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The Essential Mortgage Math Formulas
These calculations appear on the NMLS exam regularly. Practice each one until it becomes automatic.
1. Loan-to-Value (LTV)
Formula
LTV = Loan Amount ÷ Appraised Value × 100
Example: $320,000 loan ÷ $400,000 value × 100 = 80% LTV
PMI required when LTV exceeds 80%. Request cancel at 80%. Auto-cancel at 78% — both based on ORIGINAL purchase price.
2. CLTV (Combined Loan-to-Value)
Formula
CLTV = (All Liens Combined) ÷ Appraised Value × 100
Example: $280K first + $40K HELOC = $320K ÷ $400K = 80% CLTV
Texas 50(a)(6): ALL liens combined cannot exceed 80% of fair market value.
3. Debt-to-Income (DTI)
Back-End DTI (Most Important)
DTI = (Housing Payment + All Monthly Debts) ÷ Gross Monthly Income × 100
Example: $1,800 PITIA + $600 car + $200 student = $2,600 ÷ $6,000 = 43.3% DTI
QM maximum: 43% · Conforming standard: 45% · Max with strong AUS: 50%
4. Points
Formula
1 point = 1% of the loan amount
Example: 2 points on $300,000 = 2% × $300,000 = $6,000
Break-even: $6,000 cost ÷ $75/month savings = 80 months to break even
5. Texas 50(a)(6) Maximum HEL
Formula
Max HEL = (Home Value × 80%) − All Existing Liens
Example: $500K × 80% = $400K cap − $320K first = $80K maximum home equity loan
Fee cap: 3% × loan amount = maximum allowed fees
6. Escrow Cushion (RESPA Section 10)
Formula
Max Cushion = Monthly Escrow Payment × 2
Example: $4,800 taxes + $1,200 insurance = $6,000 ÷ 12 = $500/month × 2 = $1,000 max cushion
7. TRID 10% Tolerance
Formula
Max Increase = Sum of ALL 10% category fees on LE × 10%
Example: $200 + $150 + $180 = $530 × 10% = $53 max allowed increase
If actual increase is $60 → violation of $7 → cure by refunding $7 within 3 calendar years
8. QM Points and Fees Cap
Formula
Max QM Fees = Loan Amount × 3% (loans ≥ $100,000)
Example: $250,000 × 3% = $7,500 maximum
If fees = $8,200 → exceeds by $700 → NOT a QM → lender loses ATR safe harbor
Quick Reference Table
| Calculation | Formula | Key Threshold |
|---|
| LTV | Loan ÷ Value × 100 | 80% PMI threshold · 78% auto-cancel |
| DTI (back-end) | All debts ÷ Gross income × 100 | 43% QM max · 45% conforming standard |
| Points cost | Points × Loan amount | 1 point = 1% of loan |
| QM fee cap | Loan × 3% | Cannot exceed 3% on loans ≥ $100K |
| HOEPA fee test | Loan × 5% | Exceeding 5% triggers HOEPA |
| Texas max CLTV | All liens ÷ Value × 100 | Cannot exceed 80% |
| Texas fee cap | Loan × 3% | Max fees on 50(a)(6) loans |
| Escrow cushion | Monthly escrow × 2 | 2 months max per RESPA Section 10 |