Closing costs, cash reserves and moving costs also come out of your savings; keep them apart from the down payment.
With $50,000.00 down, the most you can pay is $332,531.51: a $282,531.51 loan whose full housing payment of $2,333.33 a month uses the 28% front-end limit. At a rate 1 point higher the price falls to $309,744.83.
Housing budget: front-end cap and back-end cap after debts
Monthly payment at the maximum price
Principal and interest76.5%Property tax13.1%Insurance5.4%PMI5.0%
Home price you can afford by interest rate
Home price you can afford at other interest rates Rows: 7
The down payment is under 20% of the price, so PMI is included in the payment. Here m = 0.5% ÷ 12 is the monthly PMI per dollar of loan.
Check: payment at that price
1,785.79+304.82+125.00+0.00+117.72=2,333.33
Front-end ratio 28%, back-end ratio 34%.
About the house affordability calculator
Lenders cap the housing payment in two ways. The front-end ratio limits principal, interest, property tax, insurance, HOA dues and mortgage insurance to a share of gross monthly income, 28% by default; the back-end ratio limits that payment plus your other monthly debts, 36% by default. The lower of the two caps is your housing budget, and the calculator finds the home price whose full payment equals it, adding PMI whenever the down payment is under 20% of the price.
With the defaults, a $100,000 household income, $500 of monthly debts and $50,000 down at 6.5% for 30 years allow a home of $332,531.51. The front-end cap of $2,333.33 a month is the tighter one.
The 28% and 36% defaults are Freddie Mac's guidelines for manually underwritten loans; Fannie Mae's automated Desktop Underwriter accepts total ratios up to 50%. Closing costs and cash reserves are not included.
How much house can I afford?
Under the 28/36 rule, housing can take 28% of gross monthly income and all debt payments 36%. The lower limit is your housing budget, and the answer is the price whose full payment fits it. On 100,000 a year with 500 of other debts, 50,000 down and a 6.5% 30-year loan, that is 332,531.51.
The 28/36 rule worked by hand
Gross monthly income: 100,000 ÷ 12 = 8,333.33.
Front-end limit: 28% × 8,333.33 = 2,333.33 for housing.
Back-end limit: 36% × 8,333.33 = 3,000 for all debts, which leaves 3,000 − 500 = 2,500 for housing.
Housing budget: the lower of the two, 2,333.33.
Price: P = (budget − insurance ÷ 12 − HOA + D × (a + m)) ÷ (a + t + m) = 332,531.51, with a and the budget unrounded.
In step 5, D is the down payment and a = 0.00632068 is the monthly payment per unit borrowed at 6.5% over 30 years. Monthly property tax per unit of price is t = 1.1% ÷ 12, and monthly PMI per unit of loan is m = 0.5% ÷ 12, or 0 with 20% down.
At that price the loan is 282,531.51. The payment splits into 1,785.79 of principal and interest, 304.82 of property tax, 125.00 of insurance and 117.72 of PMI, 2,333.33 in all. With the 500 of other debts, payments take 34% of income, inside the 36% limit.
Affordability examples
Scenario
Modeled maximum home price
Monthly housing payment
Default
332531.51
2333.33
Back-end cap
233471.96
1800.00
PMI boundary
360000.00
2275.36
Default is the example above. Back-end cap has 1,200 of other debts, 30,000 down, a 7% rate, 1% property tax, 1,200 of yearly insurance, 50 of monthly HOA dues and 0.6% PMI. Its debts leave 3,000 − 1,200 = 1,800 for housing, below the 2,333.33 front-end limit.
PMI boundary is the first example with 72,000 down, explained in the next section.
Why 20% down changes the answer
PMI applies while the down payment is under 20% of the price, so a price of five times the down payment is a boundary. With 72,000 down, a 360,000 home is exactly 20% down and costs 2,275.36 a month with no PMI.
Any higher price adds PMI and pushes the payment over the 2,333.33 budget, so the maximum stops at 360,000 with 57.97 of the budget unused. With 100,000 down, the same income buys 392,464.45.
How rates, debts and term change the price
Interest rate: at 6% the first example buys 345,067.22, at 7% 320,774.23 and at 7.5% 309,744.83, so each half point moves the price by 11,000 to 12,600.
