Overview
This study guide covers the essential mathematical concepts tested on the NMLS SAFE Exam, including LTV ratios, DTI ratios, points and fees, amortization, APR, down payments, equity, and closing cost prorations. Mastering these calculations requires understanding both the formulas and the why behind each concept. Expect calculation-based questions that test your ability to apply these formulas accurately under exam conditions.
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1. Loan-to-Value (LTV) Ratios
Core Concept
LTV measures the relationship between the loan amount and the property value, expressed as a percentage. It is the lender's primary risk assessment tool.
Formula:
> LTV = Loan Amount ÷ Property Value × 100
Key Rules
• Always use the lesser of the appraised value or purchase price as the denominator
• LTV above 80% on conventional loans → PMI required
• LTV at or below 80% → No PMI required
• Higher LTV = greater lender risk = stricter requirements
Worked Example
• Home appraised at $250,000; down payment of $50,000
• Loan amount = $250,000 − $50,000 = $200,000
• LTV = $200,000 ÷ $250,000 = 80%
Key Terms
• Loan-to-Value (LTV): Ratio of loan amount to property value
• Appraised Value: The estimated market value determined by a licensed appraiser
• Private Mortgage Insurance (PMI): Insurance protecting the lender when LTV exceeds 80%
• Purchase Price: The agreed-upon sale price between buyer and seller
> ⚠️ Watch Out For: When appraised value and purchase price differ, always use the lower value in your LTV calculation — never the higher one. This is a common trap on the SAFE Exam.
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2. Debt-to-Income (DTI) Ratios
Core Concept
DTI ratios measure a borrower's ability to manage monthly debt payments relative to their gross monthly income. Two types are tested:
| Ratio | What It Includes | Formula |
|---|---|---|
| Front-End (Housing) DTI | PITI only | PITI ÷ Gross Monthly Income |
| Back-End (Total) DTI | PITI + all recurring debts | Total Monthly Debts ÷ Gross Monthly Income |
Key Rules
• PITI = Principal, Interest, Taxes, Insurance
• Conventional loan guideline: Back-end DTI ≤ 43%
• Always use gross (pre-tax) monthly income, never net income
• Recurring debts include: installment loans, revolving credit minimums, student loans, car payments
Worked Example
• Gross monthly income: $5,500
• PITI: $1,210 | Other debts: $440
• Total debts = $1,210 + $440 = $1,650
• Back-end DTI = $1,650 ÷ $5,500 = 30% ✓ (meets 43% guideline)
Key Terms
• Front-End DTI: Housing expense ratio (PITI only)
• Back-End DTI: Total debt ratio (all recurring monthly obligations)
• Gross Monthly Income: Pre-tax income used for qualification
• PITI: Principal, Interest, Taxes, Insurance — the total housing payment
> ⚠️ Watch Out For: Exam questions may try to get you to use net (after-tax) income instead of gross income. DTI always uses gross monthly income.
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3. Points & Fees
Core Concept
Discount points are prepaid interest paid at closing to permanently buy down the interest rate. Understanding how to calculate point costs and break-even periods is essential.
Formulas:
> Cost of Points = Number of Points × 1% × Loan Amount
> Break-Even Period (months) = Cost of Points ÷ Monthly Savings
Key Rules
• 1 point = 1% of the loan amount (not the purchase price)
• Each point typically reduces the rate by 0.125% to 0.25%
• Points make sense only if the borrower keeps the loan past the break-even point
• Origination points compensate the lender; discount points buy down the rate
Worked Example
• Loan: $320,000 | 2 discount points
• Cost = 2% × $320,000 = $6,400
• Points cost: $4,500 | Monthly savings: $75/month
• Break-even = $4,500 ÷ $75 = 60 months (5 years)
Key Terms
• Discount Points: Prepaid interest to permanently reduce the interest rate
• Origination Points/Fees: Fees charged by the lender to process the loan
• Break-Even Period: Time needed for monthly savings to offset upfront point cost
• Rate Buydown: Using points to secure a lower interest rate
> ⚠️ Watch Out For: Points are calculated on the loan amount, not the purchase price or appraised value. Also, distinguish between discount points (buy down rate) and origination fees (lender compensation) — they are NOT the same thing.
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4. Amortization & Monthly Payments
Core Concept
Amortization is the process of paying off a loan through scheduled payments over time. Each payment covers both interest and principal, with the allocation shifting over the loan's life.
