Loading...
Loading...
Navigation
The Catalyst Project
How much house can you actually afford? Uses conservative 28/36 DTI rules.
The mortgage industry's default underwriting ratio. The 28/36 rule sets a ceiling on what banks will lend you — not what is wise to borrow. Target 20-25% of gross income on PITI for a comfortable margin.
Front-end ratio (housing only):
PITI / gross_monthly_income ≤ 28 %
Back-end ratio (all debts):
total_monthly_debt / gross_monthly_income ≤ 36 %
PITI = P&I + property tax + homeowners insurance + PMI(if <20% down)
Amortization (monthly P&I):
P&I = L × [r(1+r)^n] / [(1+r)^n − 1]
L = loan principal
r = monthly rate = APR / 12
n = number of months = 12 × years
Quick approximation (20% down, 7% rate, 30-yr):
max_home_price ≈ 4 × annual_gross_income
monthly_PITI_per_$100k_loan ≈ $730 at 7%, $480 at 4%$100k gross income, $40k down payment, 7% rate, 30-yr loan:
gross_monthly = 100,000 / 12 = $8,333
max_PITI = 8,333 × 0.28 = $2,333
Estimate non-P&I components for a ~$300k home:
property_tax = 300,000 × 0.012 / 12 = $300/mo
insurance = ~$100/mo
-> max_P&I = 2,333 − 300 − 100 = $1,933
Solving amortization at 7%/360 months for $1,933/mo P&I:
principal ≈ $290,400
max_home_price = principal + down_payment
= 290,400 + 40,000
= ~$330,000
(Conservative target at 22% PITI: ~$260,000)Front-end ratio: PITI (mortgage principal + interest + taxes + insurance) should be ≤ 28% of gross monthly income. Back-end ratio: total monthly debt (PITI + car loans + student loans + minimum credit card payments) ≤ 36% of gross monthly income. Most conservative banks lend to these limits; FHA loans allow up to 31% front-end and 43% back-end.
Quick approximation: max_home_price ≈ 4× annual gross income (assumes 20% down, 7% rate, conservative ratios). At $100k income: ~$400k max home. Detailed: solve PITI from the 28% rule (P ≤ 0.28 × income/12 − tax − insurance), then back-solve principal from the amortization formula at the prevailing rate.
Principal + Interest + Taxes + Insurance — the four components of the all-in monthly housing payment. P&I comes from the mortgage amortization formula. Taxes (property tax) typically 1-2% of home value annually. Insurance (homeowner's) $1,200-3,000/year. HOA dues separately on condos/townhomes. PMI added if down payment under 20%.
Conventional loan: 20% to avoid private mortgage insurance (PMI). 3-5% conventional with PMI. 3.5% FHA. 0% VA (for eligible veterans). Lower down payment → larger loan → more interest paid → PMI cost → higher monthly payment. Trade-off: keeping cash for emergency fund vs reducing total interest paid.
Massive impact. A $400k loan at 4% = $1,910/mo; at 7% = $2,661/mo. That $751/mo difference is $9,012/year — directly limits the home price you qualify for. A 1% rate increase reduces affordability by ~10-12%. When rates were 3% in 2021, buyers afforded 30-40% more home than at today's 7%.
Almost never. Banks qualify you to the limit — they don't care about your other financial goals. Borrowing the max squeezes out retirement savings, emergency fund building, and discretionary spending. Rule of thumb: target 20-25% of gross income on PITI (not the 28% ceiling) to keep room for everything else. Be especially conservative if income is variable.