Mortgage Formulas Cheat Sheet
Core Mortgage Formulas
Where M = monthly payment, P = loan principal, r = monthly interest rate (annual rate ÷ 12), and n = total number of payments (years × 12).
Monthly Payment Quick Reference
Monthly payment per $100,000 borrowed at various rates (30-year fixed):
| Interest Rate | Monthly Payment per $100K | Total Interest (30-Year) | Total Cost per $100K |
|---|---|---|---|
| 4.0% | $477 | $71,870 | $171,870 |
| 5.0% | $537 | $93,256 | $193,256 |
| 5.5% | $568 | $104,404 | $204,404 |
| 6.0% | $600 | $115,838 | $215,838 |
| 6.5% | $632 | $127,544 | $227,544 |
| 7.0% | $665 | $139,509 | $239,509 |
| 7.5% | $699 | $151,717 | $251,717 |
| 8.0% | $734 | $164,155 | $264,155 |
15-Year vs. 30-Year Comparison
Example: $400,000 loan at 6.5% interest rate.
| Feature | 30-Year Fixed | 15-Year Fixed |
|---|---|---|
| Monthly Payment | $2,528 | $3,484 |
| Total Interest Paid | $510,177 | $227,151 |
| Total Cost | $910,177 | $627,151 |
| Interest Savings | — | $283,026 saved |
| Monthly Difference | — | $956 more per month |
| Best For | Lower monthly payments, more cash flow | Building equity fast, less total interest |
Amortization Breakdown
Early payments are almost entirely interest. Here’s how a $400,000 loan at 6.5% (30-year) breaks down:
| Payment # | Monthly Payment | Principal | Interest | Remaining Balance |
|---|---|---|---|---|
| 1 | $2,528 | $361 | $2,167 | $399,639 |
| 12 (Year 1) | $2,528 | $387 | $2,141 | $395,469 |
| 60 (Year 5) | $2,528 | $484 | $2,044 | $375,671 |
| 120 (Year 10) | $2,528 | $658 | $1,870 | $341,709 |
| 180 (Year 15) | $2,528 | $895 | $1,633 | $293,116 |
| 240 (Year 20) | $2,528 | $1,218 | $1,310 | $222,832 |
| 300 (Year 25) | $2,528 | $1,657 | $871 | $118,893 |
| 360 (Year 30) | $2,528 | $2,514 | $14 | $0 |
Key Mortgage Ratios & Thresholds
| Metric | Formula | Target | Why It Matters |
|---|---|---|---|
| LTV (Loan-to-Value) | Loan ÷ Property Value | ≤ 80% | Below 80% avoids PMI ($100–300/month) |
| Front-End DTI | Housing Costs ÷ Gross Income | ≤ 28% | Max housing burden for conventional loans |
| Back-End DTI | All Debt Payments ÷ Gross Income | ≤ 36% (up to 43%) | Total debt burden including mortgage |
| Home Price to Income | Home Price ÷ Annual Income | ≤ 3–4x | General affordability guideline |
Refinancing Break-Even Formula
If refinancing costs $6,000 and saves $200/month, break-even = 30 months. Only refinance if you plan to stay in the home longer than the break-even period.
Key Takeaways
- The monthly payment formula M = P × [r(1+r)ⁿ ÷ ((1+r)ⁿ−1)] is the foundation of all mortgage math
- A 15-year mortgage saves massive interest but requires ~38% higher monthly payments
- Keep LTV below 80% to avoid PMI and DTI below 36% for best loan terms
- Early payments are almost entirely interest — extra principal payments save the most in year 1–10
- Calculate the refinancing break-even point before committing to closing costs
Frequently Asked Questions
How much house can I afford?
A common rule of thumb is 3–4x your annual gross income. More precisely, keep your front-end DTI (housing costs including mortgage, taxes, insurance) below 28% of gross monthly income and total DTI below 36%.
What is PMI and how do I avoid it?
Private Mortgage Insurance is required when your down payment is below 20% (LTV above 80%). It typically costs 0.5–1% of the loan annually. Avoid it by putting 20% down, or request removal once your equity reaches 20%. Some lenders offer lender-paid PMI at a slightly higher rate.
Is it better to pay extra on principal or invest the difference?
If your mortgage rate is below your expected investment return (after tax), investing typically wins mathematically. At a 6.5% mortgage rate, the guaranteed “return” from extra payments is compelling. At 3.5%, investing in index funds historically outperforms. Risk tolerance matters too — paying off the mortgage is a guaranteed return.
How does an amortization schedule work?
Each fixed monthly payment is split between principal and interest. Early payments are mostly interest because the balance is high. Over time, the interest portion shrinks and the principal portion grows. By the final years, payments are almost entirely principal. See our amortization schedule glossary entry for details.
When does refinancing make sense?
Refinancing generally makes sense when you can lower your rate by at least 0.75–1%, you plan to stay in the home past the break-even point, and closing costs are reasonable (typically 2–5% of the loan). Calculate the break-even: closing costs ÷ monthly savings = months to recoup costs.