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LTV vs DTI

Loan-to-value is the loan divided by the property value. Debt-to-income is monthly debt payments divided by gross pay. On a $400,000 home with $20,000 down, LTV is 95 percent. On debts of $2,400.17 against $7,500 of pay, DTI is 32.00 percent. Two ceilings, two teaching sheets.

 Loan-to-valueDebt-to-income
FormulaLoan / property value.Monthly debt payments / gross monthly income.
Teaching sheet$380,000 loan on a $400,000 home is 95 percent LTV. PMI is $190 a month for 124 months, $23,560 in total.$2,400.17 of debts on $7,500 of pay is 32.00 percent DTI. Room under 43 percent is $824.83 a month.
What it asksHow much of the property is borrowed.Whether the payments fit inside pay.
What it does not knowWhether the payment is affordable. A 95 percent LTV can sit on a small loan or a large one.How large a down payment you brought. A 32 percent DTI can sit on any LTV.
The usual US switch80 percent LTV is the conventional PMI cancellation point on original price.43 percent DTI is the figure most often quoted as the edge of a mainstream mortgage.
When you would pick itAsking whether PMI is on, which is how PMI works.Asking whether a lender will underwrite the payment, which is how debt-to-income works.
On this page

A collateral ratio, against a payment ratio

LTV is principal over collateral. On a $400,000 home with $20,000 down the loan is $380,000 and starting LTV is 95 percent. Conventional private mortgage insurance on that sheet is $190 a month for 124 months, $23,560 in total, on top of a $2,401.86 principal-and-interest payment. The PMI calculator returns starting LTV alongside that rider.

DTI is payments over pay. Housing of $1,580.17 plus a car of $450, student loans of $220 and card minimums of $150 is $2,400.17 a month. Against $7,500 of gross pay that is 32.00 percent, with $824.83 of room under a 43 percent limit. The debt-to-income calculator is that identity.

Those are two teaching sheets, not one applicant. A 95 percent LTV does not imply a 32 percent DTI, and a 32 percent DTI does not imply a 95 percent LTV. How loan-to-value works is the collateral ratio. How debt-to-income works is the payment ratio. Front-end against back-end DTI splits housing from the rest of the debts.

Two ceilings, two different failures

A file can clear DTI and fail LTV: the payment fits, but the down payment is thin, so PMI is on. A file can clear LTV and fail DTI: 20 percent down, no PMI, and still too much car and card payment against pay.

Folding the PMI rate into the loan rate and amortising it for 30 years describes a different loan, one whose extra charge lasts the whole term instead of stopping at 80 percent LTV. Adding a new car payment into a 32.00 percent DTI is judged on what it does to this ratio, not on the car in isolation.

This is educational material, not financial advice, and not an underwriting decision.

Worked examples

5 percent down on a \$400,000 home

Home $400,000, down payment $20,000, rate 6.5 percent, 30 years, PMI 0.60 percent of the original loan. Monthly PMI, months of PMI, total PMI?

  1. Loan: 400000−20000=380000400000 - 20000 = 380000, so $380,000. Starting LTV: 95 percent.
  2. Monthly PMI: 380000×0.006/12=190380000 \times 0.006 / 12 = 190, so $190.
  3. Scheduled principal and interest: $2,401.86.
  4. The balance reaches 80 percent of $400,000, which is $320,000, in month 124. Total PMI: 124×190=23560124 \times 190 = 23560.

Monthly PMI is $190 for 124 months, $23,560 in total, on a $380,000 loan whose scheduled payment is $2,401.86. Starting loan-to-value is 95 percent.

Back-end DTI on \$7,500 a month

Your housing payment is $1,580.17, the car loan takes $450, student loans take $220 and card minimums take $150. Gross pay is $7,500 a month. What is your DTI, and how much room is left under a 43 percent limit?

  1. Add the required monthly payments: $1,580.17 + $450 + $220 + $150 = $2,400.17.
  2. Divide by gross monthly income: 2400.177500=0.3200\frac{2400.17}{7500} = 0.3200.
  3. Multiply by 100 to read it as a percentage: 32.00 percent.
  4. Find the ceiling at the limit: 0.43×7500=0.43 \times 7500 = $3,225.00 of monthly debt.
  5. Take the debts off the ceiling: $3,225.00 minus $2,400.17 = $824.83.

The DTI is 32.00 percent. At a 43 percent limit the ceiling is $3,225.00 of monthly payments, so there is $824.83 a month of room left, which is what a new loan would have to fit inside.

20 percent down on the same \$400,000 home

Home $400,000, down $80,000, same 6.5 percent 30-year loan, PMI rate 0.60 percent. How many months of PMI, and what is the loan?

  1. Loan: 400000−80000=320000400000 - 80000 = 320000, so $320,000. Starting LTV: 80 percent.
  2. The balance is already at the 80 percent threshold, so months of PMI is 0 and total PMI is $0.

Months of PMI is 0 because a $320,000 loan on a $400,000 home is already 80 percent LTV. That is the collateral switch. It says nothing about DTI on the other teaching sheet.

Common questions

Does a high LTV mean a high DTI?

No. LTV is a down-payment fact. DTI is a payment-against-pay fact. A small loan on a cheap house can be 95 percent LTV with an easy DTI. A large loan on a 20 percent down payment can clear LTV and fail DTI.

Which one turns PMI on?

LTV. Conventional PMI in the United States is typically charged until the amortised balance hits 80 percent of original price. DTI does not switch that rider.

Are these the same borrower?

Not on this page. The 95 percent LTV is a $400,000 purchase sheet. The 32.00 percent DTI is a $7,500 pay sheet. They are the two ceilings a file has to clear, shown on the sheets this site has already verified.

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.