Other debts: up to about 666.67 a month they change nothing, because the 28% housing limit still binds. Above that, each extra 100 a month of payments cuts the price by about 13,065.
Loan term: a 15-year loan at 6.5% lowers the price to 265,293.94, because each unit borrowed costs more a month.
Lender limits other than 28/36
The 28% and 36% ratios are Freddie Mac's guidelines for manually underwritten loans. Other programs allow more:
Fannie Mae: total debts up to 36% when manually underwritten, 45% with credit-score and reserve requirements, and 50% through Desktop Underwriter (Selling Guide B3-6-02).
FHA manual underwriting: 31% for housing and 43% in total without compensating factors (HUD Handbook 4000.1). With 31/43, the first example allows 365,194.11.
A higher ratio is what a lender may approve, which can be more than your budget comfortably carries.
What the estimate leaves out
Closing costs, cash reserves, maintenance, utilities and moving costs are extra, so keep cash for them on top of the down payment. Property tax and insurance vary by home and change over time, and the rate is assumed fixed for the whole term.
Inputs worth checking
Income: gross yearly income, before tax, of everyone on the mortgage.
Other debts: monthly payments on car and student loans, card minimums, personal loans and child support; not rent, utilities or groceries.
Property tax and insurance: tax as a yearly percentage of the price, insurance as a yearly amount, HOA dues per month.
PMI: a yearly percentage of the loan, charged only when the down payment is under 20% of the price.
Checked against: Search as above: 36% × 8,333.33 − 1,200 = 1,800 is below the 2,333.33 front-end cap
PMI cliff at 20% down (edge)
Gross household income (per year)
100,000
Other monthly debt payments
500
Down payment
72,000
Interest rate (per year)
6.5%
Loan term
30 years
Property tax (per year, of home price)
1.1%
Homeowners insurance (per year)
1500
HOA dues (per month)
0
PMI (per year, of loan amount)
0.5%
Front-end ratio: housing costs, % of gross income
28%
Back-end ratio: all debts, % of gross income
36%
Home price you can afford
360,000.00
PMI per month
0.00
Down payment as a share of the price
20.00%
Monthly housing payment
2,275.36
Checked against: search: a price of 360,000 (20% down, no PMI) costs 2,275.36 a month; any higher price adds PMI and exceeds the 2,333.33 cap
Questions
What is the 28/36 rule?
Housing costs should take no more than 28% of gross monthly income, and all debt payments including housing no more than 36%. These are Freddie Mac's guideline ratios for manually underwritten mortgages (Seller/Servicer Guide 5401.1 and 5401.2). On $100,000 a year, gross monthly income is $8,333.33, so housing may cost $2,333.33 and all debts $3,000.
How much house can I afford on a $100,000 salary?
About $332,500 with $50,000 down, $500 of other monthly debts and a 6.5% 30-year rate, under the 28/36 rule, including 1.1% property tax, $1,500 a year of insurance and 0.5% PMI. With FHA-style ratios of 31% and 43%, the same inputs allow $365,194.11. Other debts up to $666.67 a month leave the price unchanged, because the 28% front-end cap stays the tighter one.
What debt-to-income ratio do lenders allow?
Fannie Mae's maximum is 36% for manually underwritten loans, 45% with credit-score and reserve requirements, and 50% for loans run through Desktop Underwriter (Selling Guide B3-6-02). FHA's manual-underwriting limits without compensating factors are 31% for housing and 43% in total (HUD Handbook 4000.1). The CFPB suggests keeping total debt payments at 36% or less.
How does the down payment change how much house I can afford?
Each dollar of down payment adds a dollar to the price, and more once PMI drops away at 20% down. On a $2,333.33 budget at 6.5%, $50,000 down allows $332,531.51 with PMI, while $72,000 down allows exactly $360,000: at 20% down there is no PMI, but any higher price would bring PMI back and push the payment over the budget.
For planning only. Lenders, tax authorities and markets apply their own rounding, fees and rules; confirm figures with them before you commit.
Checked against references
This calculator includes 5 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.
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