Math questions make up 8-12% of most state real estate exams. That's 8-18 questions depending on your state. The good news: real estate exam math is predictable. The same types of problems appear on every exam. If you learn the formulas and practice the calculations, these become some of the easiest points on the test. This guide covers every math concept you'll encounter.
Why math matters: Many test-takers skip math preparation because they're "not math people." This is a mistake. Real estate math is arithmetic — addition, subtraction, multiplication, and division. No algebra, no calculus. If you can use a calculator, you can ace these questions.
Commission Calculations
Commission problems are the most common math questions on the exam. They test your ability to calculate total commission, individual shares, and work backward from known amounts.
The Basic Formula
Example 1: Simple Commission
A home sells for $350,000 with a 6% commission. What is the total commission?
$350,000 × 0.06 = $21,000
Example 2: Commission Split
The total commission is 6%, split 60/40 between the listing and selling brokers. If the home sells for $425,000, how much does the selling broker receive?
Total commission: $425,000 × 0.06 = $25,500
Selling broker's share: $25,500 × 0.40 = $10,200
Example 3: Working Backward
A broker received $15,000 in commission at a 5% rate. What was the sale price?
Sale Price = Commission ÷ Rate
$15,000 ÷ 0.05 = $300,000
Example 4: Agent's Share After Splits
A home sells for $500,000 at 6% commission. The listing broker and selling broker split 50/50. The selling agent gets 70% of their broker's share. What does the selling agent earn?
Total commission: $500,000 × 0.06 = $30,000
Selling broker's share: $30,000 × 0.50 = $15,000
Selling agent's share: $15,000 × 0.70 = $10,500
Proration Calculations
Prorations divide expenses between the buyer and seller based on who occupies the property for each portion of the billing period. Property taxes are the most commonly prorated item on the exam.
The Proration Process
- Determine the annual amount
- Calculate the daily rate (annual amount ÷ 365)
- Count the number of days each party is responsible for
- Multiply the daily rate by the number of days
Example: Property Tax Proration
Annual property taxes are $4,380. The closing date is March 15. The seller is responsible through the day of closing. How much does the seller owe?
Daily rate: $4,380 ÷ 365 = $12.00/day
Days seller is responsible: January (31) + February (28) + March 1-15 (15) = 74 days
Seller's share: 74 × $12.00 = $888.00
Example: Rent Proration
Monthly rent is $2,400. The sale closes on October 10. The tenant has already paid rent for the full month. How much rent is credited to the buyer?
Daily rate: $2,400 ÷ 31 (days in October) = $77.42/day
Buyer's days: October 11-31 = 21 days
Buyer's credit: 21 × $77.42 = $1,625.82
Area and Volume Calculations
Area problems test your ability to calculate square footage, acreage, and building measurements.
Key Formulas
Rectangle area = Length × Width
Triangle area = (Base × Height) ÷ 2
1 acre = 43,560 square feet
1 square mile = 640 acres
Example: Price Per Square Foot
A house has 2,400 square feet and sold for $360,000. What was the price per square foot?
$360,000 ÷ 2,400 = $150 per square foot
Example: Acreage Calculation
A lot is 300 feet by 435.6 feet. How many acres is it?
Area: 300 × 435.6 = 130,680 sq ft
Acres: 130,680 ÷ 43,560 = 3 acres
Loan and Mortgage Calculations
Loan problems test your understanding of loan-to-value ratios, down payments, interest calculations, and qualifying ratios.
Loan-to-Value (LTV) Ratio
Example: LTV and Down Payment
A buyer purchases a home for $400,000 with a 90% LTV conventional loan. What is the down payment?
Loan amount: $400,000 × 0.90 = $360,000
Down payment: $400,000 - $360,000 = $40,000
Annual Interest
Example: Monthly Interest Payment
A borrower has a $250,000 loan at 6% annual interest. What is the monthly interest payment?
Annual interest: $250,000 × 0.06 = $15,000
Monthly interest: $15,000 ÷ 12 = $1,250
Qualifying Ratios
Lenders use two key ratios to determine if a borrower qualifies for a loan:
- Housing ratio (front-end): Monthly housing payment ÷ Gross monthly income (typically max 28%)
- Total debt ratio (back-end): Total monthly debt payments ÷ Gross monthly income (typically max 36%)
Example: Qualifying Ratio
A borrower earns $8,000/month gross. Their proposed mortgage payment (PITI) is $2,000 and they have $400/month in other debt. Do they qualify under the 28/36 rule?
