How debt-to-income limits set the budget
Debt-to-income (DTI) is your monthly debt payments divided by your gross monthly income; lenders use it to judge whether you can manage the payments (CFPB: what is a debt-to-income ratio?). This calculator applies two limits you choose:
- Housing limit (front-end): the full housing payment (principal, interest, property tax, insurance, PMI and HOA dues) as a share of income. In the example, 28% of $8,333.33 a month is $2,333.33.
- Total debt limit (back-end): the housing payment plus your other debt payments. 36% of income, minus $500.00 of other debts, leaves $2,500.00.
The smaller of the two is your housing budget, and the calculator finds the highest price whose full payment fits it. The common 28% and 36% figures are rules of thumb, not law: lenders set their own limits and may approve higher ratios, and a limit a lender allows is not the same as a payment that is comfortable for you.
When other debts cost you house
With $500.00 of other debt payments, the example is limited by the housing limit and could afford about $320,463. At $1,200.00 a month, the total debt limit takes over and the price falls to about $250,783; paying those debts off would restore about $69,680 of buying power. Our loan payoff calculator shows how extra payments shorten a loan.
What moves the number
- Rate: the results table shows the example price at one point lower and higher: from $346,176 to $297,843.
- Down payment: $80,000 down instead of $40,000 raises the price to about $371,543, partly because 20% down removes PMI.
- Limits: at 36% housing and 43% total debt, the example price is about $407,563, with a $3,000.00 monthly payment instead of $2,333.33.
How the price is calculated
- Housing budget = the smaller of (income ÷ 12 × housing limit) and (income ÷ 12 × total debt limit − other debt payments).
- For a candidate price: loan = price − down payment; principal and interest use the standard payment formula, the same as our mortgage calculator; property tax = price × tax rate ÷ 12; insurance = yearly amount ÷ 12; PMI = loan × PMI rate ÷ 12, only when the loan is more than 80% of the price.
- The calculator searches for the highest price whose total monthly payment is within the budget, to within a fraction of a cent.
What this calculator does not include
- Closing costs and cash reserves. Keep them on top of the down payment; your Loan Estimate lists closing costs.
- FHA, VA and USDA loans, whose mortgage insurance, fees and limits follow different rules.
- Credit scores, loan limits, underwriting rules and changes in taxes or insurance. Results are estimates, not a pre-approval, loan offer or financial advice.
Methodology and testing
Automated tests compare the calculator with an independent implementation: for 200 varied cases the solved price's payment fits the budget and one dollar more does not, and worked examples match separately computed reference prices. How we build and test calculators.
Sources
- What is a debt-to-income ratio?, Consumer Financial Protection Bureau. Debt-to-income is all monthly debt payments divided by gross monthly income; lenders use it to measure the ability to manage payments.
- What is private mortgage insurance?, Consumer Financial Protection Bureau. You may be required to pay private mortgage insurance on a conventional loan with less than 20% down; it protects the lender, not you, and is not required with 20% down.
- Loan Estimate explainer, Consumer Financial Protection Bureau. The Loan Estimate lists a mortgage’s expected closing costs.
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