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How mortgage affordability works

Lenders cap total monthly debt at a share of gross pay. On $9,000 a month with $650 of other debts and $500 of tax and insurance, a 43 percent rule leaves $2,720.00 for principal and interest and lends $430,333.43 over 30 years at 6.5 percent. A 28 percent housing test stops at $319,585.86.

Ceiling once both tests are applied

$319,585.86

A price of $379,585.86 with $60,000.00 down. The 28% housing test is the binding one on these numbers. It is the most the rules permit, not the loan to take.

Total debt allowed at 43%
$3,870.00
Housing budget, other debts out
$3,220.00
Principal and interest budget
$2,720.00
Total debt test at 43% lends
$430,333.43
Housing test at 28% of income lends
$319,585.86
Binding ceiling, the lower of the two
$319,585.86
$

Before tax and deductions, which is what a lender uses.

$

Car loans, student loans, card minimums, support orders.

%

The note rate, divided by 12 here. Not the APR, which folds in fees.

yr
$

Property tax, homeowners insurance and any association dues.

$

Added to the loan at the end, so it buys price rather than borrowing power.

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In short

  • On $9,000 of gross monthly pay, a 43 percent back-end limit allows $3,870.00 of total monthly debt. Subtract $650 of other debts and $500 of tax and insurance and $2,720.00 is left for principal and interest.
  • That $2,720.00 at 6.5 percent over 30 years is a loan of $430,333.43. With $60,000 down, the price ceiling is $490,333.43. These are maxima, not targets.
  • A 28 percent front-end test on the same $9,000 allows $2,520.00 of housing. After $500 of tax and insurance, $2,020.00 of principal and interest lends $319,585.86. Both tests have to pass, so the lower one governs.
  • Hold the $2,720.00 budget still and raise the rate to 7.5 percent. The loan ceiling falls to $389,007.95. The budget did not move. The present-value factor did.
  • The test uses gross pay. It does not know tax, childcare, or a saving rate. How mortgages work is the loan. This page is the ceiling a ratio puts on it.

A ceiling, not a budget

Mortgage affordability in underwriting is a debt-to-income ratio, not a household budget. Gross monthly pay is multiplied by a limit. Other required debts come out. Tax and insurance come out. What is left is the most principal and interest the rule will allow, and that payment is turned into a loan size.

On $9,000 a month, 43 percent is $3,870.00 of total debt. Subtract $650 of other debts (a car loan, student loans, card minimums) and $3,220.00 is left for housing. Subtract $500 of tax and insurance and $2,720.00 is left for principal and interest. At 6.5 percent over 30 years that payment is a loan of $430,333.43. Add a $60,000 deposit and the price ceiling is $490,333.43.

The mortgage affordability calculator on this page is that chain. Every figure in it is a maximum. Principal and interest are what the loan formula can support at the rate and term you type. How mortgages work is what that loan then does, month by month.

The debt-to-income calculator is the ratio on its own, without turning it into a loan size.

A lender's ceiling is not a reason to buy. Renting against buying is the comparison once a loan size exists, and the rent against buy crossover is that comparison as a drag on how long you stay.

Front-end against back-end

The back-end test caps all monthly debt. The front-end test caps housing alone. On the same $9,000, a 28 percent front-end rule allows $2,520.00 of housing. Other debts play no part in that line. Tax and insurance still come out, so $2,020.00 is left for principal and interest, which lends $319,585.86 and, with $60,000 down, a price of $379,585.86.

Both tests have to pass. The lower loan governs. Here the front-end test is the binding one: $319,585.86 against $430,333.43. The gap is the distance between $3,220.00 of back-end housing room and $2,520.00 of front-end housing room, turned into a loan at 6.5 percent.

15-year against 30-year is a different question, asked after a loan size exists.

The two tests on this page are the two rows of front-end against back-end DTI: housing costs alone, then housing plus the rest of the monthly debt. A file can clear one and fail the other.

Those two names are the same pair as how debt-to-income works, which is the ratio on its own, including the room left under a 43 percent ceiling before any house price is attached.

The rate moves the ceiling with no change to the applicant

Hold gross pay at $9,000, other debts at $650, tax and insurance at $500, the limit at 43 percent, the term at 30 years and the deposit at $60,000. Raise the mortgage rate from 6.5 percent to 7.5 percent.

The budget is untouched: $3,870.00 of total debt, $3,220.00 for housing, $2,720.00 for principal and interest. Only the factor that turns a payment into a loan shrinks. The ceiling falls from $430,333.43 to $389,007.95, and the price from $490,333.43 to $449,007.95.

One percentage point on the rate took about 9.6 percent off what the rule would lend, with no change to income, debts or savings. That is the single fastest way for a buyer to lose ground while doing nothing on the application.

What this page is not doing

It is not the amount a household should borrow, not a residual-income test, and not tax, insurance or HOA quoted from a listing. The three sheets are the 43 percent ceiling on $9,000 a month ($430,333.43), the 28 percent housing test ($319,585.86), and the same 43 percent applicant at 7.5 percent ($389,007.95). This is educational material, not financial advice.

