Financial
Illustrative mortgage payment caps and loan principal with PV
Combine assumed housing and debt-payment caps, subtract housing costs, and model loan principal.
Enforce the stricter of Front-End (28%) and Back-End (36%) DTI caps
This scenario assumes housing and total-debt caps of 28% and 36% of gross monthly income. Actual lending rules vary.
Subtract the modeled housing costs to obtain available principal-and-interest payment, then apply PV under fixed monthly amortization assumptions.
| Underwriting Step ($10,000/mo Income, 6% nominal annual rate, 30 Yr) | Other Debt = $600 | Other Debt = $1,100 |
|---|---|---|
| Front-End Housing Cap (28%) | $2,800 (Binding!) | $2,800 |
| Back-End Housing Cap (36% - Debt) | $3,000 | $2,500 (Binding!) |
| Max P&I (less $550 Tax/Ins/HOA) | $2,250 / mo | $1,950 / mo |
| Max Qualified Loan = PV(6%/12, 360, -PI) | $375,281.13 | $325,243.65 |
Illustrative mortgage principal and DTI-cap formulas
Pass -maxPI as negative cash outflow into PV so the illustrative loan principal returns positive.
=LET(maxPiti, MIN(A2 * 0.28, A2 * 0.36 - B2), maxPi, MAX(0, maxPiti - C2), ROUND(PV(D2 / 12, E2 * 12, -maxPi), 2))Binding maximum monthly housing payment (PITI + HOA)
This is the tighter of the two assumed caps, not an underwriting approval.
=ROUND(MIN(A2 * 0.28, A2 * 0.36 - B2), 2)Inputs and interpretation
The 28/36 percentages are illustrative planning caps, not universal underwriting criteria or an approval. Use a nominal annual loan rate, positive income and term, and include applicable housing costs such as mortgage insurance in the cost input. Lenders also assess collateral, credit, assets and other requirements. This assumes fixed monthly amortizing payments and no fees.
Try the example
Use the original values or change them to test your understanding.