Mortgage Rate Sensitivity: A Worked $400,000 Loan Example
A transparent amortization model showing how five assumed fixed rates change principal-and-interest payments on one $400,000, 30-year loan. It is not a rate forecast or lending quote.
Published:
Research Question
How do five assumed fixed rates change the principal-and-interest payment and total interest in one 30-year amortization model?
Methodology
We computed monthly payments and total interest for a $400,000 30-year fixed-rate mortgage at illustrative 0.5% intervals from 5.5% to 7.5%. Payments use the standard amortization formula. No property tax, insurance, or PMI is included, so the page isolates only the stated principal-and-interest effect.
| Rate | Monthly Payment | Total Interest | vs. Previous Step |
|---|---|---|---|
| 5.5% | $2,271 | $418,000 | - |
| 6.0% | $2,398 | $463,000 | +$127/mo |
| 6.5% | $2,528 | $510,000 | +$130/mo |
| 7.0% | $2,661 | $558,000 | +$133/mo |
| 7.5% | $2,797 | $607,000 | +$136/mo |
Monthly payment by interest rate
$400K loan, 30-year fixed
Total interest paid over 30 years
$400K loan, 30-year fixed, sensitivity to rate
What this model shows
The payment difference in this five-rate example is $526 per month
For a $400,000 principal-and-interest loan amortized over 360 monthly payments, the model produces a $2,271 payment at 5.5% and a $2,797 payment at 7.5%. The table and charts use only these stated inputs, so the figures can be reproduced with the standard amortization formula.
Total interest depends on holding every input constant
Under the same full-term assumption, modeled total interest ranges from about $418,000 to about $607,000 across the five rates. Those totals are not quotes, forecasts, or estimates of a borrower's actual cost. They exclude taxes, insurance, mortgage insurance, fees, discount points, changes in the rate, and any early payoff or refinancing.
How to use the example
Use the comparison to understand the direction and scale of rate sensitivity, then enter an actual loan amount, term, and offered rate in the related calculator. A lender's disclosures and loan estimate control for a real borrowing decision because they include terms this simplified model does not.
Formula and limits
Monthly payment is calculated as P × r × (1 + r)n ÷ ((1 + r)n − 1), where P is principal, r is the monthly rate, and n is the number of payments. This page assumes a fixed rate for all 30 years and does not model adjustable-rate loans, closing costs, regional taxes, or property costs.