Monthly Interest Formula:
> Monthly Interest = Outstanding Balance × (Annual Rate ÷ 12)
Key Rules
• Early payments: mostly interest, little principal
• Later payments: mostly principal, little interest
• Interest is calculated on the declining balance each month
• Extra principal payments reduce total interest paid and shorten the loan term
• A fully amortizing loan has a $0 balance at the end of the term
Worked Example
• Loan: $200,000 | Rate: 6% annual
• Month 1 interest = $200,000 × (0.06 ÷ 12) = $200,000 × 0.005 = $1,000
Amortization Pattern (Conceptual)
```
Early Loan Life: [████████████ Interest | ██ Principal]
Mid Loan Life: [████████ Interest | ██████ Principal]
Late Loan Life: [███ Interest | █████████████ Principal]
```
Key Terms
• Amortization: Gradual repayment of a loan through scheduled payments
• Fully Amortizing Loan: A loan where all scheduled payments result in a zero balance at term end
• Principal: The outstanding loan balance
• Negative Amortization: When payments don't cover the interest due, causing the balance to grow
> ⚠️ Watch Out For: The exam may ask which portion of a payment (interest or principal) is larger at various points in the loan. Early = more interest; late = more principal. Extra payments attack the principal, not future interest directly.
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5. Annual Percentage Rate (APR)
Core Concept
APR is the true cost of borrowing, expressed as a yearly rate. It is always equal to or higher than the note (contract) interest rate because it incorporates fees spread over the loan term.
What APR Includes
• Note interest rate
• Origination fees
• Discount points
• Mortgage insurance premiums (MIP/PMI)
• Most mandatory closing costs/finance charges
What APR Does NOT Include
• Appraisal fees
• Title insurance
• Homeowners insurance
• Property taxes
Key Rules
• APR ≥ Note Rate (always)
• The larger the fees relative to loan size → the greater the gap between APR and note rate
• Under TILA (Truth in Lending Act), lenders must disclose APR
• The Loan Estimate must be delivered within 3 business days of receiving a complete application
Disclosure Timeline
```
Completed Application Received
↓
3 Business Days
↓
Loan Estimate Delivered (contains APR disclosure)
```
Key Terms
• APR (Annual Percentage Rate): The all-in cost of borrowing expressed as a yearly rate
• Note Rate: The contractual interest rate stated in the promissory note
• Finance Charges: Fees included in the APR calculation under TILA
• Loan Estimate: TILA-required disclosure delivered within 3 business days of application
• TILA (Truth in Lending Act): Federal law requiring APR disclosure
> ⚠️ Watch Out For: The exam may ask whether APR can be lower than the note rate — it cannot (unless there are no fees at all, in which case they are equal). Also remember: 3 business days for the Loan Estimate, not 3 calendar days.
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6. Down Payments & Equity
Core Concept
Down payment is the borrower's upfront cash contribution to the purchase. Equity is the homeowner's ownership stake in the property.
Formulas:
> Down Payment = Purchase Price × Down Payment %
> Loan Amount = Purchase Price − Down Payment
> Equity % = (Property Value − Loan Balance) ÷ Property Value
Key Rules
• Minimum down payment varies by loan type:
- Conventional: typically 5% (3% for some programs)
- FHA: 3.5% (with 580+ credit score)
- VA/USDA: 0% (no down payment required)
• Homeowners Protection Act (HPA): Lender must automatically cancel PMI when balance reaches 78% LTV (based on original amortization schedule and original value), provided borrower is current
• Borrower may request cancellation at 80% LTV
Worked Example
• Home: $300,000 | Down payment: 5%
• Down payment = 5% × $300,000 = $15,000
• Loan amount = $300,000 − $15,000 = $285,000
• Property value: $400,000 | Loan balance: $310,000
• Equity = ($400,000 − $310,000) ÷ $400,000 = $90,000 ÷ $400,000 = 22.5%
PMI Cancellation Thresholds
| LTV | Action |
|---|---|
| Below 80% | Borrower can request PMI cancellation |
| Reaches 78% | Lender must automatically cancel PMI |
Key Terms
• Down Payment: Borrower's upfront cash contribution toward purchase price
• Equity: Difference between property value and outstanding mortgage balance
• Homeowners Protection Act (HPA): Federal law governing PMI cancellation rights
• Automatic Cancellation: Mandatory PMI termination at 78% LTV under HPA
> ⚠️ Watch Out For: Know the difference between 80% LTV (borrower request) and 78% LTV (automatic cancellation). The exam tests both thresholds. Also, HPA automatic cancellation is based on the original property value and amortization schedule, not a new appraisal.
