How it works
The 28/36 rule: total housing costs (PITI — principal, interest, taxes, insurance — plus HOA) should be no more than 28% of gross monthly income (front-end DTI), and housing plus all other debt payments no more than 36% (back-end DTI).
The calculator takes the lower of the two limits, subtracts monthly tax, insurance and HOA to get the maximum principal-and-interest payment, then reverses M = P × r(1 + r)n / ((1 + r)n − 1) to find the loan amount. Home price = loan + down payment (or loan ÷ (1 − down %) when you enter a percentage). When the down payment is under 20%, private mortgage insurance (loan × PMI rate ÷ 12, default 0.5% a year) is counted inside the housing budget, so the loan solves loan × (payment factor + PMI rate ÷ 12) = the budget left after tax, insurance and HOA.
Worked examples
$100,000 income, $500/mo debts, 20% down, 6.5% 30-year, $3,600 tax, $1,200 insurance
Max home price: $382,342.81 (loan $305,874.25, down $76,468.56). PITI: $2,333.33/mo; front-end DTI 28.0%, back-end 34.0%; limited by the front-end (28%) limit.
$70,000 income, $800/mo debts, $15,000 down, 7% 30-year, $2,400 tax, $1,000 insurance, $150 HOA, 0.5% PMI
Max home price: $137,589.03 (loan $122,589.03). The down payment is only 10.9% of the price, so $51.08/mo of PMI is included in the budget. Total payment: $1,300.00/mo; front-end DTI 22.3%, back-end 36.0%; limited by the back-end (36%) limit.
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