How this calculator estimates what you can afford
Lenders look at two ratios. The front-end ratio compares housing costs to gross monthly income, and the back-end ratio adds your other debts. The calculator finds the largest monthly housing payment that satisfies both, subtracts insurance and HOA dues, and then works backward through the mortgage formula to find the loan and price that fit, including property tax that grows with the price.
The formulas, and what every variable means
max housing payment = the smaller of: front % × monthly income, or back % × monthly income − other debts
budget for loan and tax = max housing payment − insurance − HOA
price = (budget + f × down payment) ÷ (f + t)
| Symbol | Meaning | How it is found |
|---|---|---|
| Monthly income | Gross (pre-tax) income per month | Annual income ÷ 12 |
| Front % | Share of income allowed for housing | 28% by default |
| Back % | Share of income allowed for housing plus all other debts | 36% by default |
| f | Monthly loan payment per $1 borrowed | r ÷ (1 − (1 + r)−n), where r is the monthly rate and n the number of payments |
| t | Monthly property tax per $1 of home price | Annual tax rate ÷ 12 |
| Down payment | Cash you put down | Entered directly |
The last formula comes from the fact that the budget must cover the loan payment and the tax: budget = f × (price − down payment) + t × price. Solving that equation for the price gives the formula above.
Worked example 1, by hand: $100,000 income
$100,000 a year, $400 a month in other debts, $40,000 down, a 6.5% rate, a 30-year term, 1.1% property tax and $1,800 a year in insurance.
- Monthly income: $100,000 ÷ 12 = $8,333.33.
- Front limit: 28% × $8,333.33 = $2,333.33.
- Back limit: 36% × $8,333.33 − $400 = $2,600.00.
- The smaller limit wins, so the maximum housing payment is $2,333.33.
- Budget for loan and tax: $2,333.33 − $150.00 insurance = $2,183.33.
- Loan factor f = 0.006321 and tax factor t = 0.000917.
- Price = ($2,183.33 + 0.006321 × $40,000) ÷ (0.006321 + 0.000917) ≈ $336,610.
That means a loan of $296,610, with a monthly payment of $1,874.77 for principal and interest, $308.56 for property tax and $150.00 for insurance. Here the 28% housing limit is the one that decides the answer.
Worked example 2: heavy debts change the answer
Keep everything the same but add car and student loan payments of $1,500 a month instead of $400.
| $400 of debt | $1,500 of debt | |
|---|---|---|
| Maximum housing payment | $2,333.33 | $1,500.00 |
| Limiting rule | 28% housing | 36% total debt |
| Home price you can afford | $336,610 | $221,466 |
Extra debt of $1,100 a month lowers the price by about $115,143. Paying down a car loan or credit card before applying can raise what you qualify for.
Worked example 3: the interest rate
The same $100,000 buyer at three different rates:
| Rate | Home price | Loan amount |
|---|---|---|
| 5.5% | $365,521 | $325,521 |
| 6.5% | $336,610 | $296,610 |
| 7.5% | $311,427 | $271,427 |
The monthly budget is unchanged. Only the rate moves, yet the affordable price falls by $54,094 between the lowest and highest rate. Shopping for a lower rate is worth real effort.
Worked example 4: the down payment
| Down payment | Home price | Loan amount |
|---|---|---|
| $20,000 | $319,143 | $299,143 |
| $40,000 | $336,610 | $296,610 |
| $80,000 | $371,543 | $291,543 |
Because your monthly budget is fixed by your income, an extra $1,000 down raises the price you can reach by about $873, not the full $1,000, since a pricier home also carries more property tax. The calculator does not add PMI, which matters when the down payment is under 20%.
An affordable payment is not the same as a comfortable one
- Keep an emergency fund of several months of expenses after closing.
- Budget for maintenance, often around 1% of the home's value each year.
- Remember closing costs, which are usually a few percent of the price.
- Consider commuting costs, utilities and furnishing.
Common mistakes to avoid
- Treating the maximum as a target. The result is a ceiling, not a recommendation.
- Leaving out debts. Car loans, student loans and card minimums all count.
- Ignoring PMI. With under 20% down, the real payment is higher than shown.
- Using an old or optimistic rate. Try a rate a point higher than today's quote as a stress test.
- Forgetting other costs. Insurance and property tax vary a lot by location, so use local figures.
Once you have a target price, test the real monthly payment in the mortgage calculator, and see how your pay compares with the paycheck calculator. A lender's preapproval letter can show a higher amount than the one you are comfortable with. See mortgage pre-approval vs prequalification for what the letter means and how it affects your credit.
Sources and review
The 28/36 ratios are a traditional rule of thumb, and the price formula is the standard loan payment formula solved for the home price. Lenders' real limits differ: the CFPB says different loan products and lenders have different debt-to-income limits, and the Fannie Mae Selling Guide (section B3-6-02) lists a 36% maximum for manually underwritten loans, up to 45% with strong credit and reserves, and up to 50% through automated underwriting. For buyer guidance see the CFPB's page on figuring out how much you want to spend. Last reviewed September 2026. Planning your first purchase? See the first-time home buyer guide for the cash you need at each price. Read about our methodology.