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7. Prorations & Closing Costs
Core Concept
Prorations divide periodic expenses (taxes, insurance) between buyer and seller based on the closing date. The exam commonly uses a 360-day year (12 months × 30 days) unless stated otherwise.
Formulas:
> Daily Rate = Annual Amount ÷ 360
> Proration Amount = Daily Rate × Number of Days
> Monthly Escrow = Annual Premium ÷ 12
Key Rules
• If seller prepaid taxes: buyer reimburses seller for seller's overpayment
• If taxes unpaid: seller credits buyer for seller's portion
• Escrow impound accounts collect monthly reserves for taxes and insurance
• Lenders may collect 2–3 months of reserves at closing as a cushion
Worked Example: Tax Proration
• Annual taxes: $3,600 | Closing: October 1
• Seller prepaid full year → Buyer owes seller for Oct, Nov, Dec (3 months)
• Daily rate = $3,600 ÷ 360 = $10/day
• 3 months × 30 days = 90 days
• Amount owed = 90 × $10 = $900
Worked Example: Escrow Impound
• Annual homeowners insurance: $1,800
• Monthly premium = $1,800 ÷ 12 = $150/month
• 3 months collected at closing = 3 × $150 = $450
Key Terms
• Proration: Division of income or expense between buyer and seller at closing
• Escrow Impound Account: Account held by lender to pay taxes and insurance on borrower's behalf
• Per Diem: Daily rate used for proration calculations
• 360-Day Year: Banker's year used in most real estate proration calculations (30 days × 12 months)
> ⚠️ Watch Out For: Always clarify who owes whom in proration problems. If the seller prepaid, the buyer reimburses the seller. If the seller hasn't paid, the seller credits the buyer. Also confirm whether the exam question specifies a 360-day or 365-day year.
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Master Formula Reference Sheet
| Calculation | Formula |
|---|---|
| LTV | Loan Amount ÷ Property Value |
| Loan Amount | Purchase Price − Down Payment |
| Front-End DTI | PITI ÷ Gross Monthly Income |
| Back-End DTI | Total Monthly Debts ÷ Gross Monthly Income |
| Cost of Points | Points × 1% × Loan Amount |
| Break-Even | Cost of Points ÷ Monthly Savings |
| Monthly Interest | Balance × (Annual Rate ÷ 12) |
| Equity % | (Value − Balance) ÷ Value |
| Daily Proration Rate | Annual Amount ÷ 360 |
| Monthly Escrow | Annual Amount ÷ 12 |
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Quick Review Checklist
Use this checklist before your exam to confirm mastery:
• [ ] LTV Formula: Can calculate LTV using the lesser of appraised value or purchase price
• [ ] PMI Threshold: LTV > 80% requires PMI; PMI auto-cancels at 78% LTV under HPA
• [ ] DTI Types: Know the difference between front-end (PITI only) and back-end (all debts) DTI
• [ ] DTI Income: Always use gross monthly income, never net
• [ ] Conventional DTI Limit: Maximum back-end DTI is 43%
• [ ] Points Calculation: 1 point = 1% of the loan amount; know break-even formula
• [ ] APR vs. Note Rate: APR is always ≥ note rate due to included fees
• [ ] Loan Estimate Timing: Delivered within 3 business days of completed application (TILA)
• [ ] Amortization Pattern: Early payments = more interest; later payments = more principal
• [ ] Extra Payments: Reduce total interest paid and shorten the loan term
• [ ] HPA Thresholds: Borrower requests cancellation at 80%; automatic at 78%
• [ ] Proration Calculation: Daily rate = Annual ÷ 360; multiply by days remaining
• [ ] Escrow Impound: Monthly amount = Annual premium ÷ 12
• [ ] Equity Formula: (Property Value − Loan Balance) ÷ Property Value
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Focus your practice on calculation speed and formula recall. The NMLS SAFE Exam rewards candidates who can set up problems correctly before computing — always identify the right formula first, then plug in numbers.