Mortgage Affordability with Debt Ratios
Find the maximum home purchase price you can afford based on your income, existing debts, and FHA, VA, or conventional debt-to-income ratio rules. Use it before house-hunting to set a realistic budget.
About this calculator
Lenders use two debt-to-income (DTI) ratios to cap your mortgage. The front-end ratio limits housing costs (PITI) as a share of gross monthly income: conventional 28%, FHA 31%, VA has no hard front-end cap. The back-end ratio limits all monthly debt payments: conventional 36%, FHA 43%, VA 41%. The calculator takes the lesser of (grossIncome × frontRatio) and (grossIncome × backRatio − monthlyDebts) to find the maximum allowable monthly housing payment. It then reverse-solves the amortization formula — maxLoan = maxPayment × [(1+r)^n − 1] / [r × (1+r)^n] — for the maximum loan amount and adds your down payment to get the maximum home price. This ensures both DTI constraints are satisfied simultaneously.
How to use
Say your gross income is $8,000/month, monthly debts are $500, down payment is $40,000, rate is 7%, and you're using a conventional loan. Front-end cap: $8,000 × 0.28 = $2,240. Back-end cap: $8,000 × 0.36 − $500 = $2,380. Binding limit = $2,240/month. Monthly rate r = 0.07/12 ≈ 0.005833, n = 360. Max loan = $2,240 × [(1.005833)^360 − 1] / [0.005833 × (1.005833)^360] ≈ $337,300. Maximum home price = $337,300 + $40,000 = $377,300.
Frequently asked questions
What is the difference between front-end and back-end debt-to-income ratios for a mortgage?
The front-end ratio (also called the housing ratio) compares only your projected mortgage payment — including principal, interest, taxes, and insurance — to your gross monthly income. The back-end ratio compares all monthly debt obligations (mortgage plus car loans, student loans, credit cards, etc.) to gross income. Lenders enforce both limits simultaneously, so the stricter constraint determines how much you can borrow. Paying down existing debts before applying can increase your back-end headroom and qualify you for a larger mortgage.
How do FHA debt-to-income ratio limits differ from conventional loan limits?
FHA loans allow a front-end DTI of up to 31% and a back-end DTI of up to 43%, compared to conventional guidelines of 28% / 36%. This makes FHA loans accessible to borrowers with more existing debt or lower income relative to the home price. However, FHA loans require mortgage insurance premiums (MIP) for the life of the loan in many cases, which adds to the monthly cost. VA loans are the most flexible, with no front-end cap and a 41% back-end limit, and they don't require private mortgage insurance.
Why does my maximum mortgage amount decrease when interest rates rise?
The amortization formula shows an inverse relationship between rate and loan amount for a given monthly payment. When rates rise, a larger share of each payment covers interest, leaving less to pay down principal, so the same monthly payment supports a smaller loan balance. For example, at 5% a $2,000 payment supports roughly $372,000 in loan principal; at 7% the same payment only covers about $301,000. This is why affordability tightens quickly as rates climb, and why locking a rate before rates rise can significantly increase your purchasing power.