How mortgage payments are calculated
A fixed-rate mortgage is an amortizing loan: every monthly payment is the same dollar amount, but the split between interest and principal changes over time. Early payments are mostly interest; late payments are almost entirely principal. The exact monthly payment can be derived from the standard amortization formula:
M = P × r(1 + r)ⁿ / ((1 + r)ⁿ − 1)where M is the monthly payment, P is the loan principal (the amount borrowed after the down payment), r is the monthly interest rate (annual rate divided by 12), and n is the total number of monthly payments (years × 12).
A worked example
Suppose you borrow $300,000 at a fixed annual rate of 6.5% for 30 years. The monthly rate is 0.065 / 12 ≈ 0.005417 and the term is 360 months.
M = 300000 × 0.005417 × (1.005417)³⁶⁰ / ((1.005417)³⁶⁰ − 1) ≈ $1,896.20Over the full 30 years you will pay roughly $682,633 — meaning the interest alone is $382,633, more than the original loan. The first payment is about $1,625 interest and $271 principal; the last payment is about $10 interest and $1,886 principal.
What changes the payment
| Factor | What happens if it increases | Why it matters |
|---|---|---|
| Loan amount | Payment rises proportionally | Borrowing more directly raises the monthly cost |
| Interest rate | Payment rises more than proportionally | A 1-point rate increase on a $300k 30-year loan adds roughly $190 / month |
| Loan term | Payment falls, total interest rises | A 15-year loan costs ~50% more per month but saves more than half the interest |
| Down payment | Payment falls, may remove PMI | A 20% down payment typically eliminates private mortgage insurance |
| Property tax & insurance | Escrow payment rises | Lenders bundle these into the monthly escrow; they are not in the loan formula |
15-year vs 30-year mortgages
The same $300,000 loan at 6.5%:
- 30-year: $1,896 / month, $382,633 total interest.
- 15-year: $2,613 / month, $170,440 total interest.
The 15-year loan saves $212,000 in interest at the cost of an extra $717 per month. Lenders also typically offer 15-year loans at a 0.5 to 0.75 percentage point lower rate, which widens the gap further. The trade-off is the lower payment of the 30-year giving more cash-flow flexibility — important if the borrower expects irregular income or wants to invest the difference.
Total cost of ownership beyond the loan formula
The monthly payment your lender quotes (often called PITI) typically bundles four items:
- Principal: the portion that reduces the loan balance.
- Interest: the lender's compensation for lending.
- Taxes: annual property tax divided by 12, held in escrow.
- Insurance: homeowner's insurance and, if down payment is below 20%, private mortgage insurance (PMI).
On top of PITI, expect homeowners' association (HOA) dues, maintenance (a common rule of thumb is 1% of home value per year), and utilities. A $300,000 home in many U.S. markets carries an all-in monthly cost 30 to 50% above the headline mortgage payment.
How much house can you afford?
Two common benchmarks lenders use:
- The 28/36 rule: housing costs should not exceed 28% of gross monthly income, and total debt payments should not exceed 36%.
- The 25% net rule: some financial planners argue housing should not exceed 25% of take-home pay on a 15-year mortgage — stricter, but reflects taxes and other realities.
A household earning $8,000 gross per month should keep housing costs under roughly $2,240 by the 28% rule. Using our example loan ($1,896 PI plus $400 taxes/insurance ≈ $2,300), this is right at the limit.