Loan-to-Value, Down Payment and Qualifying Math

These formulas organize the math. They do not establish that an applicant will receive a loan.

What formulas should students know?

Write percentages as decimals while calculating. An 80% LTV is 0.80, and a 35% ratio is 0.35.

Official source map

The New York State Department of State 77-hour curriculum lists Basic Mortgage Qualifying under Subject 10, Real Estate Mathematics. Real Estate Finance separately covers mortgage concepts, the primary and secondary markets, financing instruments and government programs.

The Department of State salesperson page says the multiple-choice examination is based on that curriculum and allows 1 1/2 hours after instructions. The Department does not publish an official number or percentage of mortgage-math questions.

The Consumer Financial Protection Bureau defines loan-to-value ratio as a comparison of the amount financed with the property's appraised value. It explains that a larger down payment lowers LTV.

The CFPB defines debt-to-income ratio as all monthly debt payments divided by gross monthly income. Current Regulation Z requires creditors covered by its ability-to-repay rule to consider and verify relevant income or assets and debt obligations. Its official interpretation of section 1026.43 does not prescribe one specific DTI ratio for every covered transaction.

What is loan-to-value ratio?

LTV shows the loan amount as a percentage of the stated property value:

LTV = Loan amount ÷ Property value

Multiply the decimal result by 100 to state a percentage.

Example 1: Calculate LTV

A property has a stated value of $500,000 and a $400,000 loan.

LTV = $400,000 ÷ $500,000 = 0.80

LTV = 80%

The loan-to-value ratio is 80%.

The remaining 20% is the difference between the stated value and the loan amount. Do not automatically call that amount the borrower's cash down payment because equity, other liens, financed costs or a difference between price and value may change the relationship.

Which value belongs in the LTV denominator?

Use the value identified in the problem. The CFPB describes mortgage LTV using appraised value. A loan program may apply more detailed rules when purchase price and appraised value differ.

For an educational question:

• if it says “loan-to-appraised-value,” use appraised value
• if it supplies one value and calls it the value for LTV, use that number
• if it provides a program rule such as “use the lower of price or appraised value,” follow that rule
• if it gives price and value but no rule, do not invent the denominator

Example 2: Follow the stated base

A problem says to calculate LTV using a $620,000 appraised value. The loan is $465,000.

LTV = $465,000 ÷ $620,000 = 0.75 = 75%

The LTV is 75% under the denominator specified by the problem.

How do you calculate the loan amount from LTV?

Use:

Loan amount = Property value × LTV

Example 3

A lender in a simplified problem will make a loan at 78% of a stated $450,000 value.

Loan amount = $450,000 × 0.78

Loan amount = $351,000

The indicated loan amount is $351,000.

This result applies the stated ratio. It does not account for closing costs, program limits or underwriting requirements that the problem does not provide.

How do you calculate value from loan amount and LTV?

Rearrange the formula:

Property value = Loan amount ÷ LTV

Example 4

A $408,000 loan represents 80% of the value used in the problem.

Property value = $408,000 ÷ 0.80

Property value = $510,000

Check:

$408,000 ÷ $510,000 = 0.80

The stated value is $510,000.

For help identifying the base and rate, review Part, Rate and Whole for New York Real Estate Math.

How do you calculate a down payment amount?

In a basic purchase problem with one loan and no other financed amount:

Down payment = Purchase price - Loan amount

Example 5: Dollar down payment

A buyer agrees to a $600,000 purchase price and obtains a $480,000 loan. The problem states no other financing adjustment.

Down payment = $600,000 - $480,000 = $120,000

The down payment is $120,000.

Do not subtract the loan from appraised value when the question asks for cash applied to the purchase price. Price and value serve different roles.

How do you calculate down payment percentage?

Use:

Down payment percentage = Down payment ÷ Purchase price

Example 6

A buyer pays $87,500 down on a $500,000 purchase.

$87,500 ÷ $500,000 = 0.175

Down payment = 17.5%

The down payment is 17.5% of the purchase price.

How do you calculate a loan from down payment percentage?

If the down payment and loan together equal the purchase price:

Loan rate = 1.00 - Down payment rate

Loan amount = Purchase price × Loan percentage

Example 7

A buyer makes a 12% down payment on a $425,000 purchase.

Down payment = $425,000 × 0.12 = $51,000

Loan amount = $425,000 - $51,000 = $374,000

The down payment is $51,000 and the loan amount is $374,000.

The shortcut is $425,000 × 0.88 = $374,000 because 88% remains after a 12% down payment.

Does an 80% LTV necessarily mean a 20% down payment?

