Mortgage calculator
- Runs in your browser
- No signup
- Formula shown below
- Reviewed
A mortgage calculator estimates a monthly payment from the loan principal, annual interest rate, and term using the amortization formula M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1], where r is the monthly rate and n is the total number of payments. A $320,000 loan at 6.5% over 30 years gives a principal-and-interest payment of $2,022.62 per month.
Result
Total monthly payment
$2,572.62
M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1]
- Principal and interest
- $2,022.62
- Tax and insurance
- $550.00
- Loan amount
- $320,000
- Loan-to-value
- 80.0%
- Total interest paid
- $408,142
- Total of all payments
- $728,142
A $320,000 mortgage at 6.50% over 30 years has a principal-and-interest payment of $2,022.62 per month, or $2,572.62 per month including property tax and insurance. Total interest over the full term is $408,142.
How to use the mortgage calculator
- 01
Enter the home price
Type the purchase price of the property. Use the agreed sale price, not the listing price or the appraised value.
- 02
Enter the down payment
Type the cash amount being put down. A 20% down payment usually removes the requirement for private mortgage insurance in the United States.
- 03
Enter the rate and term
Type the annual interest rate quoted by the lender and the term in years. Thirty and fifteen years are the two most common fixed terms.
- 04
Add tax and insurance
Enter annual property tax and home insurance so the result reflects the full escrowed payment rather than principal and interest alone.
- 05
Read the breakdown
The result strip shows the total monthly payment, and the rows beneath separate principal and interest from escrow, and show total interest across the term.
The formula
M = P × [r(1 + r)ⁿ] ÷ [(1 + r)ⁿ − 1]
- M
- The level monthly payment covering principal and interest.
- P
- The loan principal — the home price minus the down payment.
- r
- The periodic interest rate: the annual nominal rate divided by 100, then divided by 12.
- n
- The total number of monthly payments, equal to the term in years multiplied by 12.
The formula assumes a fixed rate and a level payment. Property tax, home insurance and HOA dues are added separately because they are escrow items, not interest-bearing debt. At a 0% rate the formula divides by zero; the correct payment in that case is simply P ÷ n.
Worked example
- Home price
- $400,000
- Down payment
- $80,000 (20%)
- Interest rate
- 6.5%
- Term
- 30 years
- Property tax
- $4,800 per year
- Home insurance
- $1,800 per year
- Result
- $2,022.62 principal and interest, $2,572.62 total monthly
The loan principal is $400,000 − $80,000 = $320,000. The monthly rate r is 6.5 ÷ 100 ÷ 12 = 0.00541667, and n is 30 × 12 = 360 payments. Substituting: (1 + r)ⁿ = 6.99179, so M = 320,000 × (0.00541667 × 6.99179) ÷ (6.99179 − 1) = $2,022.62. Escrow adds $4,800 ÷ 12 = $400 of tax and $1,800 ÷ 12 = $150 of insurance, giving $2,572.62 per month. Over the full term, total interest reaches $408,142.
Frequently asked questions
What is the formula for a monthly mortgage payment?
The standard amortization formula is M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1]. P is the loan principal, r is the monthly interest rate found by dividing the annual rate by 12, and n is the total number of monthly payments. The formula produces a level payment in which the interest share falls and the principal share rises over the life of the loan.
What does PITI mean in a mortgage payment?
PITI stands for principal, interest, taxes and insurance — the four components of a fully escrowed monthly housing payment. Principal and interest repay the loan itself. Taxes and insurance are collected by the servicer and paid on the borrower's behalf. Lenders assess affordability against PITI, not against principal and interest alone.
How much does a 1% higher interest rate cost on a mortgage?
On a $320,000 loan over 30 years, moving from 6.5% to 7.5% raises the monthly payment from $2,022.62 to $2,237.49, an increase of $214.87 per month. Across the full 360 payments that difference totals $77,353 in additional interest. Rate sensitivity rises with both the principal and the term.
Does making one extra mortgage payment a year make a difference?
Substantially. On a $320,000 loan at 6.5% over 30 years, adding $170 a month — roughly one extra payment a year — clears the loan in 290 months instead of 360. That is five years and ten months early, and it saves $93,667 in interest. Extra payments apply entirely to principal, which reduces every interest charge that follows.
What is private mortgage insurance and when does it apply?
Private mortgage insurance protects the lender when the down payment is below 20% of the home value. It typically costs between 0.3% and 1.5% of the original loan amount each year. Under the US Homeowners Protection Act, a borrower may request cancellation at 80% loan-to-value, and the servicer must terminate it automatically at 78%.
Is a 15-year or a 30-year mortgage cheaper?
A 15-year mortgage costs far less in total interest but requires a much higher monthly payment. A $320,000 loan at 6.5% costs $2,022.62 a month over 30 years and $2,787.54 a month over 15 years, but total interest falls from $408,142 to $181,758. Fifteen-year loans also usually carry a lower quoted rate.
Why does so little of an early mortgage payment reduce the balance?
Interest is charged on the outstanding balance, which is at its largest at the start. On a $320,000 loan at 6.5%, the first payment of $2,022.62 includes $1,733.33 of interest and only $289.29 of principal. The principal share grows every month, and first exceeds half the payment at month 233 of the 360-payment term.
Sources
- Understanding loan estimates and mortgage costs — US Consumer Financial Protection Bureau
- Homeowners Protection Act — PMI cancellation rules — US Federal Reserve
- Primary Mortgage Market Survey — historical rates — Freddie Mac
Last reviewed: · Formula and sources verified by Syed Aqeel Ahmad Gillani. See the methodology for how every calculation is derived.