What is a mortgage?
A mortgage is a long-term loan used to buy a home. You borrow a principal amount and repay it over time with interest. Fixed-rate mortgages keep the same interest rate and payment schedule; adjustable-rate (ARM) mortgages can change after an initial period.
Key terms at a glance
- Principal: The amount you borrow (home price minus down payment).
- Interest rate: The stated cost of borrowing (e.g., 6.50%).
- APR: Interest rate plus certain fees/points, expressed annually—useful for apples-to-apples comparison.
- Term: Length of the loan (e.g., 30 years → 360 monthly payments).
- PMI: Private Mortgage Insurance, usually required with < 20% down.
- Points: Upfront fees you can pay to lower your interest rate.
- Escrow: A monthly set-aside for property taxes and insurance (not part of the math below, but part of your total payment to the servicer).
How the payment is calculated (fixed-rate)
Most mortgages use an amortizing payment:
Formula
M = P × r / (1 − (1 + r)^(-n))
Where:
P= principal (amount financed)r= monthly interest rate (annual rate ÷ 12)n= total number of monthly payments (years × 12)
Try it fast with the Mortgage Calculator. Change rate, term, or down payment to see the monthly impact immediately.
Worked example
- Home price: $500,000
- Down payment: $100,000 → P = $400,000
- Interest rate: 6.50% → r = 0.065 / 12 ≈ 0.005417
- Term: 30 years → n = 360
Using the formula, the principal-and-interest payment is about $2,528/mo.
(Your total monthly to the servicer may be higher if you escrow taxes/insurance/PMI.)
Amortization: paying interest first, then more principal
Each payment covers interest on the current balance and the rest reduces principal. Early on, interest is a bigger share; later, principal dominates. That’s why extra principal payments early in the loan save the most interest.
Tip: Make a small extra payment each month (or one 13th payment per year). Be sure it’s applied to principal.
APR vs interest rate
- Interest rate: cost of the loan’s principal.
- APR: includes the rate plus certain required fees and points.
Two loans can share the same rate but have different APRs if one has more upfront costs. When comparing lenders, APR is a better “true cost” yardstick, but still check fees, prepayment penalties, and timelines.
PMI (Private Mortgage Insurance)
If your down payment < 20%, many conventional loans require PMI. It doesn’t protect you; it protects the lender. You can usually request PMI removal at 80% LTV; it typically drops off automatically at 78% if you pay on schedule. An appraisal can sometimes speed removal if your home value rises.
Points and closing costs
- Points are prepaid interest (usually 1 point = 1% of the loan). Paying points can lower your rate.
- Break-even: Divide the upfront cost by the monthly savings from the lower rate to estimate months to recover the cost.
To evaluate a refi or buying points, try the Refinance Break-Even Calculator.
Adjustable-rate mortgages (ARMs)
ARMs begin with a fixed “teaser” rate, then adjust at intervals based on an index + margin, subject to caps. They can lower payments upfront but add rate risk later. They’re best when you plan to sell or refinance before resets.
How much house can I afford?
Lenders often look at Debt-to-Income (DTI) ratios. A common rule of thumb is ≤ 36% total debt (housing + other debts) of gross monthly income—programs vary.
Use the Home Affordability Calculator to estimate a safe price based on income, debts, down payment, rate, and term.
Common mistakes to avoid
- Focusing only on payment, not total interest and fees.
- Ignoring PMI costs and removal timeline.
- Stretching the term to hit a target payment without assessing lifetime cost.
- Not comparing multiple lenders (rate quotes can vary by tenths, which really add up).
- Skipping an emergency fund after closing.
Quick checklist before you apply
- Recent pay stubs, W-2s/1099s, and tax returns
- Bank/asset statements (down payment + reserves)
- Debt details (student loans, auto, cards)
- Proof of additional income (bonuses, alimony, etc.)
Next step: run your numbers
Open the Mortgage Calculator and experiment:
- Increase/downsize your down payment
- Compare 30-year vs 15-year terms
- Try different interest rates to see sensitivity
- Add an extra principal amount to see interest saved
References & further reading
- Your lender’s Loan Estimate and Closing Disclosure explain costs line by line.
- Local regulations and PMI rules vary—check your lender’s guidelines.