No. Those percentages complement each other only when the purchase price and LTV value are the same base, one loan finances the balance, and no other amount changes the relationship.

Example 8: Price and value differ

A property has a $520,000 purchase price and a $500,000 value used for LTV. The loan is $400,000.

LTV:

$400,000 ÷ $500,000 = 80%

Down payment against price:

$520,000 - $400,000 = $120,000

$120,000 ÷ $520,000 = 23.0769...%

The LTV is 80%, but the down payment is approximately 23.08% of the purchase price. The denominators differ.

Is there one required down payment percentage?

No. The CFPB explains that down payment requirements vary by loan and lender. A larger down payment can affect LTV, rate, approval and mortgage-insurance requirements, but available options depend on the loan program and applicant.

Do not import a familiar percentage into a question. If the problem states 10%, use 10%. If it asks for the percentage, calculate it from the supplied price and down payment.

Also keep down payment separate from closing costs. Points, lender charges, prepaid items and reserves can require additional funds. Review Discount Points and Loan Charges for the New York Exam for those calculations.

What is gross monthly income?

Gross income is income before taxes and other deductions. When a problem gives gross annual income:

Gross monthly income = Gross annual income ÷ 12

Example 9

An applicant has $108,000 in stated gross annual income.

$108,000 ÷ 12 = $9,000

Gross monthly income is $9,000.

Do not divide net annual take-home pay by 12 when the problem asks for a ratio based on gross income.

Example 10: Combine stated monthly income

A problem supplies $7,200 in gross monthly salary and $1,100 in additional verified monthly income for the qualifying calculation.

Total stated gross monthly income = $7,200 + $1,100 = $8,300

Use only income the problem says qualifies. Real underwriting requires documentation and program-specific treatment of income.

What is a housing expense ratio?

A basic housing expense ratio compares the monthly housing expense specified by the problem with gross monthly income:

Housing expense ratio = Monthly housing expense ÷ Gross monthly income

The housing amount may include principal, interest, property taxes and insurance. Depending on the question or underwriting rule, it can also include mortgage insurance, association dues or other housing obligations.

The CFPB identifies principal, interest, taxes and insurance as PITI. Read the list supplied by the problem rather than assuming PITI is the complete monthly obligation in every case.

Example 11: Calculate a housing ratio

A problem states a $2,700 total monthly housing expense and $9,000 gross monthly income.

$2,700 ÷ $9,000 = 0.30 = 30%

The stated housing expense ratio is 30%.

Is 28% a mandatory mortgage limit?

No. A CFPB home-loan toolkit describes 28% as a mortgage-lending rule of thumb for a consumer budgeting exercise and expressly notes that lenders may approve more or less. It is not a universal New York exam rule or federal approval cutoff.

Use 28%, 30% or any other housing ratio only when the educational problem supplies it. A ratio can be useful for calculating a maximum amount without becoming a legal entitlement or approval standard.

How do you find maximum housing expense from a stated ratio?

Use:

Maximum housing expense = Gross monthly income × Stated housing ratio

Example 12

A problem instructs you to apply a 30% housing ratio to $8,500 gross monthly income.

$8,500 × 0.30 = $2,550

The maximum monthly housing expense under that stated ratio is $2,550.

This does not prove the applicant qualifies. It answers the specified ratio calculation.

What is debt-to-income ratio?

The CFPB formula is:

DTI = All monthly debt payments ÷ Gross monthly income

Multiply by 100 to state the result as a percentage.

Example 13: Calculate total DTI

An applicant has:

• proposed monthly housing expense: $2,450
• auto loan payment: $425
• student loan payment included by the problem: $275
• credit-card payment included by the problem: $150
• gross monthly income: $9,500

First total the included debts:

$2,450 + $425 + $275 + $150 = $3,300

Then calculate DTI:

$3,300 ÷ $9,500 = 0.347368...

The total DTI is approximately 34.74%.

Which monthly expenses belong in DTI?

Use the obligations the question identifies. In real underwriting, Regulation Z and a loan program can specify how to treat the proposed transaction payment, simultaneous loans, mortgage-related obligations, existing debts, alimony, child support and income.

Do not automatically include ordinary living expenses such as groceries in a classroom DTI numerator unless the problem directs you to do so. Do not automatically exclude an obligation merely because it has a familiar label. The facts and applicable rule control.

The mathematical workflow is:

1. total the included monthly debt payments
2. divide by gross monthly income
3. convert the decimal to a percentage

Is there one universal DTI limit?

No. The CFPB says different loan products and lenders have different DTI limits. Current Regulation Z requires consideration of DTI or residual income in covered ability-to-repay analysis but does not set one DTI ratio for every covered loan.

