | $400,000 |
|---|---|
| Down payment | $80,000 |
| Interest rate | 6.5 |
| Loan term | 30 |
| Property tax | $4,800 |
| Home insurance | $1,500 |
| HOA dues | $50 |
| Result | $2,597.62 |
Loan amount: $400,000 home price − $80,000 down payment = $320,000.
Borrowing $320,000 at 6.5% a year for 30 years means 360 monthly payments of $2,022.62 for principal and interest.
Rounding each month to the cent leaves a small difference, so the last payment is $2,020.06.
Adding up the schedule, you repay $728,140.64 in total, of which $408,140.64 is interest.
Monthly costs: $4,800 property tax ÷ 12 = $400, and $1,500 home insurance ÷ 12 = $125.
Total monthly payment: $2,022.62 + $400 + $125 + $50 HOA = $2,597.62.
Add $4,800 a year in property tax, $1,500 a year in home insurance and $50 a month in HOA dues to the same loan. Tax adds $400 and insurance $125 a month, so the total monthly payment is $2,597.62.
Example: the same loan over 15 years
| Home price | $400,000 |
|---|---|
| Down payment | $80,000 |
| Interest rate | 6.5 |
| Loan term | 15 |
| Property tax | $0 |
| Home insurance | $0 |
| HOA dues | $0 |
| Result | $2,787.54 |
Loan amount: $400,000 home price − $80,000 down payment = $320,000.
Borrowing $320,000 at 6.5% a year for 15 years means 180 monthly payments of $2,787.54 for principal and interest.
Rounding each month to the cent leaves a small difference, so the last payment is $2,788.55.
Adding up the schedule, you repay $501,758.21 in total, of which $181,758.21 is interest.
Shortening the term to 15 years raises the payment to $2,787.54 but cuts total interest from $408,140.64 to $181,758.21.
Example: $1,000 at 12% for one year
| Home price | $1,000 |
|---|---|
| Down payment | $0 |
| Interest rate | 12 |
| Loan term | 1 |
| Property tax | $0 |
| Home insurance | $0 |
| HOA dues | $0 |
| Result | $88.85 |
Loan amount: $1,000 home price − $0 down payment = $1,000.
Borrowing $1,000 at 12% a year for 1 years means 12 monthly payments of $88.85 for principal and interest.
Rounding each month to the cent leaves a small difference, so the last payment is $88.84.
Adding up the schedule, you repay $1,066.19 in total, of which $66.19 is interest.
A small loan shows the cent rounding clearly. Twelve monthly payments of $88.85 would overpay by a cent, so the final payment is $88.84 and the total repaid is $1,066.19.
Diagram of this result
A bar splits the total of loan payments into the loan amount and the interest, summed from the cent-settled schedule. When you enter tax, insurance or HOA, a second bar splits the monthly payment into those parts.
The loan amount, total interest and total of loan payments are listed as exact dollar amounts; the monthly breakdown lists each part of the payment; the yearly schedule lists interest, principal and the remaining balance, which ends at zero.
Read the actual schedule
The formula gives a high-precision regular payment, which is rounded to the cent. The schedule then rounds each month's interest to the cent, subtracts the principal part of the payment from the balance, and lets the final payment clear whatever is left. Total paid and total interest are sums of these schedule rows, not a second rounded formula.
Why the final payment can differ
The mathematical payment usually has fractions of a cent. Rounding it and every month's interest shifts the balance slightly, so the last payment is adjusted to pay the remaining balance and that month's interest exactly. The calculator rejects cent schedules that fail to reduce the loan or would pay it off before the final month.
Scope and limitations
The home price is positive USD in whole cents, the down payment is zero or more and less than the price, the annual rate is fixed from 0% through 100%, and the term is 1–100 whole years. The schedule assumes one payment each month, no extra payments and no rate changes. Property tax, insurance and HOA are the amounts you enter, held constant; real tax and insurance bills change over time. PMI, which lenders often require with less than 20% down, closing costs and fees are not included. The rate is not a regulated, fee-inclusive APR, and this estimate is not a lender quote. Educational estimates only, not financial, tax or investment advice.
Should I pick a 15-year or a 30-year term?
A 15-year loan has a higher monthly payment but far less total interest, because the balance is paid down twice as fast. A 30-year loan keeps the payment lower. Compare both here with the same rate, although 15-year loans are often offered at a lower rate.
How does the down payment change the payment?
Every dollar of down payment is a dollar you do not borrow, so the principal and interest payment falls in proportion to the loan amount. Putting less than 20% down often adds PMI, which this calculator does not include.
What happens when the rate is zero?
The payment is the loan amount divided by the number of months, rounded to the cent, and any leftover cents go into the final payment. A $12,000 loan over one year at 0% is twelve payments of $1,000.
Is the interest rate an APR?
No. It is the nominal annual interest rate, divided by 12 for each month. An APR also folds in lender fees, so it is usually a little higher than the rate used here.
Formula and reference
This calculator uses the level-payment annuity relation M = P × i / (1 − (1 + i)^−N), with loan amount P, monthly rate i = R/1200, and N months. At zero rate, the payment is P/N. Monthly interest is rounded half-up to cents, and the final payment clears the remaining balance. For how amortization splits payments between interest and principal, see the Consumer Financial Protection Bureau (CFPB): https://www.consumerfinance.gov/ask-cfpb/what-is-amortization-and-how-could-it-affect-my-auto-loan-en-771/ . That page explains payment allocation; it is not the source of the annuity equation above.