People type this into search every day: how much house can I afford.
A salary multiple skips the rate, the term, the debts you already pay, and the tax and insurance bill. Those four change the price a payment can carry.
This page uses the house affordability calculator. It is payment math with the limits you type. It is not a pre-approval, and it is not a lending offer.
Two caps, then the loan those caps can buy
The Consumer Financial Protection Bureau defines a debt-to-income ratio as monthly debt payments divided by gross monthly income. The same page says lenders set their own limits. The calculator leaves both percentages in your hands.
The defaults are 28% for housing and 36% for all debt. The tool calls those common screening starting points. Lenders still set their own limits.
Housing cap = gross monthly income × housing %
DTI cap = gross monthly income × DTI % − other monthly debts
The tighter cap is the maximum for principal, interest, taxes, insurance, and HOA. The mortgage payment post walks the fixed-rate payment forward. CFPB’s page on how lenders calculate monthly payments describes that same payment. This calculator runs the relationship backward, from a payment to a loan.
Principal and interest room = maximum housing payment − the taxes, insurance, and HOA you typed
If that room is zero or below, the result is “No affordable price”.
Monthly rate r = annual rate ÷ 100 ÷ 12
Months n = years × 12, rounded
Loan = payment × ((1 + r)^n − 1) ÷ (r × (1 + r)^n)
When the rate is 0, loan = payment × months.
Price = loan ÷ (1 − down payment %)
Down payment cash = price − loan
Housing binds when its cap is less than or equal to the DTI cap. Otherwise the binding limit is total DTI.
Total DTI at the cap = (maximum housing payment + other debts) ÷ income
Fig 1
Income caps, then a price
Gross monthly income feeds both screens
The tighter cap, minus taxes, insurance, and HOA, is the principal and interest the loan can use. Price is that loan divided by one minus the down payment.
A zero rate, so the loan is ordinary multiplication
Keep every default except the rate. Income $7,500, other debts $400, housing 28%, total DTI 36%, 30 years, 20% down, extras $600. Rate 0%.
Housing cap: 7500 × 0.28 = $2,100.00
DTI cap: 7500 × 0.36 − 400 = $2,300.00
The housing cap is tighter. Principal and interest: 2100 − 600 = $1,500.00
Loan: 1500 × 360 = $540,000.00
Price: 540000 ÷ 0.80 = $675,000.00
Down payment: 675000 − 540000 = $135,000.00
Total DTI at the cap: (2100 + 400) ÷ 7500 = 33.3%
A rate above zero supports a smaller loan from the same $1,500. The rest of the examples use that present-value step. Running the payment formula forward brings each of those loans back to the principal-and-interest figure in the example, within a fraction of a cent.
Example 1: the published $7,500 month
$7,500 a month is $90,000 a year. These are the calculator defaults.
- gross monthly income: $7,500
- other monthly debts: $400
- housing share: 28%
- total DTI share: 36%
- rate: 6.5%
- term: 30 years
- down payment: 20%
- taxes, insurance, and HOA: $600
Housing cap: 7500 × 0.28 = $2,100.00
DTI cap: 7500 × 0.36 − 400 = $2,300.00
Housing wins by $200. Principal and interest: 2100 − 600 = $1,500.00
The 6.5% loan that $1,500 pays off in 360 months is $237,316.23.
Price: 237316.23 ÷ 0.80 = $296,645.29
Down payment: 296645.29 − 237316.23 = $59,329.06
Total DTI at the cap: (2100 + 400) ÷ 7500 = 33.3%
The binding limit is the housing ratio. The $400 of other debts does not cut this price. It would start to cut the price only after it uses up that $200 of slack, which is other debts above $600. Example 8 goes past that line.
Calculator result
House affordability
- Gross monthly income
- $7,500.00
- Other monthly debt payments
- $400.00
- Maximum housing cost share
- 28%
- Maximum total debt-to-income
- 36%
- Annual mortgage rate
- 6.5%
- Loan term
- 30 years
- Down payment
- 20%
- Monthly taxes, insurance, and HOA
- $600.00
$296,645.29
estimated maximum home price
- Maximum principal and interest
- $1,500.00
- Maximum PITI
- $2,100.00
- Binding limit
- Housing ratio
Fig 2 · 1/2
Where the $2,100 housing cap goes
Defaults. Other debts sit outside this $2,100.
Principal and interest
$1,500.00
Taxes, insurance, HOA
$600.00
Principal and interest can use $1,500.00.
Taxes, insurance, and HOA use the other $600.00.
1500 ÷ 2100 = 71.4%. 600 ÷ 2100 = 28.6%. The down payment post is the cash side of the $59,329.06. The DTI post is the ratio on its own.