Housing ratio: $2,000 ÷ $8,000 = 25% (under 28% — passes)
Total debt ratio: ($2,000 + $400) ÷ $8,000 = 30% (under 36% — passes)
Yes, the borrower qualifies.
Transfer Tax and Stamp Tax Calculations
Transfer taxes vary by state. Some states charge a flat rate, others use a graduated scale. Here are the key state-specific calculations:
Florida Documentary Stamp Tax
A Florida property sells for $325,000 (outside Miami-Dade). Calculate the documentary stamp tax on the deed.
Rate: $0.70 per $100 of consideration
$325,000 ÷ $100 = 3,250 × $0.70 = $2,275
California Proposition 13 Tax
A California home is purchased for $650,000. What is the annual property tax under Proposition 13?
Base rate: 1% of assessed value
$650,000 × 0.01 = $6,500/year
(Additional voter-approved assessments may increase this slightly)
Capitalization Rate (Cap Rate)
The cap rate is used to estimate the value of income-producing property.
Cap Rate = Net Operating Income (NOI) ÷ Property Value
Property Value = NOI ÷ Cap Rate
NOI = Property Value × Cap Rate
Example: Finding Property Value
An investment property generates $48,000 in net operating income. Comparable properties are selling at an 8% cap rate. What is the estimated value?
Value = NOI ÷ Cap Rate
$48,000 ÷ 0.08 = $600,000
Gross Rent Multiplier (GRM)
GRM = Sale Price ÷ Gross Monthly Rent
Estimated Value = Monthly Rent × GRM
Example: Using GRM
A comparable rental property sold for $300,000 with monthly rent of $2,500. What is the GRM? If a similar property rents for $2,800/month, what is its estimated value?
GRM: $300,000 ÷ $2,500 = 120
Estimated value: $2,800 × 120 = $336,000
Depreciation (Cost Approach)
Example: Straight-Line Depreciation
A building has a replacement cost of $400,000 and a useful life of 50 years. It's 10 years old. The land is worth $100,000. What is the estimated property value?
Annual depreciation: $400,000 ÷ 50 = $8,000/year
Total depreciation: $8,000 × 10 = $80,000
Depreciated building value: $400,000 - $80,000 = $320,000
Property value: $320,000 + $100,000 = $420,000
Net-to-Seller Calculations
A seller wants to net $280,000 after paying a 6% commission. What must the sale price be?
Net = Sale Price - Commission
$280,000 = Sale Price - (Sale Price × 0.06)
$280,000 = Sale Price × 0.94
Sale Price = $280,000 ÷ 0.94 = $297,872.34
Quick Reference: All Formulas
Commission: Sale Price × Rate = Commission
Proration: Annual Amount ÷ 365 = Daily Rate × Days = Share
Area: Length × Width (rectangle); Base × Height ÷ 2 (triangle)
Acres: Square Feet ÷ 43,560
LTV: Loan Amount ÷ Property Value
Interest: Loan Balance × Rate = Annual Interest
Cap Rate: NOI ÷ Value
GRM: Price ÷ Monthly Rent
Depreciation: Cost ÷ Useful Life × Age = Total Depreciation
Net to Seller: Desired Net ÷ (1 - Commission Rate) = Required Sale Price
Housing Ratio: PITI ÷ Gross Monthly Income ≤ 28%
Debt Ratio: Total Monthly Debt ÷ Gross Monthly Income ≤ 36%
Math Tips for Exam Day
- Use the on-screen calculator: Every testing center provides one — don't try to do calculations in your head
- Convert percentages first: Always convert percentages to decimals before calculating (6% = 0.06)
- Check your units: Make sure you're dividing by the right number (365 for daily, 12 for monthly)
- Read the question twice: Math questions often test whether you can identify what's being asked, not just whether you can calculate
- Estimate first: Before calculating, estimate the answer. If your calculation is wildly different from your estimate, you likely made an error
- Watch for distractors: Wrong answers on math problems are often the result of common mistakes (forgetting to split a commission, using the wrong time period)
The bottom line: Real estate math is pattern-based. Once you learn the formulas and practice each type of problem 10-20 times, math questions become among the most reliable points on the entire exam. Don't skip them — drill them.
Practice Real Estate Math Questions
Our practice exams include state-specific math problems with step-by-step explanations.
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