Worked examples

The ceiling on \$9,000 a month

Gross pay is $9,000 a month. Other debts take $650: a car loan, student loans and card minimums. Property tax and insurance on the home you want run $500 a month. Your lender works to a 43 percent back-end limit, the loan would be 30 years at 6.5 percent, and you have $60,000 for the deposit. What is the most it would lend?

  1. Apply the limit to gross pay: 0.43×9000=0.43 \times 9000 = $3,870.00 of total monthly debt allowed.
  2. Subtract the debts you already carry: $3,870.00 minus $650 leaves $3,220.00 for housing.
  3. Subtract tax and insurance, which sit inside the housing payment: $3,220.00 minus $500 leaves $2,720.00 for principal and interest.
  4. Turn that payment into a loan. The period rate is i=0.065/12i = 0.065/12, a decimal that does not terminate, and n=360n = 360. Keep ii unrounded: 1−(1+i)−360i≈158.21082\frac{1 - (1 + i)^{-360}}{i} \approx 158.21082. Round ii to 0.00541667 before raising it to the power and the factor arrives at 158.21075 instead, which is how two calculators come to disagree over the same loan.
  5. Multiply the budget by the factor: 2720×158.210822720 \times 158.21082, which is $430,333.43.
  6. Add the deposit to read it as a price: $430,333.43 plus $60,000.

The rule stops at a loan of $430,333.43, which with $60,000 down is a price of $490,333.43. Every figure in that chain is a maximum: $3,870.00 is the most debt the rule allows, $3,220.00 the most housing, and $2,720.00 the most principal and interest.

The front-end test on the same income

The same applicant is measured by the housing test instead. A 28 percent front-end rule caps the housing payment on its own, so the other debts play no part. Same $9,000 of gross pay, same $500 of tax and insurance, same 30 years at 6.5 percent, same $60,000 deposit. Where does this test stop?

  1. The front-end test looks at housing alone, so nothing is set aside for other debts: 0.28×9000=0.28 \times 9000 = $2,520.00.
  2. There is nothing else to take off at this stage, so the whole $2,520.00 is the housing budget.
  3. Tax and insurance still come out of it: $2,520.00 minus $500 leaves $2,020.00 for principal and interest.
  4. Apply the same factor as before: 2020×158.210822020 \times 158.21082, which is $319,585.86.
  5. Add the deposit: $319,585.86 plus $60,000 gives $379,585.86.

The housing test allows a loan of $319,585.86 and a price of $379,585.86, against $430,333.43 from the back-end test in the first example. Both tests have to pass, so the lower one governs and this applicant is capped by housing, not by total debt. Compare the two on the same footing to see where it goes: the back-end test left $3,220.00 for housing, the front-end test allows only $2,520.00, and that gap in the monthly budget is the whole distance between $430,333.43 and $319,585.86 of borrowing power.

The same applicant after a one percentage point rate rise

Nothing about the applicant changes. Gross pay is still $9,000, other debts still $650, tax and insurance still $500, the limit still 43 percent, the term still 30 years and the deposit still $60,000. The mortgage rate goes from 6.5 percent to 7.5 percent. What happens to the ceiling?

  1. The budget is untouched, because it comes from income and debts rather than from the rate: $3,870.00 of total debt, $3,220.00 for housing, $2,720.00 for principal and interest.
  2. Only the factor changes. At 7.5 percent the period rate is exactly i=0.075/12=0.00625i = 0.075/12 = 0.00625, so nothing is lost to rounding this time, and 1−(1.00625)−3600.00625≈143.01763\frac{1 - (1.00625)^{-360}}{0.00625} \approx 143.01763.
  3. Multiply the same budget by the smaller factor: 2720×143.017632720 \times 143.01763, which is $389,007.95.
  4. Add the deposit: $389,007.95 plus $60,000 gives $449,007.95.

The same $2,720.00 a month now borrows $389,007.95 rather than $430,333.43, and the price ceiling falls from $490,333.43 to $449,007.95. One percentage point on the rate took about 9.6 percent off what the rule would lend and about 8.4 percent off the price, the smaller share because the deposit does not move, with no change to income, to debts or to savings. It is the single fastest way for a buyer to lose ground while doing nothing wrong.

Common questions

Is this the amount I should borrow?

No. It is the largest loan a debt-to-income rule would allow on the figures you type. On the first sheet that ceiling is $430,333.43. The test uses gross pay and a single ratio, so it takes no account of tax, childcare, or a saving rate.

Why does the deposit barely move the loan size?

Because the loan is set by the principal-and-interest budget, and the deposit is added at the end. $60,000 down turns a $430,333.43 loan into a $490,333.43 price, dollar for dollar. It does not raise what the ratio will lend.

What counts as other monthly debts?

In United States underwriting, the required payments a lender will find on a credit report: car loans and leases, student loans, personal loans, card minimums, court-ordered support, and any other loan that will still be open. Utilities and groceries are not in the ratio, which is one reason a passing ratio can still be a tight month.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.