Example 2: $4,200 a month, 10% down, smaller extras
A different household from example 1.
- gross monthly income: $4,200 ($50,400 a year)
- other monthly debts: $250
- housing share: 28%
- total DTI share: 36%
- rate: 6.5%
- term: 30 years
- down payment: 10%
- taxes, insurance, and HOA: $350
Housing cap: 4200 × 0.28 = $1,176.00
DTI cap: 4200 × 0.36 − 250 = $1,262.00
Housing binds. Principal and interest: 1176 − 350 = $826.00
Loan: $130,682.14
Price: 130682.14 ÷ 0.90 = $145,202.37
Down payment: 145202.37 − 130682.14 = $14,520.24
Total DTI at the cap: (1176 + 250) ÷ 4200 = 34%
Calculator result
House affordability
- Gross monthly income
- $4,200.00
- Other monthly debt payments
- $250.00
- Down payment
- 10%
- Monthly taxes, insurance, and HOA
- $350.00
$145,202.37
estimated maximum home price
- Maximum principal and interest
- $826.00
- Maximum PITI
- $1,176.00
- Binding limit
- Housing ratio
The price is 145202.37 ÷ 296645.29 = 49.0% of example 1, while income is 4200 ÷ 7500 = 56%. The smaller down payment and the lower extras do not make up for the smaller payment.
Example 3: the same defaults on a $72,000 salary
$72,000 a year is $6,000 a month. Every other input stays on the example 1 defaults, including the $600 of extras and the $400 of other debts.
Housing cap: 6000 × 0.28 = $1,680.00
DTI cap: 6000 × 0.36 − 400 = $1,760.00
Housing binds. Principal and interest: 1680 − 600 = $1,080.00
Loan: $170,867.69
Price: 170867.69 ÷ 0.80 = $213,584.61
Down payment: 213584.61 − 170867.69 = $42,716.92
Total DTI at the cap: (1680 + 400) ÷ 6000 = 34.7%
Against example 1, income fell by $1,500 and the price fell by 296645.29 − 213584.61 = $83,060.68. The $600 extras did not shrink, so they take a larger share of the smaller housing cap. 600 ÷ 1680 = 35.7%, against 28.6% in example 1.
Example 4: $11,000 a month, and total DTI binds
- gross monthly income: $11,000 ($132,000 a year)
- other monthly debts: $900
- housing share: 28%
- total DTI share: 36%
- rate: 6.5%
- term: 30 years
- down payment: 20%
- taxes, insurance, and HOA: $850
Housing cap: 11000 × 0.28 = $3,080.00
DTI cap: 11000 × 0.36 − 900 = $3,060.00
Total DTI is tighter by $20. Principal and interest: 3060 − 850 = $2,210.00
Loan: $349,645.91
Price: 349645.91 ÷ 0.80 = $437,057.39
Down payment: 437057.39 − 349645.91 = $87,411.48
Total DTI at the cap: (3060 + 900) ÷ 11000 = 36%
A higher income did not automatically leave the housing ratio in charge. The $900 of other debts used the slack.
Example 5: what if the rate is 5.5% or 7.5%?
Same inputs as example 1. The caps do not move. Principal and interest stays $1,500.00. Only the rate changes, so only the loan changes.
At 5.5% the loan is $264,182.64. Price: 264182.64 ÷ 0.80 = $330,228.31. Down payment $66,045.66.
At 6.5% the price is the example 1 result, $296,645.29.
At 7.5% the loan is $214,526.44. Price: 214526.44 ÷ 0.80 = $268,158.05. Down payment $53,631.61.
One point below the default adds 330228.31 − 296645.29 = $33,583.02 of price. One point above removes 296645.29 − 268158.05 = $28,487.24. The steps are not equal. A higher rate bites a smaller loan, so the next point removes fewer dollars of price.
Calculator result
House affordability
- Annual mortgage rate
- 7.5%
$268,158.05
estimated maximum home price
- Maximum principal and interest
- $1,500.00
- Maximum PITI
- $2,100.00
- Binding limit
- Housing ratio
Fig 3 · 1/3
Same $1,500 payment, three rates
Example 1 inputs. The axis rounds to thousands. Captions keep the cents.
Maximum price
- Maximum price
| Category | Maximum price |
|---|---|
| 5.5% | $330k |
| 6.5% | $297k |
| 7.5% | $268k |
At 5.5% the price is $330,228.31.
At 6.5% the price is $296,645.29.
At 7.5% the price is $268,158.05.
Example 6: 5%, 10%, and 20% down
Same $1,500 of principal and interest, so the loan stays $237,316.23. The down payment percent changes the price.
At 5% down, price = 237316.23 ÷ 0.95 = $249,806.56. Cash down: 249806.56 − 237316.23 = $12,490.33.
