Mortgage Math on the NMLS Exam: Formulas and Worked Examples
Calculation questions are part of the origination section (27% of the test). You get a basic calculator. Most problems take one or two steps; the traps are using the wrong base or forgetting a component.
The formulas
| Calculation | Formula |
|---|---|
| Front-end ratio | Housing payment (PITIA) / gross monthly income |
| Back-end ratio | (PITIA + recurring debts) / gross monthly income |
| LTV (purchase) | Loan / lesser of price or appraised value |
| CLTV | All liens / value |
| Discount points | Loan amount x points % |
| Per diem interest | Loan x rate / 365 x days |
| Monthly escrow | (Annual taxes + insurance) / 12 |
| ARM new rate | Index + margin, limited by caps |
| 10% tolerance cure | Closing total - (LE total x 1.10) |
Worked examples
Back-end DTI
Income $6,500; PITIA $1,780; car $420; card $95; student loan $310.
Back-end DTI = ($1,780 + $420 + $95 + $310) / $6,500 = $2,605 / $6,500 = 40.1%.
Purchase LTV
Price $310,000; appraisal $300,000; loan $270,000.
LTV = $270,000 / $300,000 = 90% (use the lower value).
Prepaid interest
$300,000 at 6.75% closes April 20; interest April 20-30 inclusive (11 days), 365-day year.
Daily = $300,000 x 0.0675 / 365 = $55.48; 11 x $55.48 = $610.28.
ARM adjustment
5/1 ARM, 2/2/5 caps, start 5.25%, margin 2.75%, index 4.10% at first change.
Fully indexed = 6.85%; cap allows 7.25%; new rate 6.85%.
Tolerance cure
10% bucket on the LE: $1,600; at closing: $1,880.
Limit = $1,600 x 1.10 = $1,760; cure = $1,880 - $1,760 = $120.
Drill these in the Financial Calculations topic and the math study note.
Frequently asked questions
Is there a calculator on the NMLS test?
Yes, a basic on-screen calculator is provided.
What math is on the test?
DTI ratios, LTV and CLTV, points, prepaid interest, PITI and escrow, ARM adjustments and similar one- or two-step problems.
Go deeper: study notes
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