Older material may refer to a 43% General Qualified Mortgage threshold. The CFPB's later rule replaced that fixed General QM DTI limit with price-based thresholds. Do not present 43% as the current universal mortgage limit.

For exam math, a question can validly provide a hypothetical maximum such as 38% or 42%. Treat it as a stated input for that problem, not a statewide or federal constant.

How do you find maximum total debt from a stated DTI?

Use:

Maximum total monthly debt = Gross monthly income × Stated DTI

Example 14

A problem applies a 40% total DTI limit to $10,000 gross monthly income.

$10,000 × 0.40 = $4,000

The maximum total monthly debt under the problem's stated ratio is $4,000.

If the applicant already has $1,150 in other included monthly debt:

$4,000 - $1,150 = $2,850

The amount remaining for the proposed housing obligation under that stated DTI is $2,850.

How do two stated qualifying ratios work together?

A simplified problem may provide both:

• a maximum housing expense ratio
• a maximum total DTI ratio

Calculate both limits. The lower allowable housing amount controls within that simplified comparison.

Example 15: Apply both stated limits

A problem provides:

• gross monthly income: $8,000
• housing ratio: 30%
• total DTI ratio: 40%
• other included monthly debt: $1,050

Housing-ratio limit:

$8,000 × 0.30 = $2,400

Total-debt limit:

$8,000 × 0.40 = $3,200

Amount remaining after other debt:

$3,200 - $1,050 = $2,150

The housing ratio permits $2,400, but the total DTI calculation leaves $2,150. Under the two stated ratios, $2,150 is the lower allowable housing amount.

This is a simplified screening calculation. A real creditor applies the loan program, verified data, payment calculation and underwriting requirements.

What happens when other monthly debt changes?

Other included debt affects total DTI but does not change a housing-only ratio if income and housing expense stay the same.

Example 16

Gross monthly income is $9,000 and proposed housing expense is $2,700.

Housing ratio:

$2,700 ÷ $9,000 = 30%

If other monthly debt is $900:

Total DTI = ($2,700 + $900) ÷ $9,000 = 40%

If the other debt falls to $450:

Total DTI = ($2,700 + $450) ÷ $9,000 = 35%

The housing ratio remains 30%, while total DTI changes.

Is LTV the same as DTI?

No.

LTV uses property and loan dollars. DTI uses monthly payment and monthly income dollars. Do not place a property value in a DTI formula or gross income in an LTV formula.

Is qualifying math the same as affordability?

No. A lender's approval analysis and a household's comfortable budget answer different questions. The CFPB warns consumers to consider the total monthly payment and other costs, not only the amount a lender may be willing to lend.

An applicant can satisfy a stated classroom ratio and still face property taxes, insurance, maintenance, utilities, association charges, closing costs and other financial needs. This article teaches exam relationships, not personalized borrowing advice.

What are the most common mistakes?

Dividing value by loan amount

LTV is loan divided by value. Reversing the order can produce a ratio greater than the full stated value in an ordinary example.

Using purchase price as the LTV denominator without instruction

Use the value or program base named in the problem.

Treating LTV and down payment percentage as automatic complements

They complement each other only when they use the same base and the financing facts support it.

Using net income instead of gross income

DTI uses gross monthly income under the CFPB definition.

Dividing annual debt by monthly income

Match the periods. Convert annual income to monthly income before using monthly debt payments.

Omitting the proposed housing payment from total DTI

Total DTI includes the monthly debts identified by the problem, including the proposed housing obligation when stated.

Applying a memorized ratio

Use the ratio supplied by the question. There is no single universal approval cutoff.

Returning a percentage as a dollar answer

Check whether the question asks for LTV, loan amount, down payment, maximum payment or income.

Treating the result as loan approval

Basic math does not account for every underwriting, documentation, collateral or program requirement.

What is a reliable exam-day workflow?

1. Circle the requested amount or ratio.
2. Label purchase price, property value, loan, income and monthly debts separately.
3. Convert annual income to monthly income when needed.
4. Use the base named in the question.
5. Convert percentages to decimals.
6. Calculate each ratio separately.
7. If two qualifying limits are supplied, choose the lower allowable amount.
8. Reverse the formula and estimate the result.

Quick check: a loan smaller than the stated value ordinarily produces an LTV below the full-value ratio. A $400,000 loan on $500,000 value should be 80%, not 125%.

Use the New York real estate math formula map and the Real Estate Mathematics study guide to connect these ratios with interest, points, commissions, taxes and closing math.

Can you solve these original practice questions?

