Work the setup, then the numbers
Mortgage qualifying-ratio exercise
Calculate the housing allowance under stated front-end and total-debt assumptions, then use the smaller result.
- Gross monthly income
- $8,000.00
- Front-end housing allowance
- $2,240.00
- Back-end allowance after other debt
- $2,180.00
- Housing allowance under stated assumptions
- $2,180.00
- Loan principal
- $280,000.00
- Monthly principal and interest
- $1,724.01
- Monthly housing including taxes, insurance and HOA
- $2,174.01
- Calculated front-end ratio
- 27.18%
- Calculated back-end ratio
- 35.93%
Follow the arithmetic
Income 96,000 / 12 = 8,000; compare 8,000 x 0.28 with (8,000 x 0.36) - 700. Payment uses P x r / (1 - (1 + r)^(-n)), where r is the annual rate / 1200 and n is years x 12. At zero interest, payment is principal / n. Housing adds annual taxes / 12, monthly insurance and HOA. This excludes any mortgage insurance not entered in the insurance field. Meeting entered ratios is not a loan approval.
Intermediate values keep precision; dollar results display to cents.
The formula and its assumptions
Monthly income = annual income / 12; housing allowance = smaller of (income x front-end ratio) and (income x back-end ratio - other monthly debt)
The entered ratios are exercise assumptions. Actual loan eligibility depends on program, underwriting method, credit and other conditions. Do not treat 28/36 or 31/43 as universal limits. Housing expense may include principal, interest, taxes, insurance and applicable association charges. The payment model assumes a fixed-rate, fully amortizing loan with monthly payments and no financed charges. It excludes special payment structures and lender-specific qualification rules.
Fannie Mae: debt-to-income ratios