A mortgage is the largest financial commitment most people make, yet few understand the math behind it. This guide breaks down the formulas so you know exactly what you are signing up for.
Step 1: The Payment Formula
Formula — Monthly Payment
M = P × [r(1+r)^n] / [(1+r)^n − 1] P = loan amount, r = monthly rate (annual/12), n = total payments (years × 12).
Example: $350,000 loan at 6.5% for 30 years: r = 0.065/12 = 0.005417, n = 360. M = $2,212/month (principal and interest). With taxes and insurance (PITI), expect $2,800-3,200.
Step 2: Total Interest Over the Loan
Total Interest = ($2,212 × 360) - $350,000 = $446,320. You pay 127% of the home price in interest alone. This is why extra payments and rate shopping matter enormously. Compare with the Mortgage Calculator.
Step 3: Qualification (DTI)
| Loan Type | Max Front-End DTI | Max Back-End DTI |
|---|---|---|
| Conventional | 28% | 36-43% |
| FHA | 31% | 43-50% |
| VA | N/A | 41% |
Calculate your full PITI payment with rate presets and refi analysis
Try the Mortgage Calculator →Key Takeaways
- You will pay more in interest than the home costs on a 30-year loan at current rates.
- DTI under 36% is ideal — above 43% disqualifies you from most conventional loans.
- A 1% lower rate on $350K saves about $250/month and $90K over the life of the loan.
- 15-year mortgages have lower rates and save 60%+ on total interest.