Practice 1

A $420,000 loan is based on a stated property value of $560,000. What is the LTV?

A. 25%
B. 75%
C. 80%
D. 133.33%

Answer: B. $420,000 ÷ $560,000 = 0.75, or 75%.

Practice 2

A problem permits an 82% LTV on a stated $625,000 value. What loan amount does that ratio produce?

A. $112,500
B. $512,500
C. $518,750
D. $762,195

Answer: B. $625,000 × 0.82 = $512,500.

Practice 3

A buyer purchases for $480,000 and obtains a $408,000 loan. No other financing adjustment is stated. What is the down payment?

A. $40,800
B. $72,000
C. $81,600
D. $88,000

Answer: B. $480,000 - $408,000 = $72,000.

Practice 4

An applicant has $126,000 in gross annual income. What is gross monthly income?

A. $8,750
B. $10,000
C. $10,500
D. $12,600

Answer: C. $126,000 ÷ 12 = $10,500.

Practice 5

A problem states $2,850 in monthly housing expense and $9,500 in gross monthly income. What is the housing ratio?

A. 27%
B. 28.5%
C. 30%
D. 33.33%

Answer: C. $2,850 ÷ $9,500 = 0.30, or 30%.

Practice 6

An applicant has $2,600 in proposed monthly housing expense, $500 in an auto payment and $300 in other included monthly debt. Gross monthly income is $8,500. What is total DTI?

A. 30%
B. 36%
C. 40%
D. 45%

Answer: C. Total monthly debt is $2,600 + $500 + $300 = $3,400. $3,400 ÷ $8,500 = 0.40, or 40%.

Practice 7

A problem applies a 38% total DTI to $10,000 gross monthly income. Other included monthly debt is $900. How much remains for the proposed housing obligation under that ratio?

A. $2,900
B. $3,800
C. $4,700
D. $9,100

Answer: A. Maximum total debt is $10,000 × 0.38 = $3,800. Subtract $900 to leave $2,900.

Practice 8

Which statement is accurate?

A. Every mortgage uses the same DTI limit.
B. LTV equals value divided by loan.
C. Gross monthly income is gross annual income divided by 12.
D. An 80% LTV proves the cash down payment was 20% of purchase price.

Answer: C. DTI limits vary, LTV is loan divided by value, and LTV and down payment percentages may use different bases.

Frequently asked questions

What is the loan-to-value formula?

Divide the loan amount by the property value specified for the calculation, then multiply by 100 to express the result as a percentage.

How do I calculate a down payment?

In a basic one-loan purchase problem, subtract the loan amount from the purchase price. Divide that amount by price to find the down payment percentage.

Is an 80% LTV the same as a 20% down payment?

Only when LTV value and purchase price are the same base and no other financing fact changes the relationship.

What income is used for DTI?

The CFPB definition uses gross monthly income, meaning income before taxes and other deductions, with income eligibility and verification governed by the applicable underwriting rules.

What is included in total DTI?

Add the monthly debt payments and housing obligations identified by the problem, then divide by gross monthly income.

Is 28% a required housing ratio?

No. CFPB consumer material uses 28% as a budgeting rule of thumb and says lenders may approve more or less. Use a ratio only when the question supplies it.

Is 43% the universal mortgage DTI limit?

No. Current federal rules do not make 43% a universal limit for every mortgage. Lenders and loan products can use different thresholds and underwriting requirements.

Does passing the ratio calculation mean the loan is approved?

No. Approval can also depend on verified income, assets, debts, credit, collateral, program terms and other underwriting requirements.

Does New York publish an official number of qualifying-math questions?

No. The curriculum includes Basic Mortgage Qualifying, but the Department of State does not publish a topic-level question count or weighting.

Sources and verification notes

This article was checked against official sources available on August 27, 2026. Its ratios and scenarios are original educational examples, not loan offers or state examination questions.

• New York State Department of State, Real Estate Salesperson 77-Hour Curriculum
• New York State Department of State, Real Estate Salesperson
• Consumer Financial Protection Bureau, Loan-to-value ratio
• Consumer Financial Protection Bureau, Debt-to-income ratio
• Consumer Financial Protection Bureau, Regulation Z section 1026.43 and official interpretations
• Consumer Financial Protection Bureau, Down payments and mortgage terms
• Consumer Financial Protection Bureau, PITI
• Consumer Financial Protection Bureau, Your Home Loan Toolkit
• Consumer Financial Protection Bureau, Qualified Mortgage definition update

Use this lesson for education and exam preparation. For an actual mortgage, compare loan options and rely on the creditor's verified underwriting, disclosures and applicable program requirements.