At 10% down, price = 237316.23 ÷ 0.90 = $263,684.70. Cash down: $26,368.47.
At 20% down, price = $296,645.29. Cash down: $59,329.06.
A smaller down payment lowers the price this formula will name. The loan is capped by the payment. Price is that loan divided by the share you finance. Financing 95% instead of 80% means a smaller purchase price from the same loan. 296645.29 − 249806.56 = $46,838.73 less price at 5% down than at 20% down.
Cash to close is a separate pile. The cash to close calculator is the one that adds fees on top of the down payment.
Example 7: a 15-year term, and the years around it
Same example 1 inputs, term changed to 15 years. The $1,500 payment now covers 180 months.
Loan: $172,194.62
Price: 172194.62 ÷ 0.80 = $215,243.27
Down payment: $43,048.65
The 30-year price was $296,645.29. Shortening the term removes 296645.29 − 215243.27 = $81,402.02 of price. The monthly cap did not change. Fewer months repay less principal at the same rate.
The same $1,500, still at 6.5% and 20% down, produces these prices as the term changes:
- 10 years: $165,128.44 (loan $132,102.75)
- 15 years: $215,243.27
- 20 years: $251,484.38 (loan $201,187.51)
- 25 years: $277,692.55 (loan $222,154.04)
- 30 years: $296,645.29
Fig 4 · 1/5
Price the $1,500 payment can carry
6.5%, 20% down, example 1 caps. Axis labels round.
Maximum price
- Maximum price
| Point | Maximum price |
|---|---|
| 10y | $165k |
| 15y | $215k |
| 20y | $251k |
| 25y | $278k |
| 30y | $297k |
10 years supports a $165,128.44 price.
15 years supports $215,243.27.
20 years supports $251,484.38.
25 years supports $277,692.55.
30 years supports $296,645.29.
The jump from 10 to 15 years adds $50,114.83. The jump from 25 to 30 years adds $18,952.74. Later years add less price because the extra payments sit further out.
Example 8: other debts, and the $200 of slack
Example 1 had $200 between the housing cap ($2,100) and the DTI cap ($2,300). Other debts can rise by $200, from $400 to $600, before total DTI takes over.
At $600 of other debts, and every other example 1 input unchanged:
DTI cap: 2700 − 600 = $2,100.00
The two caps match. Housing still binds, because the formula keeps housing when the caps are equal. Principal and interest stays $1,500.00. The price stays $296,645.29.
Total DTI at the cap: (2100 + 600) ÷ 7500 = 36%
One more dollar changes the binding limit. At $601 of other debts the DTI cap is $2,099, principal and interest is $1,499, and the price is $296,447.52.
At $1,200 of other debts the picture is no longer a small trim.
DTI cap: 2700 − 1200 = $1,500.00
Housing cap is still $2,100, so total DTI binds. Principal and interest: 1500 − 600 = $900.00
Loan: $142,389.74
Price: 142389.74 ÷ 0.80 = $177,987.17
Down payment: $35,597.43
Total DTI at the cap is 36%. The price is 296645.29 − 177987.17 = $118,658.12 below example 1. A car payment that pushes other debts from $400 to $1,200 is the whole of that gap in this model. The DTI calculator will show the ratio on whatever payment you type. This page shows what that ratio does to the price.
Example 9: leaving taxes and insurance at $0
A common miss is an empty extras box. Same inputs as example 1, monthly extras $0.
Housing still caps the payment at $2,100.00. All of it can go to principal and interest.
Loan: $332,242.72
Price: 332242.72 ÷ 0.80 = $415,303.40
Down payment: $83,060.68
Total DTI at the cap stays 33.3%, because the $400 of other debts is still in the numerator and the housing payment is still $2,100.
The price is 415303.40 − 296645.29 = $118,658.11 higher than example 1. That gap is the $600 a month the empty box ignored. If the tax and insurance bill is real, the $415,303.40 price does not fit the 28% screen.
Example 10: typing take-home pay in the income box
CFPB’s DTI uses gross monthly income. Suppose the gross is the example 1 figure, $7,500, and take-home is $5,400. Putting $5,400 in the income box reruns every cap.
Housing cap: 5400 × 0.28 = $1,512.00
DTI cap: 5400 × 0.36 − 400 = $1,544.00
Housing binds. Principal and interest: 1512 − 600 = $912.00
Loan: $144,288.27
Price: 144288.27 ÷ 0.80 = $180,360.33
Down payment: $36,072.07
Total DTI at the cap: (1512 + 400) ÷ 5400 = 35.4%
The price is 296645.29 − 180360.33 = $116,284.96 below the gross-income result. A lender can still define income in its own way. This gap is what the calculator does when the income field changes.
