How to calculate how much house you can afford, step by step
To calculate how much house you can afford, take 28% of your gross monthly pay for the housing payment and 36% for the housing payment plus all other debts, take the lower of the two caps, and turn that cap into a loan and a price. That is the whole method. The 28/36 rule is a guideline lenders use: the housing payment on its own, and then the housing payment with everything else you owe. The lower of the two caps is the one that binds, and the binding cap is what decides the loan.
The worked example: $120,000 a year
The worked example. Step 1 — monthly pay: $120,000 a year divided by 12 months is $10,000 a month. Step 2 — the front-end cap: 28% of $10,000 is $2,800.00 a month. Step 3 — the back-end cap: 36% of $10,000 is $3,600, less $500 a month of other debts, which is $3,100.00 a month. Step 4 — the binding cap: the lower one, $2,800.00 a month, so the front-end limit binds. Step 5 — the loan: $2,800.00 a month divided by the amortization factor at 6.5% over 30 years is $442,990.29. Step 6 — the price: the loan is 80% of the price with 20% down, so the price is $553,737.87. Step 7 — the down payment: 20% of the price is $110,747.57. The max price is $553,737.87, and the three numbers to remember are the two caps and the binding one: $2,800.00, $3,100.00, and $2,800.00 again.
The 28/36 rule, in plain words
The front-end limit is about the house on its own: the housing payment — principal and interest, on this page — may take at most 28% of gross monthly pay. The back-end limit is about everything together: the housing payment plus car loans, cards, student loans and anything else you pay monthly may take at most 36% of gross monthly pay. Gross pay means before tax, and monthly pay means the annual figure divided by 12. The rule uses gross pay because that is the number a lender sees first, and percentages because the same rule has to work at $80,000 a year and at $150,000 a year. On $80,000 a year the front-end cap is $1,866.67 a month; on $150,000 a year it is $3,500.00 a month.
When the back-end limit binds
Sometimes the back-end limit is the lower one, and then it binds instead. With $1,500 a month of other debts, the back-end cap is 36% of $10,000 less $1,500, which is $2,100.00 a month — below the front-end cap of $2,800.00 — so the back-end limit binds and the max price falls to $415,303.40, with a loan of $332,242.72 and a down payment of $83,060.68. The debts only matter once they are big enough to flip the binding limit: with $500 a month of debts the back-end cap is $3,100.00 and the front-end limit still binds, so clearing $500 of debts changes nothing, while $1,500 of debts costs about $138,434 of home. The smallest monthly debts where the back-end limit binds is $801 a month — at $800 the two caps tie at $2,800.00 and the front-end limit still wins the tie.
Reversing it: what income does a $400,000 house need?
Sometimes you know the price and you need the income. A $400,000 home with 20% down needs a $320,000 loan, and the down payment is $80,000. The principal and interest on that loan at 6.5% over 30 years is $2,022.62 a month. The front-end rule then needs $86,683.61 a year of income — the payment is 28% of the monthly pay it allows. Run the reverse check before you fall for a listing: if your income is below $86,683.61 a year, the $400,000 home is out of reach under the rule, however much you like the kitchen. The how-much-house-calculator page runs the same check for any price you type.
A second example: the down payment
Take a second example to make the pattern stick. The loan is fixed by the binding cap: on $120,000 a year it is $442,990.29, whatever the down payment. What the down payment changes is how far that loan stretches. At 20% down the max price is $553,737.87, and the down payment is $110,747.57. At 10% down the same loan buys $492,211.44 of home, and the down payment is $49,221.14. With no down payment at all the price is the loan itself, $442,990.29. A bigger deposit does not let you borrow more; it lets the same borrowing buy more house. And the rate matters just as much: at 5.00% the same income buys $651,985.66 of home, and at 8.00% it buys $476,992.23.
Checking your answer
Whatever method you used, check it with the numbers you already have. First, check the caps: the front-end cap is 28% of monthly pay, and the back-end cap is 36% of monthly pay less the other debts — on $120,000 a year with $500 a month of debts, those are $2,800.00 and $3,100.00, and the lower one binds. Second, check the price against the loan: with 20% down, $442,990.29 of loan buys $553,737.87 of home, and the down payment is 20% of the price, $110,747.57. Third, check the reverse: a $400,000 home needs $86,683.61 a year, so if your income is $120,000 a year, a $400,000 home is inside the rule and a $553,737.87 home is the top of it. Run your numbers through the how-much-house-calculator and compare.
Common mistakes
The first mistake is using take-home pay instead of gross pay: the rule is written on gross pay, before tax, so using the smaller take-home figure understates what you can afford. The second is forgetting the other debts: the back-end cap subtracts them, so a household with $1,500 a month of debts can afford $415,303.40 of home, not $553,737.87, even on the same $120,000 a year. The third is treating the down payment as extra borrowing: the loan is fixed by the binding cap, and the down payment only decides how much home that loan stretches to — at 10% down the max price is $492,211.44, not $553,737.87. And the fourth is forgetting what the rule leaves out: taxes, insurance, HOA dues and PMI are not in the payment this page counts.
A quick check you can do in your head
You can sanity-check any affordability answer without a calculator. First, find the monthly pay and take 28% of it: on $120,000 a year that is $10,000 a month, and 28% of $10,000 is $2,800.00. Second, check the back-end cap: 36% of $10,000 is $3,600, less the other debts — with $500 a month of debts that is $3,100.00, so the front-end limit binds. Third, check the size: a $400,000 home needs $86,683.61 a year, so on $120,000 a year a $400,000 home is comfortable and the top of the range is $553,737.87. If a calculator says the max price on $120,000 a year is anything but $553,737.87 at these terms, the numbers are wrong.