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How PITI works on a mortgage

PITI is the housing payment: principal, interest, tax and insurance. On $9,000 a month at a 43 percent back-end cap, PITI is $3,220.00. After $500 of tax and insurance, $2,720.00 is left for principal and interest.

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.

On this page

Next on Buying a home

Debt-to-income

In short

  • PITI is principal, interest, tax and insurance, which is the housing payment in underwriting. On $9,000 a month at 43 percent, after $650 of other debts, PITI is $3,220.00.
  • Tax and insurance of $500 sit inside that $3,220.00. What is left for principal and interest is $2,720.00, which at 6.5 percent over 30 years is a loan of $430,333.43.
  • A 28 percent front-end test caps PITI on its own at $2,520.00. After the same $500, principal and interest are $2,020.00 and the loan is $319,585.86.
  • Hold PITI still and raise the rate to 7.5 percent. The housing payment does not move. The loan ceiling falls to $389,007.95, because the factor that turns principal and interest into a loan shrank.
  • How mortgage affordability works is the whole chain to a price. This page owns the housing payment in the middle of it.

Four letters, one housing payment

PITI is principal, interest, taxes and insurance. In United States underwriting it is the housing payment: what the back-end test has left after other debts, and what the front-end test caps on its own.

On $9,000 of gross monthly pay, 43 percent is $3,870.00 of total monthly debt. Subtract $650 of other debts and $3,220.00 is left for housing. That $3,220.00 is PITI. Subtract $500 of tax and insurance and $2,720.00 is left for principal and interest.

The mortgage affordability calculator on this page is that chain. Principal and interest are what the loan formula can support. Tax and insurance are the other two letters, and they come out before the formula runs.

How mortgages work is the loan those letters sit on. How amortisation works is how principal and interest split over time.

Front-end PITI is a different cap

A 28 percent front-end rule caps housing alone. On the same $9,000, PITI cannot exceed $2,520.00. 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.

Both tests have to pass. Here the front-end cap on PITI is the binding one: $2,520.00 against $3,220.00 of back-end housing room. Front-end against back-end DTI is that pair. How debt-to-income works is the ratio without a loan size.

The rate moves the loan, not PITI

Hold gross pay at $9,000, other debts at $650, tax and insurance at $500, the limit at 43 percent. PITI is still $3,220.00. Principal and interest are still $2,720.00. Raise the mortgage rate from 6.5 percent to 7.5 percent.

The housing payment does not move. Only the factor that turns $2,720.00 into a loan shrinks. The ceiling falls from $430,333.43 to $389,007.95. PITI is a budget. The loan is a present value of that budget.

Tax and insurance are inside the letters

A listing's tax and insurance are not a side bill in this test. They sit in PITI. Raise them and principal and interest fall one for one, so the loan falls. A $500 line on this sheet is why $3,220.00 of housing is not $3,220.00 of loan payment.

How PMI works is a third housing add-on when the loan is above 80 percent of value. On a teaching sheet it often sits in the same tax-and-insurance box. Take it out after 20 percent equity and PITI shrinks, which hands the saving back as principal-and-interest room.

PITI is not a household budget

The test uses gross pay. It does not know tax, childcare, or a saving rate. A file can clear a 43 percent PITI cap and still be a tight month. The 50/30/20 split is a leftover question, asked after a payment exists.

A lender's PITI ceiling is not a reason to buy. Renting against buying is the comparison once a loan size exists.

What this page is not doing

It is not the amount a household should borrow, not residual income, and not tax quoted from a listing. The three sheets are the 43 percent PITI of $3,220.00 (loan $430,333.43), the 28 percent PITI of $2,520.00 (loan $319,585.86), and the same $3,220.00 of PITI at 7.5 percent (loan $389,007.95). This is educational material, not financial advice.

Worked examples

PITI on \$9,000 a month at 43 percent

Gross pay is $9,000 a month. Other debts take $650. Property tax and insurance run $500 a month. The lender works to a 43 percent back-end limit, 30 years at 6.5 percent, $60,000 down. What is PITI, and what loan does that leave?

  1. Apply the limit to gross pay: 0.43×90000.43 \times 9000 is $3,870.00 of total monthly debt allowed.
  2. Subtract other debts: $3,870.00 minus $650 leaves $3,220.00 for housing. That is PITI.
  3. Subtract tax and insurance: $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, and n=360n = 360. The factor 1−(1+i)−360i≈158.21082\frac{1 - (1 + i)^{-360}}{i} \approx 158.21082.
  5. Multiply: 2720×158.210822720 \times 158.21082, which is $430,333.43.
  6. Add the deposit: $430,333.43 plus $60,000 is a price of $490,333.43.

PITI is $3,220.00. Principal and interest are $2,720.00. The rule stops at a loan of $430,333.43, which with $60,000 down is a price of $490,333.43.

Front-end PITI on the same income

A 28 percent front-end rule caps housing on its own. Same $9,000, same $500 of tax and insurance, same 30 years at 6.5 percent, same $60,000 deposit. Other debts play no part. What is PITI?

  1. Front-end PITI: 0.28×90000.28 \times 9000 is $2,520.00.
  2. Tax and insurance still come out: $2,520.00 minus $500 leaves $2,020.00 for principal and interest.
  3. Apply the same factor: 2020×158.210822020 \times 158.21082, which is $319,585.86.
  4. Add the deposit: $319,585.86 plus $60,000 gives $379,585.86.

Front-end PITI is $2,520.00. Principal and interest are $2,020.00. The housing test allows a loan of $319,585.86 and a price of $379,585.86. Both tests have to pass, so the lower loan governs.

The same PITI after a one point rate rise

Nothing about the applicant changes. PITI is still the 43 percent housing room. The mortgage rate goes from 6.5 percent to 7.5 percent. What happens to the loan?

  1. PITI is untouched: $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, i=0.075/12=0.00625i = 0.075/12 = 0.00625, and 1−(1.00625)−3600.00625≈143.01763\frac{1 - (1.00625)^{-360}}{0.00625} \approx 143.01763.
  3. Multiply the same principal-and-interest budget: 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.

PITI is still $3,220.00. The same $2,720.00 a month now borrows $389,007.95 rather than $430,333.43. The housing payment did not move. The present-value factor did.

Common questions

Is PITI the same as the loan payment?

No. PITI is housing: principal, interest, tax and insurance. On the first sheet that is $3,220.00. The loan payment is the principal-and-interest piece, $2,720.00, after tax and insurance come out.

Does a higher rate raise PITI?

Not in this test. PITI is set by income, other debts and the DTI cap. A higher rate shrinks the loan that the leftover principal and interest can support. On the third sheet PITI stays $3,220.00 and the loan falls to $389,007.95.

Where does PMI sit?

In the housing payment, often in the same box as tax and insurance on a teaching sheet. How PMI works is that line. Taking it out after 20 percent equity shrinks PITI and hands the saving back as principal-and-interest room.

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.