NMLS Mortgage Math Cheat Sheet: LTV, DTI, PITI, APR, and Points

Reviewed by the NMLSApproved team
Last updated: July 15, 2026

Mortgage math is one of the most manageable parts of the NMLS SAFE MLO exam once you know which formula the question is testing.

Most exam problems do not require advanced mathematics. They test whether you can identify the correct numbers, choose the correct formula, and avoid common traps—such as using the sales price when the appraised value is lower.

This NMLS mortgage math cheat sheet covers the formulas and calculations you are most likely to need: loan-to-value ratio (LTV), debt-to-income ratio (DTI), PITI, discount points, qualifying monthly income, and the difference between APR and the note rate.

Mortgage math formulas at a glance

How to calculate LTV

Loan-to-value ratio compares the loan amount with the value of the property securing the loan.

For a purchase transaction, exam questions commonly use the lower of the sales price or appraised value as the property value. For a refinance, the appraised value is generally used unless the question gives another specific instruction.

LTV example 1: straightforward purchase

The sales price is $250,000, the appraised value is $255,000, and the loan amount is $200,000.

Use the lower value: $250,000.

LTV example 2: appraisal is lower

The sales price is $300,000, the appraisal is $290,000, and the loan amount is $261,000.

Use $290,000 because it is lower than the sales price.

Reverse the LTV formula to find a loan amount

Some questions give you the maximum LTV and ask for the maximum loan amount.

If a property is worth $240,000 and the maximum LTV is 80%:

How to calculate DTI

Debt-to-income ratio compares monthly debt obligations with gross monthly income. Gross income means income before taxes and other deductions.

Two related ratios may appear:

• The housing expense ratio, sometimes called the front-end ratio.
• The total debt-to-income ratio, sometimes called the back-end ratio.

DTI example

A borrower has gross monthly income of $6,000. The proposed monthly housing expense is $1,500. The borrower also has a $400 auto payment and a $200 minimum credit-card payment.

Housing expense ratio:

Total monthly obligations:

$1,500 + $400 + $200 = $2,100

Total DTI:

Do not automatically include every household expense in DTI. Exam questions generally focus on the housing obligation and recurring debts identified in the scenario. Read the wording carefully before deciding which payments belong in the numerator.

Also avoid treating one ratio limit as universal. Acceptable ratios can vary by loan program, underwriting system, compensating factors, and current guidelines. The exam may provide the applicable ratio in the question.

What PITI means

PITI stands for:

• Principal.
• Interest.
• Taxes.
• Insurance.

Principal reduces the loan balance. Interest is the lender’s charge for borrowing. Taxes usually refer to property taxes. Insurance generally includes homeowners insurance.

The basic formula is:

When determining the full monthly housing expense, a question may also include mortgage insurance, homeowners association dues, or another required housing obligation. Those items are not letters in the acronym PITI, but they may still be part of the qualifying housing expense if the scenario includes them.

PITI example

A proposed payment includes:

• Principal and interest: $1,260.
• Property taxes: $310.
• Homeowners insurance: $120.

If the question also gives $140 in monthly mortgage insurance, the total qualifying housing expense would be $1,830 unless the question instructs otherwise.

How to calculate discount points

A discount point equals 1% of the loan amount—not 1% of the sales price.

Discount points example

A borrower obtains a $225,000 loan and pays 2 discount points.

The two points cost $4,500.

Discount points are prepaid interest and may be used to obtain a lower interest rate. Do not assume that one point always lowers the rate by a fixed amount. The pricing effect varies by lender, market, and loan.

Combined LTV and points example

A home sells for $200,000, the loan has a 75% LTV, and the borrower pays 2 points.

First calculate the loan amount:

$200,000 × 0.75 = $150,000

Then calculate the points:

The points cost $3,000.

How to convert income to a monthly amount

Mortgage qualification uses gross monthly income, so exam questions may require converting weekly, biweekly, semimonthly, hourly, or annual pay.

Weekly-income example

A borrower earns $750 per week.

