Complete Guide To Mortgage Calculations 2026
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PITI: the four real components of a mortgage payment
Most mortgage calculators tell you a monthly number and stop. This guide goes the other direction — it’s a complete reference for every calculation that matters when you’re buying, refinancing, or accelerating payoff on a home loan. Every formula is included with a worked example, every fee is broken out, and every common mistake is flagged.
The amortization formula
It’s organized so you can read it end-to-end (it takes ~15 minutes) or jump to the section you need. If you’re house-hunting, start with affordability and PITI. If you already have a mortgage, skip to amortization, prepayment, and refinance break-even. If you’re a first-time buyer, read the whole thing once.
APR vs interest rate vs APY
Worked example: $400,000 home, 20% down ($80,000), $320,000 loan, 6.5% rate, 30 years, 1.2% property tax, $1,500/year insurance:
Affordability: 28/36 rule and beyond
The monthly principal-and-interest payment on a fixed-rate mortgage uses a single formula. Memorize this:
Down payment: the 20% myth + reality
Where: M = monthly payment, P = loan principal, r = monthly interest rate (annual rate ÷ 12), n = total number of monthly payments (years × 12). Worked example with $320,000, 6.5% rate, 30 years:
PMI math and how to drop it
Month 1: interest = 320,000 × 0.005417 = $1,733.44; principal = 2,022.62 - 1,733.44 = $289.18. Month 360 (last): interest is pennies, principal is the entire payment. The shift happens gradually; the crossover (where principal exceeds interest in a single payment) is around month 230 of a 360-month loan at 6.5%.
Closing costs by category
Three terms get confused constantly. Lender quotes use rate; comparison should use APR; savings accounts use APY.
Prepayment: where extra dollars hit hardest
Example: Lender A quotes 6.0% rate with $4,000 in fees on a $300K loan. Lender B quotes 6.5% rate with no fees. APR comparison:
Refinance break-even formula
Lender A wins on APR despite the higher fees, because $4,000 amortized over 30 years is less impactful than 0.5% rate for the full term. But if you only stay 5 years, Lender B’s no-fees structure is cheaper. Always compute APR for your actual time horizon.
Escrow accounts: how they work
The classic affordability metric uses two ratios:
Fixed vs ARM: when ARMs make sense
The “20% down” rule isn’t legally required — it’s the threshold below which Private Mortgage Insurance (PMI) kicks in on conventional loans. Reality:
15-year vs 30-year: the real comparison
Private Mortgage Insurance protects the lender (not you) if you default with less than 20% equity. Cost: 0.3-1.5% of original loan annually, paid monthly. $300K loan at 0.5% PMI = $1,500/year = $125/month.
Mortgage interest deduction (US)
Closing typically runs 2-5% of loan amount. Breakdown for a $300K loan:
Top 10 mortgage mistakes
Because the amortization curve is front-loaded, the timing of extra principal payments matters enormously. On a $300K loan at 6.5% over 30 years:
Putting it all together
The first 7 years contribute most of the lifetime savings. Why? Because each extra principal dollar in year 1 skips 30 years of compounding interest charges; the same dollar in year 25 only skips 5 years.