Math & Calculations
Master every math problem type on the real estate exam: commission splits, area calculations, tax mill rates, property proration, profit and loss, and more.
1. Commission Calculations
Commission calculations are the most common math problems on the real estate exam, appearing in 3-5 questions. The basic formula is straightforward, but the exam often adds layers (split between brokers, split between agent and broker).
Example 1: A property sells for $350,000 at a 6% commission. Commission = $350,000 × 0.06 = $21,000.
Commission Splits: The total commission is typically split between the listing broker and the selling (buyer's) broker, often 50/50. Then each broker splits their share with their agent per an agreement.
Example 2: A property sells for $400,000 at a 5% commission. The listing and selling brokers split 50/50. The selling agent has a 70/30 split with their broker (70% to agent). How much does the selling agent earn?
Total Commission = $400,000 × 0.05 = $20,000
Selling Broker's Share = $20,000 × 0.50 = $10,000
Selling Agent's Share = $10,000 × 0.70 = $7,000
Many questions state the commission percentage and ask for the agent's share after multiple splits. Work step-by-step: (1) total commission, (2) broker split, (3) agent split. Write each number down — don't try to combine percentages in your head. The exam is testing your ability to follow a multi-step calculation, not just the final number.
2. Area and Land Measurement Calculations
Area problems require memorizing key unit conversions. These appear on virtually every exam.
| Conversion | Value | Used For |
|---|---|---|
| 1 acre | 43,560 square feet | Land area problems |
| 1 mile | 5,280 feet | Distance / frontage |
| 1 section | 640 acres (1 sq mile) | Government survey |
| 1 township | 36 sections (23,040 acres) | Government survey |
| 1 square yard | 9 square feet | Carpeting, flooring |
| 1 cubic yard | 27 cubic feet | Concrete, fill |
Example 3: A rectangular lot measures 220 feet by 198 feet. How many acres is it?
Area in square feet = 220 × 198 = 43,560 sq ft
43,560 sq ft ÷ 43,560 sq ft/acre = exactly 1 acre
Example 4: A property described as "the NW 1/4 of the SW 1/4 of Section 12" contains how many acres?
1 section = 640 acres
SW 1/4 = 640 ÷ 4 = 160 acres
NW 1/4 of that = 160 ÷ 4 = 40 acres
The formula for the area of a rectangle is length × width. For a triangle: (base × height) ÷ 2. For an irregular lot described by metes and bounds, the area would typically be given rather than calculated.
3. Property Tax Calculations
Property tax problems involve tax rates, mill rates, assessed value, and equalization factors. These are high-frequency exam questions.
Or equivalently: Annual Tax = Assessed Value × Tax Rate (expressed as a decimal).
A mill is one-tenth of one cent, or $1 per $1,000 of assessed value. A mill rate of 15 means $15 per $1,000 of assessed value.
Example 5: A property has a market value of $300,000 and is assessed at 80% of market value. The mill rate is 25 mills. What is the annual property tax?
Assessed Value = $300,000 × 0.80 = $240,000
Tax per $1,000 = $25
Annual Tax = ($240,000 ÷ 1,000) × $25 = 240 × $25 = $6,000
Example 6: A property is assessed at $180,000. The tax rate is $1.85 per $100 of assessed value. Calculate the annual tax.
Tax rate as decimal = $1.85 ÷ $100 = 0.0185
Annual Tax = $180,000 × 0.0185 = $3,330
The exam will often give you market value and an assessment ratio. You MUST multiply market value by the assessment ratio to get assessed value before applying the tax rate. Skipping this step is the most common tax calculation error. Also watch for equalization factors (state equalizer) that further modify assessed value.
4. Proration Calculations
Proration is the division of ongoing expenses between buyer and seller at closing. Property taxes are the most commonly prorated item. The standard approach: determine the per diem (daily) rate, then multiply by the number of days each party is responsible for.
Two key decisions for every proration problem: (1) Who has already paid? (If the seller prepaid, the buyer reimburses the seller. If unpaid, each pays their share.) (2) Who owns the property on the closing date? Convention varies: some use a 360-day banker's year, others 365 days; the closing date may belong to the buyer or seller depending on local custom. The exam typically specifies the method.
Example 7: Annual property taxes are $3,650. Closing is on April 15 (105 days into a 365-day year). The seller has not yet paid taxes for the year. Using the 365-day method with the day of closing belonging to the buyer, what is the tax proration?
Per Diem = $3,650 ÷ 365 = $10.00/day
Seller's days (Jan 1–Apr 14) = 104 days
Seller's share = 104 × $10 = $1,040 (charged to seller at closing)
Buyer's share = 261 × $10 = $2,610
If the seller had already paid the full $3,650, the buyer would credit the seller $2,610 at closing to cover the buyer's portion of the year.
5. Profit, Loss, and Return Calculations
These problems test your ability to calculate net proceeds, profit percentage, and gain/loss on sale.
Example 8: A seller sells a home for $500,000. The mortgage balance is $280,000, the commission is 6%, and closing costs are $5,000. What are the seller's net proceeds?
Commission = $500,000 × 0.06 = $30,000
Net Proceeds = $500,000 − $280,000 − $30,000 − $5,000 = $185,000
Example 9: An investor buys a property for $200,000 and sells it for $260,000. What is the percentage profit?
Gain = $260,000 − $200,000 = $60,000
Profit % = ($60,000 ÷ $200,000) × 100 = 30%
Profit margin is always calculated as a percentage of the original cost or investment, not the sale price. A $100,000 property selling for $150,000 yields a 50% profit (not 33%). Commission is calculated on the sale price. Know the difference. Also: "net to seller" means after all deductions.
6. Amortization and Loan Calculations
While you won't be asked to build a full amortization schedule, the exam tests basic loan math: calculating loan amounts from LTV, determining down payments, computing discount points, and understanding how much interest is paid in early loan years.
Example 10: A buyer purchases a $320,000 home with an 80% LTV loan. What is the down payment?
Loan Amount = $320,000 × 0.80 = $256,000
Down Payment = $320,000 − $256,000 = $64,000 (20%)
Example 11: A buyer purchases a home for $250,000 with a $50,000 down payment. The lender charges 1.5 discount points. How much do the points cost?
Loan Amount = $250,000 − $50,000 = $200,000
Points Cost = $200,000 × 0.015 = $3,000
Discount points are calculated on the loan amount, NOT the sale price. If a question says "1 point" and gives you a sale price and a down payment, you MUST subtract the down payment first. This is probably the most common math trap on the exam — and test-writers know students fall for it.
📖 Key Terms
- Commission — Fee earned by broker (% of sale price)
- Mill Rate — Tax rate; $1 per $1,000 of assessed value
- Assessed Value — Value used for tax purposes (market × ratio)
- Proration — Dividing expenses between buyer and seller
- Per Diem — Daily rate (annual ÷ 365 or 360)
- Acre — 43,560 square feet
- Section — 640 acres (1 square mile)
- LTV — Loan-to-Value ratio (loan ÷ value)
- Discount Points — Prepaid interest; 1 point = 1% of loan amount
- Net Proceeds — Sale price minus all costs and obligations
- Assessment Ratio — Percentage of market value used for tax assessment
- Equalization Factor — State multiplier applied to assessed value
📝 Practice Questions
Keep Learning
- 📝 Practice Test — Test your knowledge
- 🃏 Flashcards — Quick review
- 📚 Exam Tips Blog — Study strategies