Mortgage Stress Test

Overview

The listed price of a home is not the cost of a home. Lenders pre-approve you to the maximum they can profitably lend, not to what leaves room for life. This skill computes the true monthly ownership cost (principal+interest, property tax, insurance, PMI, HOA, and the 1%/year maintenance reality), checks it against the 28/36 DTI rule and a 50/30/20 sanity check, stress-tests the payment against +1% and +2% rate shocks (for ARMs and refinances), and answers the only fair rent-vs-buy question: at what holding horizon does buying beat renting, if ever, given opportunity cost of the down payment?

When to Use

• "Can I afford this house?" / "How much should I spend?" — before offering
• Comparing a specific purchase against continuing to rent
• Deciding between a bigger down payment vs keeping investments
• ARM vs fixed stress check ("what if rates rise at reset?")
• Evaluating whether to wait and save more down payment
• Don't use for: investment-property cash-flow analysis (needs rental income model), commercial mortgages, or non-US tax specifics without adapting tax assumptions.

Inputs You Need

Steps

1. Run the calculator with the borrower's numbers:

   python3 scripts/mortgage_math.py --price 450000 --down 45000 --rate 6.5 \
       --tax-pct 1.1 --insurance 1600 --income 8500 --other-debt 400 \
       --rent 2100 --appreciation 3.0 --invest-return 6.0
   

2. Read the verdict block: PASS / TIGHT / FAIL on front-end (28%) and back-end (36%) DTI, plus the true monthly cost vs the naive "mortgage payment" people quote.
3. Check the rate shock table — if +2% breaks the budget, the ARM is a trap.
4. Read the rent-vs-buy break-even — buying loses money for the first N years due to closing costs and slow principal paydown; the horizon must be shorter than the planned stay.
5. If FAIL or TIGHT: rerun with bigger down payment, cheaper price, or longer horizon until PASS, and report the max price that passes.

Worked Example

$450k home, 10% down ($45k), 6.5% / 30yr, $8500/mo income, $400 other debt, rent $2100:

• P&I ≈ $2,560 — but true monthly ≈ $3,485 (P&I + $412 tax + $133 insurance + $169 PMI (0.5%) + $375 maintenance) — 36% more than the payment people budget for.
• Back-end DTI ≈ 45.8% → FAIL (36% rule; $3,485+$400 = $3,885 vs $3,060 cap).
• Max affordable price at these terms ≈ $340k (income-capped), or raise down payment to ~$135k to kill PMI and pass at $450k.
• Rent-vs-buy break-even ≈ year 4 at 3% appreciation — fine if staying 7 years, a loss if moving in 2.

The Math (summary — full detail in references/mortgage-math.md)

• Payment: M = P·r(1+r)ⁿ / ((1+r)ⁿ − 1), r = APR/12
• PMI: 0.5–1.5% of loan/yr while equity < 20% (approximate exit year computed from amortization + appreciation)
• Maintenance: 1%/yr of price (older homes: 1.5–2%)
• Closing costs: 2–5% (buyer side); selling costs ~6–7% (both sides' commissions + closing)
• Break-even year y: wealth if buying = equity(y) − Σownership costs − selling costs, compared against renting + investing (down payment + monthly difference) at the investment return. First year where buying wins = break-even horizon.

Common Pitfalls

1. Budgeting the P&I, not the PITI+M. Taxes/insurance/PMI/maintenance add 25–50%. The calculator prints both — always quote the true number.
2. Using boom-year appreciation (8–15%). Long-run national real appreciation is ~3–4%; run break-even at 0% and 3% to see how fragile the case is.
3. Forgetting selling costs. ~6–7% exit cost means short holds almost always lose; break-even horizons under 3 years are rare even in normal markets.
4. Counting the down payment as "spending" but not its opportunity cost. $90k not invested at 6% is ~$5.4k/yr foregone — the model charges this.
5. Treating PMI as forever or as nothing. It ends at ~20% equity — the script estimates the exit year and stops charging it after.
6. Lender pre-approval ≠ affordability. Pre-approval uses gross income and 43–50% back-end DTI ceilings; the 36% rule exists because retirement, childcare, and repairs don't appear on the lender's worksheet.

Verification Checklist

• True monthly cost (PITI+M+maintenance) printed and used in DTI
• Front-end ≤28% and back-end ≤36% checked with explicit PASS/FAIL
• Rate shock table (+1%, +2%) present
• Break-even horizon vs planned stay compared
• If FAIL: max passing price or required down payment reported
• Assumptions (appreciation, return, tax %) stated in the answer