What is a mortgage payment?
A mortgage payment is the regular installment paid to a lender to repay a home loan. The standard monthly payment is divided into principal (reduction of the loan balance) and interest (the cost of borrowing). In the early years of a 30-year mortgage, the vast majority of each payment is interest; as the loan ages, the principal component grows through a process called amortization.
Most homeowners think of the monthly payment as P&I (principal and interest), but the full out-of-pocket housing cost — sometimes called PITI — also includes property taxes, homeowners insurance, and, if the down payment was less than 20%, private mortgage insurance (PMI). Lenders use PITI to calculate your debt-to-income ratio when underwriting the loan.
The mortgage payment formula
The monthly P&I payment on a fixed-rate mortgage is calculated as:
M = P × [r(1 + r)^n] / [(1 + r)^n − 1]
Where:
P = Principal loan amount
r = Monthly interest rate (annual rate / 12)
n = Total number of payments (years × 12)P — the loan amount after your down payment. r — the monthly rate: divide your annual rate by 12 (a 6.75% rate = 0.5625% per month). n — total payments: a 30-year mortgage = 360 monthly payments. The formula is a present value of annuity equation — it finds the level payment that exactly amortizes the loan to zero over n periods.
Worked example
Home purchase price: $485,000. Down payment: $97,000 (20%). Loan: $388,000 at 6.875% for 30 years.
- Step 1: Monthly rate r = 6.875% / 12 = 0.5729%.
- Step 2: n = 30 × 12 = 360 payments.
- Step 3: M = $388,000 × [0.005729 × (1.005729)^360] / [(1.005729)^360 − 1]
- Step 4: (1.005729)^360 = 7.674. M = $388,000 × [0.005729 × 7.674] / [7.674 − 1] = $388,000 × 0.04397 / 6.674 = $2,556/month P&I.
Over 30 years, total payments = $2,556 × 360 = $920,160. Total interest = $920,160 − $388,000 = $532,160 — more than the original loan amount. Choosing a 15-year term at the same rate produces a payment of ~$3,450/month but total interest of only ~$233,000, saving roughly $299,000 in interest at the cost of $894/month more in the payment.
When to use the mortgage calculator
Use this calculator during home shopping, refinancing evaluation, or payoff planning.
- Determining affordability during home search: Work backward from a maximum comfortable monthly payment to find the loan amount you can support at current rates, then add your down payment to set your purchase price ceiling.
- Comparing 15-year vs. 30-year mortgages: A 15-year loan typically carries a 0.5–0.75% lower interest rate and dramatically less total interest, but the higher payment may constrain cash flow. This calculator makes the trade-off concrete.
- Evaluating a refinance: Input the new loan terms and compare the monthly savings against your closing costs. A common rule of thumb is that a refinance makes sense if it takes fewer than 24–30 months to recoup closing costs through lower monthly payments.
- Modeling extra principal payments: An extra $300/month on a $388,000, 30-year mortgage at 6.875% reduces the total loan term by roughly 7 years and saves over $150,000 in interest. Enter the extra payment to see the exact impact.
Common mistakes
Mortgage math surprises are expensive. These are the most common calculation errors.
- Forgetting PMI: If your down payment is less than 20% of the purchase price (less than 80% LTV), lenders typically require Private Mortgage Insurance. PMI typically costs 0.5–1.5% of the loan amount per year, added to your monthly payment. On a $388,000 loan at 1% PMI, that's $324/month — a significant cost that disappears once your LTV reaches 80%.
- Focusing only on the monthly payment, not the rate: A lower monthly payment achieved by extending the term from 20 to 30 years often costs far more in total interest than the payment reduction is worth. Always compare total interest paid, not just the payment.
- Not accounting for property taxes and insurance in affordability: A lender will qualify you based on PITI. Property taxes vary dramatically by location — 1–1.5% annually in many states, above 2% in New Jersey, New York, and Illinois. Budget for the full PITI when assessing affordability, not just P&I.
- Assuming the interest rate equals the APR: APR (Annual Percentage Rate) includes fees and costs spread over the loan term. A 6.875% rate with $8,000 in points and origination fees might carry an APR of 7.1%. APR is the better benchmark when comparing loan offers with different fee structures.
Limitations of mortgage calculations
Fixed-rate mortgage math is deterministic once you know the rate, term, and amount. Adjustable-rate mortgages (ARMs) are more complex: the initial rate applies for a fixed period (3, 5, or 7 years), then adjusts annually based on an index (typically SOFR) plus a margin, subject to annual and lifetime caps. This calculator models fixed-rate scenarios; for ARMs, model each rate scenario separately.
Tax deductibility of mortgage interest adds another layer. The mortgage interest deduction (MID) is available for interest paid on the first $750,000 of mortgage debt on a primary or secondary home (for mortgages originated after December 15, 2017). However, the 2017 Tax Cuts and Jobs Act roughly doubled the standard deduction, meaning most homeowners no longer itemize — making the MID effectively irrelevant for the majority of borrowers unless mortgage interest, state taxes, and charitable contributions together exceed the standard deduction.
Frequently asked questions
What is the difference between a 15-year and 30-year mortgage?
A 15-year mortgage has a higher monthly payment but a lower interest rate and far less total interest paid. On a $400,000 loan, the monthly payment difference is roughly $900/month, but total interest on the 15-year loan is typically $150,000–$200,000 less than the 30-year. The 30-year's lower payment provides cash flow flexibility, which is valuable if you invest the difference at returns exceeding the mortgage rate.
What is PMI and when can I eliminate it?
Private Mortgage Insurance (PMI) is required by most lenders when your down payment is less than 20% of the home's purchase price (i.e., LTV above 80%). It protects the lender, not you. Under the Homeowners Protection Act, you have the right to request PMI cancellation when your equity reaches 20% of the original value, and lenders must cancel it automatically at 22% equity based on the original amortization schedule.
Should I pay points to lower my mortgage rate?
One discount point costs 1% of the loan amount and typically reduces the rate by 0.25%. On a $388,000 loan, one point costs $3,880 and saves roughly $89/month. The breakeven is approximately 44 months (~3.7 years). If you plan to stay in the home longer than the breakeven period and won't refinance, buying points makes mathematical sense.
How does an ARM work?
An Adjustable Rate Mortgage has a fixed initial rate for a set period (commonly 5 or 7 years), then adjusts annually based on an index rate plus a fixed margin. Rate changes are limited by annual and lifetime caps (e.g., 2% per adjustment, 6% over the life of the loan). ARMs carry lower initial rates than fixed loans — typically 0.5–1.0% lower for a 5/1 ARM — but expose you to rate increases after the fixed period.
Related calculators
Mortgage calculations connect to broader financial planning:
- Compound Interest Calculator — model whether investing the difference between a 15-year and 30-year payment might outperform the interest saved by choosing the shorter term.