Fig 5 · 1/2
Gross income and take-home in the same box
Every other input matches example 1
Maximum price
Gross $7,500
$296,645.29
Net $5,400
$180,360.33
Gross $7,500 supports a $296,645.29 price.
Take-home $5,400 in that box supports $180,360.33.
Example 11: extras that use the whole allowance
- gross monthly income: $5,000
- other monthly debts: $400
- housing share: 28%
- total DTI share: 36%
- rate: 6.5%
- term: 30 years
- down payment: 20%
- taxes, insurance, and HOA: $1,600
Housing cap: 5000 × 0.28 = $1,400.00
DTI cap: 5000 × 0.36 − 400 = $1,400.00
Both caps are $1,400. Extras are $1,600. Principal and interest room: 1400 − 1600 = −$200.
The calculator returns No affordable price. The detail lines are the housing cap $1,400.00, the DTI cap $1,400.00, and extras $1,600.00. There is no loan and no price. Raising the rate or the term cannot help, because the payment never gets as far as the interest math.
Example 12: what if the screens are 31% and 43%?
Same dollars as example 1. Housing share 31%. Total DTI share 43%. These are numbers you might type. The tool treats them as ordinary percentages.
Housing cap: 7500 × 0.31 = $2,325.00
DTI cap: 7500 × 0.43 − 400 = $2,825.00
Housing still binds. Principal and interest: 2325 − 600 = $1,725.00
Loan: $272,913.66
Price: 272913.66 ÷ 0.80 = $341,142.08
Down payment: $68,228.42
Total DTI at the cap: (2325 + 400) ÷ 7500 = 36.3%
The wider housing screen adds 341142.08 − 296645.29 = $44,496.79 of price versus example 1. The 43% DTI screen did no work here, because $2,825 sits above $2,325. If other debts were large enough to pull the DTI cap under $2,325, the 43% field would be the one that binds.
The scenarios side by side
| Example | Income | Other debts | Rate | Years | Down | Extras | Max P&I | Price | Binds |
|---|---|---|---|---|---|---|---|---|---|
| 1. Defaults | $7,500 | $400 | 6.5% | 30 | 20% | $600 | $1,500 | $296,645.29 | Housing |
| 2. Modest household | $4,200 | $250 | 6.5% | 30 | 10% | $350 | $826 | $145,202.37 | Housing |
| 3. $72,000 salary | $6,000 | $400 | 6.5% | 30 | 20% | $600 | $1,080 | $213,584.61 | Housing |
| 4. Higher income | $11,000 | $900 | 6.5% | 30 | 20% | $850 | $2,210 | $437,057.39 | Total DTI |
| 5. Lower rate | $7,500 | $400 | 5.5% | 30 | 20% | $600 | $1,500 | $330,228.31 | Housing |
| 5. Higher rate | $7,500 | $400 | 7.5% | 30 | 20% | $600 | $1,500 | $268,158.05 | Housing |
| 6. Smaller down payment | $7,500 | $400 | 6.5% | 30 | 5% | $600 | $1,500 | $249,806.56 | Housing |
| 7. Shorter term | $7,500 | $400 | 6.5% | 15 | 20% | $600 | $1,500 | $215,243.27 | Housing |
| 8. Debts at the slack line | $7,500 | $600 | 6.5% | 30 | 20% | $600 | $1,500 | $296,645.29 | Housing |
| 8. Debts past it | $7,500 | $1,200 | 6.5% | 30 | 20% | $600 | $900 | $177,987.17 | Total DTI |
| 9. Extras left at $0 | $7,500 | $400 | 6.5% | 30 | 20% | $0 | $2,100 | $415,303.40 | Housing |
| 10. Take-home as income | $5,400 | $400 | 6.5% | 30 | 20% | $600 | $912 | $180,360.33 | Housing |
| 11. Extras use the cap | $5,000 | $400 | 6.5% | 30 | 20% | $1,600 | none | No affordable price | Both caps |
| 12. 31% and 43% screens | $7,500 | $400 | 6.5% | 30 | 20% | $600 | $1,725 | $341,142.08 | Housing |
| Zero-rate check | $7,500 | $400 | 0% | 30 | 20% | $600 | $1,500 | $675,000.00 | Housing |
A 100% down payment does not get a price. The calculator returns “No loan needed”. Income of $0 returns “Need income”.
The rent vs buy post answers a different question: the cost of owning one house against renting. The rent affordability post starts from take-home pay and a rent share. This page starts from gross income and a mortgage payment.
Open the house affordability calculator with your gross income, the debts a lender would still count, and a tax and insurance figure you can point at. Then run the mortgage payment calculator at the price you got, and check the rate on the quote.