How to calculate mortgage qualification, step by step
To calculate mortgage qualification, start with your gross annual income and turn it into a monthly figure, then work out two monthly caps: the front-end cap, which limits housing alone, and the back-end cap, which limits housing plus all your other debts. Take the smaller of the two caps — that is the binding cap, the most a lender will let you spend on housing each month. Then solve the loan from that cap: the payment left after tax, insurance and HOA is the principal and interest the loan can carry, and the loan plus your down payment is the max home price. Work it out in the mortgage-qualification-calculator.
The worked example: $100,000 a year
The worked example, step by step. Step 1 — monthly gross income: $100,000 a year divided by 12 is $8,333.33 a month. Step 2 — the front-end cap: 28% of $8,333.33 is $2,333.33 a month. Step 3 — the back-end cap: 36% of $8,333.33 is $3,000.00, minus $500 a month of other debts, which is $2,500.00 a month. Step 4 — the binding cap: the smaller of $2,333.33 and $2,500.00 is $2,333.33, so the front-end limit binds. Step 5 — the loan: the $2,333.33 binding cap, less $150 of insurance and the tax on the price, supports a loan of $296,609.61 at 6.50% over 30 years. Step 6 — the max price: $296,609.61 plus the $40,000 down payment is $336,609.61. Step 7 — check it: principal and interest of $1,874.77 plus tax of $308.56 plus $150.00 of insurance is $2,333.33, exactly the binding cap, and the front-end ratio is 28.00% with a back-end ratio of 34.00% — inside both limits.
What the front-end limit is
The front-end limit caps housing alone as a share of your gross monthly income. The common figure is 28%: on $100,000 a year, gross monthly income is $8,333.33, and 28% of that is $2,333.33 a month. Housing means everything the lender counts as a housing cost — principal, interest, property tax, homeowners insurance and HOA dues together — not just the loan payment. If your other debts are small, the front-end limit is usually the one that binds, as it does in the worked example, where $2,333.33 is smaller than the $2,500.00 back-end cap.
What the back-end limit is
The back-end limit caps housing plus all your other monthly debts as a share of your gross monthly income. The common figure is 36%: on $100,000 a year, 36% of $8,333.33 is $3,000.00, and after $500 a month of other debts the room left for housing is $2,500.00 a month. The debts that count are the ones with a monthly payment — car payments, credit cards, student loans, personal loans and child support among them. If your debts are heavy, the back-end limit is the one that binds, and paying a debt off before applying can raise the max price more than saving the same amount of cash.
Which limit binds, and why it matters
Only one limit can bind at a time: the binding cap is always the smaller of the two, and the other one is slack. On the worked example the front-end limit binds, because $2,333.33 is smaller than $2,500.00 — the household has $166.67 a month of slack on the back-end limit. Which limit binds tells you what to fix. If the front-end limit binds, the levers are income, rate, term, tax and down payment: more income, a lower rate, a longer term, a lower-tax home or a bigger down payment all raise the max price. If the back-end limit binds, the lever is your debts: every dollar of monthly debt you remove frees a dollar of housing cap.
From the binding cap to the max home price
The step most guides skip is the one from the binding cap to the max price, and it is a solve, not a lookup. The binding cap of $2,333.33 a month has to cover four things: principal and interest, property tax, insurance and HOA. Insurance is $150.00 a month and HOA is $0, so $2,183.33 is left for principal, interest and tax — but the tax depends on the price, and the price depends on the loan, so the loan is solved in one step from the cap, the rate, the term and the tax rate. At 6.50% over 30 years with a 1.10% tax rate, the binding cap supports a loan of $296,609.61, and the principal and interest on that loan is $1,874.77 a month while the tax on the resulting price is $308.56 a month. Add the $40,000 down payment and the max price is $336,609.61.
Common mistakes
The first is using take-home pay instead of gross pay: the limits are defined on gross income before tax, so $100,000 a year is $8,333.33 a month here, and using a smaller take-home figure understates what you qualify for. The second is forgetting a debt: a car payment or a student loan you left out still counts against the back-end limit, and the lender will find it. The third is treating the whole back-end cap as housing money: the back-end cap of $2,500.00 already has the $500 of debts taken out, and the housing money is what is left, not the full $3,000.00. The fourth is ignoring tax and insurance: the binding cap has to cover them, so a low-tax home buys more house than a high-tax one at the same payment. The fifth is treating the estimate as a promise: the figure is a ceiling from the lender's rules, not a pre-approval, and the real decision also weighs credit, employment and reserves. Work it out in the mortgage-qualification-calculator, and check each step against the worked example above.
A quick check you can do in your head
You cannot solve a loan in your head, but you can sanity-check an answer. The binding cap is always the smaller of the two caps: on $100,000 a year the front cap is $2,333.33 and the back cap is $2,500.00, so any binding cap above $2,333.33 is wrong. The max price is always the loan plus the down payment: $296,609.61 plus $40,000 is $336,609.61, so any max price that does not split into a loan and a down payment that add up is wrong. And the breakdown always adds back to the binding cap: $1,874.77 of principal and interest plus $308.56 of tax plus $150.00 of insurance is $2,333.33, and a breakdown that adds to anything else is wrong. If a calculator says the max price is far above $336,609.61 on these numbers, or that the monthly payment is far from $2,333.33, the number is wrong — run your numbers through the mortgage-qualification-calculator and compare them with the worked example above.