House Affordability Calculator
Find the maximum home price you can afford using 28/36 front/back-end debt-to-income ratios.
Inputs
Car loans, student loans, credit card minimums — not future housing costs.
Annual property tax as a percentage of home value.
Lender guidelines for front-end and back-end DTI limits.
Maximum Home Price
$360,985
Maximum Loan Amount
$300,985
Total Monthly Payment (PITI)
$2,333.33
Principal & Interest
$1,902.43
Est. Monthly Property Tax
$330.90
Monthly Insurance
$100.00
Down Payment %
16.6%
Loan-to-Value (LTV)
83.4%
PMI Required
true
PMI is typically required when LTV exceeds 80%.
Front-End DTI
28.0%
Back-End DTI
34.0%
Limiting Factor
front-end
Which DTI ratio is the binding constraint on your purchase price.
Step by step
Gross monthly income
$100,000 ÷ 12
= $8,333
Front-end limit (28% of gross)
$8,333 × 28%
= $2,333.33
Back-end limit (36% of gross − existing debts)
$8,333 × 36% − $500
= $2,500.00
Binding constraint: front-end
= Max PITI = $2,333.33
Maximum home price (binary search)
= $360,985
Resulting monthly PITI breakdown
P&I $1,902.43 + Tax $330.90 + Insurance $100.00
= $2,333.33
How it works
Conventional lenders apply two tests simultaneously. The front-end (housing) ratio caps your total housing payment (principal, interest, taxes, insurance — PITI) at 28% of gross monthly income. The back-end (total DTI) ratio caps all debt payments at 36%. The binding constraint is whichever produces the lower maximum payment, and from that payment limit we back-solve for the highest home price that fits. FHA guidelines are slightly more generous (31/43) and may allow a higher purchase price.
Formulas
Front-end DTI limit
Max PITI (front) = Gross Monthly Income × front-end limit %
- f_limit
- Front-end DTI limit (e.g. 28%)
Back-end DTI limit
Max PITI (back) = Gross Monthly Income × back-end limit % − Monthly debts
- b_limit
- Back-end DTI limit (e.g. 36%)
- D
- Existing monthly debt payments
This is an estimate based on conventional DTI guidelines. Actual loan qualification depends on credit score, loan type, reserves and lender discretion. Consult a licensed mortgage professional.
Frequently Asked Questions
Why does the calculator find the binding constraint automatically?
Lenders apply both tests simultaneously; you must satisfy both. The tighter one determines how much house you can afford. High existing debts typically make the back-end ratio binding.
What counts as a monthly debt?
Car loans, student loans, credit card minimum payments, personal loans, alimony and child support. Do not include utility bills, groceries or the future housing payment itself — those are not counted by underwriters.
Does a higher down payment let me buy a more expensive home?
Yes, for two reasons: a larger down payment reduces the loan, which reduces the P&I component of PITI, allowing a higher total price within the DTI limits. It also lowers LTV, potentially eliminating PMI.
What is the 20% down payment threshold for?
At 80% LTV or below, conventional lenders drop the PMI requirement. This calculator flags whether your down payment meets that threshold but does not add a PMI estimate to the payment — use the Down Payment Calculator for that detail.