What mortgage approval can I get?

How it works

Write I for the gross yearly income (a monthly amount is × 12), G = I ÷ 12 for the gross monthly income, E for the other monthly debt payments, f and b for the housing and total debt limits in percent, C for the monthly tax, insurance, HOA dues, and mortgage insurance, r for the yearly rate ÷ 1200, and n for the months (years × 12).

1. Housing budget. M = the smaller of f ÷ 100 × G and b ÷ 100 × G − E. The page says which limit sets it: “The housing limit (front-end ratio) sets the budget.” when f ÷ 100 × G is at most b ÷ 100 × G − E (so also when they are equal), else “The total debt limit (back-end ratio) sets the budget.”
2. Room for the loan payment. M − C. If it is 0 or less there is no answer.
3. Largest loan. With a = r ÷ (1 − (1 + r)^−n), the monthly payment per dollar borrowed (1 ÷ n at 0%), the largest loan is (M − C) ÷ a, and its principal and interest payment is M − C.
4. Checking a loan you want of amount A: its payment is A × a. The housing ratio is (A × a + C) ÷ G × 100 and the total ratio is (A × a + C + E) ÷ G × 100. The verdict is “Within both limits.” when the housing ratio is at most f and the total ratio at most b; otherwise “Over the housing limit.”, “Over the total debt limit.”, or “Over both limits.”. The payment, verdict, and room are shown only when you enter a loan amount. The room is the largest loan minus A. Without a loan amount, the ratios shown are those of the largest loan.

Assumptions

• Lenders compare payments with gross (before-tax) monthly income. The limits are yours to set; the defaults (30% and 36%) are examples from Freddie Mac's guidance and Fannie Mae's manual underwriting limit.
• The rate is fixed, and tax, insurance, HOA dues, and mortgage insurance are one monthly amount.
• Credit score, cash reserves, VA residual income, employment history, and down payment rules are not checked. This is an estimate, not a preapproval.
• The default rate is an example, not a current market rate.

Worked examples by hand

$100,000 a year, $500 of other debts, $500 a month of tax and insurance, 6.5% over 30 years, limits 30% and 36%. G = 8,333.33. The housing limit gives 0.30 × 8,333.33 = $2,500 and the total limit 0.36 × 8,333.33 − 500 = $2,500, so M = $2,500. The loan payment can be 2,500 − 500 = $2,000. a = 0.0065 ÷ (1 − 1.0054167^−360) = 0.00632068, so the largest loan is 2,000 ÷ 0.00632068 = $316,421.64. Its ratios are 30% and 36%.

FHA limits: $90,000 a year, $900 of other debts, $450 a month of costs, 7% over 30 years, limits 31% and 43%, checking a $350,000 loan. G = 7,500. The limits give 0.31 × 7,500 = $2,325 and 0.43 × 7,500 − 900 = $2,325, so M = $2,325 and the loan payment can be $1,875. With a = 0.00665302, the largest loan is 1,875 ÷ 0.00665302 = $281,826.69. The $350,000 loan costs 350,000 × 0.00665302 = $2,328.56 a month, so the ratios are (2,328.56 + 450) ÷ 7,500 = 37.0% and (2,328.56 + 450 + 900) ÷ 7,500 = 49.0%: over both limits, by 350,000 − 281,826.69 = $68,173.31 of loan.

VA limit: $120,000 a year, $2,500 of other debts, $400 a month of costs, 0% over 30 years, limits 30% and 41%, checking a $300,000 loan. G = 10,000. The limits give $3,000 and 4,100 − 2,500 = $1,600, so M = $1,600 (the total debt limit). At 0%, a = 1 ÷ 360, so the largest loan is (1,600 − 400) × 360 = $432,000. The $300,000 loan costs 300,000 ÷ 360 = $833.33 a month, a total ratio of (833.33 + 400 + 2,500) ÷ 10,000 = 37.3%: within both limits, with $132,000 of room.