Mortgage Math Formulas for the MLO Exam

Updated October 20, 2026

Know these cold: DTI = monthly debts ÷ gross monthly income. LTV = loan ÷ lesser of price or appraised value. CLTV = all liens ÷ value. Points = loan × points%. Daily interest = loan × rate ÷ 365 (or 360). ARM rate = index + margin, limited by the caps.

Formula sheet

Front-end (housing) ratio

Housing payment (PITI) ÷ gross monthly income

Example: $2,000 ÷ $7,000 = 28.6%

Back-end DTI

(PITI + all monthly debts) ÷ gross monthly income

Example: ($2,000 + $650) ÷ $7,000 = 37.9%

LTV

Loan amount ÷ lesser of purchase price or appraised value

Example: $270,000 ÷ $300,000 = 90%

CLTV

(1st lien + 2nd lien + other liens) ÷ value

Example: ($240,000 + $30,000) ÷ $300,000 = 90%

Discount points

Loan amount × number of points ÷ 100

Example: $250,000 × 1.5 ÷ 100 = $3,750

Prepaid (per diem) interest

Loan × rate ÷ 365 × days from closing through month-end, inclusive

Example: $300,000 × 6% ÷ 365 = $49.32/day; × 12 days = $591.78

Monthly income from hourly pay

Hourly rate × hours per week × 52 ÷ 12

Example: $25 × 40 × 52 ÷ 12 = $4,333.33

Biweekly pay to monthly

Paycheck × 26 ÷ 12

Example: $2,000 × 26 ÷ 12 = $4,333.33

ARM adjustment

New rate = index + margin, but no more than the start rate + periodic/initial cap, and no more than the lifetime cap

Example: Start 6%, 2/2/5 caps, margin 2.75%, index 5% → 7.75% fully indexed, capped at 8% → 7.75%

Monthly P&I payment

P × i ÷ (1 − (1 + i)^−n), where i = annual rate ÷ 12 and n = months

Example: $300,000 at 6% for 30 years → $1,798.65

Maximum loan from max LTV

Lesser of price or value × max LTV

Example: $400,000 × 96.5% = $386,000

Every example on this page was recomputed by script. Your exam calculator and rounding instructions on test day take priority.

Practice math questions

1. A borrower earns $11,750 gross per month. The proposed housing payment (PITI) is $2,250, and other monthly debts total $1,325. What is the front-end (housing) ratio?
  1. 30.4%
  2. 11.3%
  3. 21.6%
  4. 19.1%
Show answer and explanation

Answer: D. 19.1%
Correct — housing ÷ gross income = $2,250 ÷ $11,750 = 19.1%.

Source: CFPB: Debt-to-income ratio

2. Gross monthly income is $7,500. Proposed PITI is $1,600, a car payment is $390, and minimum credit card payments total $260. What is the back-end DTI?
  1. 21.3%
  2. 26.5%
  3. 30.0%
  4. 35.0%
Show answer and explanation

Answer: C. 30.0%
Correct — (PITI + all monthly debts) ÷ gross income = $2,250 ÷ $7,500 = 30.0%.

Source: CFPB: Debt-to-income ratio

3. Purchase price $885,000, appraised value $870,000, loan amount $739,500. What is the LTV?
  1. 85.0%
  2. 83.6%
  3. 15.0%
  4. 87.5%
Show answer and explanation

Answer: A. 85.0%
Correct — LTV uses the lesser of price or appraised value: $739,500 ÷ $870,000 = 85.0%.

Source: HUD Handbook 4000.1 II.A (Adjusted Value = lesser of price or value)

4. A home is valued at $620,000. The borrower has a first mortgage of $496,000 and a second mortgage of $62,000. What is the CLTV?
  1. 80.0%
  2. 10.0%
  3. 90.0%
  4. 95.0%
Show answer and explanation

Answer: C. 90.0%
Correct — CLTV = all liens ÷ value = $558,000 ÷ $620,000.

Source: CFPB: Loan-to-value ratio (CLTV applies the same ratio to all liens)

5. How much do 2.5 discount points cost on a $250,000 loan?
  1. $6,250.00
  2. $625.00
  3. $8,750.00
  4. $62,500.00
Show answer and explanation

Answer: A. $6,250.00
Correct — 1 point = 1% of the loan amount: $250,000 × 2.5% = $6,250.00.

Source: CFPB: Points and lender credits

6. On a $610,000 purchase, the program allows a maximum 95% LTV. What is the maximum loan amount and the minimum down payment?
  1. $549,000 loan; $61,000 down
  2. $30,500 loan; $579,500 down
  3. $579,500 loan; $30,500 down
  4. $610,000 loan; $0 down
Show answer and explanation

Answer: C. $579,500 loan; $30,500 down
Correct — $610,000 × 95% = $579,500, leaving $30,500 down.

Source: HUD Handbook 4000.1 II.A (Adjusted Value = lesser of price or value)

7. On a $350,000 purchase, the program allows a maximum 96.5% LTV. What is the maximum loan amount and the minimum down payment?
  1. $320,250 loan; $29,750 down
  2. $337,750 loan; $12,250 down
  3. $12,250 loan; $337,750 down
  4. $350,000 loan; $0 down
Show answer and explanation

Answer: B. $337,750 loan; $12,250 down
Correct — $350,000 × 96.5% = $337,750, leaving $12,250 down.

Source: HUD Handbook 4000.1 II.A (Adjusted Value = lesser of price or value)

8. A borrower earns $24.00 an hour and consistently works 36 hours a week. What is the gross monthly income?
  1. $3,456.00
  2. $3,744.00
  3. $44,928.00
  4. $1,872.00
Show answer and explanation

Answer: B. $3,744.00
Correct — $24.00 × 36 × 52 weeks ÷ 12 = $3,744.00.

Source: 12 CFR 1026.43(c)(2)(i)

9. A $540,000 loan at 7% closes on June 19. Prepaid interest is charged from the closing date through June 30, inclusive, using a 365-day year. What is the prepaid interest?
  1. $1,139.18
  2. $1,242.74
  3. $3,150.00
  4. $1,346.30
Show answer and explanation

Answer: B. $1,242.74
Correct — daily interest = $540,000 × 7% ÷ 365 = $103.56. 12 days (June 19–30 inclusive) = $1,242.74.

Source: 12 CFR 1026.37(g)(2)(iii)

10. A borrower asks the MLO to leave a car loan off the application so they qualify. The MLO should:
  1. Leave it off if the payment is small
  2. Refuse. Knowingly making a false statement on a loan application to influence a federally insured lender is a federal crime
  3. List it only verbally
  4. Ask the processor to decide
Show answer and explanation

Answer: B. Refuse. Knowingly making a false statement on a loan application to influence a federally insured lender is a federal crime
Correct. 18 U.S.C. §1014.

Source: 18 U.S.C. §1014

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FAQ

Is there math on the MLO exam?

Yes. The origination activities area includes calculations such as DTI, LTV, points, and interest.

Can I use a calculator on the SAFE MLO test?

Calculator rules are set by NMLS and the test vendor. Check the current NMLS MLO Testing Handbook before test day.

Does LTV use the price or the appraised value?

For a purchase, LTV generally uses the lesser of the purchase price or the appraised value.

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