What this mortgage calculator shows
It estimates the fixed monthly principal and interest (P&I) payment on a fully amortizing, fixed-rate home loan, the total interest over the life of the loan, and a schedule of how each payment splits between interest and principal. Property tax, insurance and HOA dues are kept separate from P&I because they are not part of the loan and change over time.
Formula
M = P × r ÷ (1 − (1 + r)^−n)
- M = monthly principal and interest payment
- P = amount borrowed
- r = monthly rate = annual rate ÷ 100 ÷ 12
- n = number of monthly payments = years × 12
Each month, interest = remaining balance × r; the rest of the payment reduces the balance. Extra principal is subtracted from the balance immediately, which lowers every later interest charge. When the annual rate is 0%, the payment is simply P ÷ n.
Worked examples
$300,000 at 6.5% for 30 years
- r = 0.065 ÷ 12 ≈ 0.00541667; n = 360.
- (1 + r)^−360 ≈ 0.14302, so M = 300,000 × 0.00541667 ÷ (1 − 0.14302) ≈ $1,896.20.
- Total paid ≈ 1,896.20 × 360 ≈ $682,633; total interest ≈ $382,633.
- First month: interest = 300,000 × 0.00541667 = $1,625.00; principal = $271.20.
Same loan with $200 extra each month
The balance reaches zero after 277 payments (23 years 1 month). Total interest falls to about $279,185, saving roughly $103,449 compared with the standard schedule.
$200,000 at 5% for 15 years
r = 0.05 ÷ 12, n = 180. M ≈ $1,581.59 per month; total interest ≈ $84,686.
Interpreting the results
- Your lender's figure may differ by a few cents because of rounding conventions, or by more if the loan has points, mortgage insurance or an adjustable rate.
- The interest rate is not the APR. APR includes certain fees and is useful for comparing offers, but payments are calculated from the note rate.
- Before making extra payments, confirm your lender applies them to principal and that the loan has no prepayment penalty.
Common mistakes
- Entering the home price instead of the loan amount after the down payment.
- Comparing a P&I-only figure with a quote that includes escrow for taxes and insurance.
- Assuming property tax and insurance stay fixed for the whole term.
Assumptions and limitations
Fixed rate, monthly payments, interest compounded monthly at the annual rate ÷ 12, and no fees, PMI or rate changes. Results are estimates for planning, not a loan offer or financial advice. The Consumer Financial Protection Bureau's Owning a Home guide explains loan estimates and closing costs.
Related: loan payment calculator for other payment frequencies, and compound interest calculator.
Frequently asked questions
Does the monthly payment include taxes and insurance?
The principal and interest figure does not. If you enter property tax, homeowners insurance or HOA dues, they are added separately to show an estimated total monthly housing payment. Actual escrow amounts are set by your lender and can change each year.
How much do extra principal payments save?
On a $300,000 loan at 6.5% for 30 years, paying an extra $200 every month pays the loan off in 277 payments instead of 360 and reduces total interest by roughly $103,000, assuming the lender applies the extra amount to principal.
Why is most of the early payment interest?
Interest each month is the remaining balance times the monthly rate. The balance is highest at the start, so interest takes the largest share; as the balance falls, more of each fixed payment goes to principal.