Do not multiply weekly income by four. A year has 52 weeks, so the accurate monthly conversion uses 52 ÷ 12, or approximately 4.333 weeks per month.

Biweekly-income example

A borrower receives $2,000 every two weeks.

Biweekly and semimonthly are not the same. Biweekly pay produces 26 checks per year; semimonthly pay produces 24.

APR vs interest rate

The note rate is the interest rate stated in the loan note. APR is a broader measure of the cost of credit expressed as an annual rate. It reflects the interest rate plus certain finance charges and is commonly higher than the note rate.

For most SAFE exam questions, focus on the concept rather than trying to calculate APR from scratch unless the question provides a specific method and all required information.

Remember:

• Note rate helps determine interest charged and the principal-and-interest payment.
• APR helps consumers compare the broader cost of credit.
• Finance charge expresses the cost of credit as a dollar amount.
• APR expresses covered credit cost as an annual percentage.

For a deeper explanation of TILA and APR, review RESPA vs TILA vs TRID.

Common NMLS mortgage math mistakes

Using the wrong property value for LTV

For a purchase, look for the lower of the sales price or appraised value unless the question tells you to use something else.

Using net income in DTI

DTI generally uses gross monthly income, not take-home pay.

Dividing weekly pay by the wrong number

Use weekly pay × 52 ÷ 12—not weekly pay × 4.

Calculating points from the sales price

Points are based on the loan amount.

Treating APR and note rate as identical

APR reflects certain costs beyond the note rate.

Rounding too early

Keep several decimal places during the calculation and round at the end unless the question gives a specific rounding instruction.

Five practice problems

Try these before checking the answers.

1. A property sells for $280,000, appraises for $275,000, and has a $247,500 loan. What is the LTV?
2. A borrower has $7,500 in gross monthly income, a $1,900 housing expense, a $450 auto payment, and $275 in other recurring debt. What is the total DTI?
3. A $180,000 loan charges 1.5 points. What is the cost of the points?
4. A borrower earns $1,100 per week. What is the gross monthly income?
5. Principal and interest are $1,420, property taxes are $360, and homeowners insurance is $140. What is PITI?

Answers

1. $247,500 ÷ $275,000 = 90% LTV.
2. ($1,900 + $450 + $275) ÷ $7,500 = 35% total DTI.
3. $180,000 × 0.015 = $2,700.
4. $1,100 × 52 ÷ 12 = $4,766.67 gross monthly income.
5. $1,420 + $360 + $140 = $1,920 PITI.

FAQ

Is there a lot of math on the NMLS exam?

Mortgage math is only one part of the broader exam, but candidates should be comfortable with common calculations such as LTV, DTI, income conversion, PITI, and points. The difficulty usually comes from choosing the correct inputs, not advanced arithmetic.

Can I use a calculator on the SAFE MLO exam?

Yes. At a Prometric test center, the Test Center Administrator provides a four-function basic calculator and writing materials. Personal calculators are not permitted. The official NMLS MLO Testing Handbook confirms this test-day policy. You should still practice setting up each problem yourself because the calculator cannot choose the correct formula.

What mortgage math formulas should I memorize?

Prioritize LTV, housing expense ratio, total DTI, point cost, and monthly-income conversions. Also understand what PITI and APR mean.

Is one discount point always equal to a 0.25% rate reduction?

No. One point always costs 1% of the loan amount, but the interest-rate reduction associated with a point is not fixed.

Should HOA dues and mortgage insurance be included in PITI?

They are not represented by the letters in PITI. However, they may be included in the total qualifying housing expense when applicable. Follow the wording of the exam question.

Final review

The safest way to approach NMLS mortgage math is to slow down before calculating:

1. Identify what the question asks you to find.
2. Write the formula.
3. Select only the relevant numbers.
4. Calculate without rounding too early.
5. Check whether the answer should be dollars or a percentage.

Once those steps become automatic, mortgage math turns into a high-confidence part of your exam preparation.