California Real Estate Exam: Math & Calculations
Complete Study Guide
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Overview
California real estate math questions test your ability to apply formulas consistently across commissions, loans, valuations, prorations, measurements, and investment analysis. Most problems follow a Part ÷ Whole = Rate (or rearranged) structure, so mastering this triangle unlocks the majority of question types. Success depends on memorizing key formulas, understanding when to multiply vs. divide, and carefully tracking what percentage belongs to whom.
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The Universal Math Triangle
```
PART
─────────
WHOLE × RATE
```
> This triangle applies to commissions, LTV, cap rates, interest calculations, and more.
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Section 1: Commission Calculations
Overview
Commission problems involve multiple layers of splitting. Always work top-down: calculate total commission first, then broker splits, then salesperson splits.
Key Formula
Total Commission = Sale Price × Commission Rate
Step-by-Step Process
1. Calculate total commission: Sale Price × Rate
2. Determine broker's share: Total Commission × Broker's %
3. Determine salesperson's share: Broker's Share × Salesperson's %
Core Examples
| Scenario | Formula | Result |
|---|---|---|
| $485,000 sale @ 6% | $485,000 × 0.06 | $29,100 total |
| Listing broker's 50% | $29,100 × 0.50 | $14,550 |
| Salesperson's 60% of broker share | $14,550 × 0.60 | $8,730 |
Working Backwards (Finding Sale Price)
When you know the salesperson's earnings:
Example: Salesperson earned $11,250; 5% commission; 50/50 split
Seller Net Proceeds (Working Backwards)
Sale Price = Net Proceeds ÷ (1 − Commission Rate)
Example: Seller nets $320,000 after 4% commission
Key Terms
⚠️ Watch Out For
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Section 2: Loan & Finance Calculations
Overview
Finance questions cover loan amounts, down payments, monthly interest, and qualifying ratios. These are straightforward if you correctly identify the base amount.
Key Formulas
| Calculation | Formula |
|---|---|
| Loan Amount | Purchase Price × LTV% |
| Down Payment | Purchase Price × (1 − LTV%) |
| Monthly Interest | (Loan Amount × Annual Rate) ÷ 12 |
| Maximum PITI | (Annual Income ÷ 12) × Qualifying Ratio |
Loan-to-Value (LTV)
Example: 80% LTV on $375,000 purchase
First Month's Interest (Simple Interest Method)
For the very first payment, no principal has been paid yet, so:
Monthly Interest = (Loan Balance × Annual Rate) ÷ 12
Example: $240,000 loan @ 7%
Income Qualifying Ratios
Maximum PITI = (Annual Gross Income ÷ 12) × Front-End Ratio
Example: $85,000 income, 28% front-end ratio
Key Terms
⚠️ Watch Out For
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Section 3: Property Valuation & Appraisal
Overview
California exam questions cover three appraisal approaches: Income, Sales Comparison, and Cost. Know when each applies and how to calculate each.
Income Approach (Capitalization)
#### Key Formula Triangle:
```
NOI
──────────────
Value × Cap Rate
```
| To Find | Formula |
|---|---|
| Value | NOI ÷ Cap Rate |
| Cap Rate | NOI ÷ Value |
| NOI | Value × Cap Rate |
Examples:
Sales Comparison Approach (Adjustments)
Rule: Always adjust the comparable, never the subject.
Memory Trick: "CBS" — Comparable Better? Subtract.
Example: Comparable sold for $410,000
Cost Approach (Depreciation)
Straight-Line Depreciation Formula:
Annual Depreciation = Building Cost ÷ Useful Life
Example: $600,000 building, 40-year useful life
> Note: Land is never depreciated — only improvements.
Key Terms
⚠️ Watch Out For
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Section 4: Proration & Closing Costs
Overview
Proration divides periodic expenses (taxes, rent, HOA dues) between buyer and seller based on the closing date. California typically uses a 360-day year (30-day months) unless stated otherwise.
The Proration Process
1. Calculate the daily rate: Annual Amount ÷ 360 (or monthly ÷ 30)
2. Count the number of days belonging to each party
3. Multiply: Daily Rate × Number of Days
Taxes Paid in Advance (Seller Prepaid)
The seller gets a credit from the buyer for days the seller already paid but won't own the property.
Example: $5,400 annual taxes; closes April 1; seller prepaid full year
Rent Proration (Tenant in Place)
Rent paid in advance by the tenant belongs to the new owner (buyer) for days after closing.
Example: $2,400/month rent; closes October 10
Discount Points
Each point = 1% of the loan amount
Example: 2 points on a $320,000 loan
> One point generally lowers the interest rate by approximately 0.25% (rule of thumb).
Prepaid Interest at Closing
Lenders collect interest from the closing date through the end of that month.
Example: Loan closes March 15
Key Terms
⚠️ Watch Out For
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Section 5: Area & Measurement Calculations
Overview
Area problems require knowing the formulas for basic shapes and understanding land measurement systems, including sections and the Public Land Survey System (PLSS).
Area Formulas
| Shape | Formula |
|---|---|
| Rectangle/Square | Length × Width |
| Triangle | ½ × Base × Height |
| Trapezoid | ½ × (Base 1 + Base 2) × Height |
Converting Square Feet to Acres
1 acre = 43,560 square feet
Acres = Square Feet ÷ 43,560
Example: 150 ft × 200 ft lot
Sections & Townships (PLSS)
| Division | Acres |
|---|---|
| 1 Section | 640 acres |
| Half Section | 320 acres |
| Quarter Section | 160 acres |
| Quarter-Quarter Section | 40 acres |
To solve section problems: Multiply fractions × 640 acres
Example: NW ¼ of the SW ¼ of a section
Property Management Fee (Area-Based)
Monthly Fee = Total Square Footage × Rate per Square Foot
Annual Fee = Monthly Fee × 12
Example: 12 units × 850 sq ft = 10,200 sq ft; $1.25/sq ft/month
Key Terms
⚠️ Watch Out For
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Section 6: Investment & Return Calculations
Overview
Investment math focuses on income potential and return metrics. These questions often require a multi-step process: calculate effective income → subtract expenses → analyze returns.
Gross Rent Multiplier (GRM)
GRM = Sale Price ÷ Gross Annual Rent
To find value: Value = GRM × Gross Annual Rent
Example: $400,000 property; $36,000 annual rent
Net Operating Income (NOI) — Full Calculation
```
Gross Potential Income (GPI)
− Vacancy & Credit Loss
= Effective Gross Income (EGI)
− Operating Expenses
= Net Operating Income (NOI)
```
Example: $42,000 gross income; 5% vacancy; $18,000 expenses
> Note: NOI does not include mortgage payments (debt service).
Percentage Gain on Investment
% Gain = (Sale Price − Purchase Price) ÷ Purchase Price
Example: Bought $350,000; sold $420,000
Summary of Investment Formulas
| Metric | Formula |
|---|---|
| GRM | Sale Price ÷ Gross Annual Rent |
| Cap Rate | NOI ÷ Value |
| NOI | EGI − Operating Expenses |
| % Gain | (Selling Price − Cost) ÷ Cost |
| Cash-on-Cash Return | Annual Cash Flow ÷ Cash Invested |