Montana Real Estate Math
Practice Questions & Answers (2026)
Real estate math questions appear on every Montana real estate exam and test a focused set of calculations: commission splits, prorations (property tax, rent, interest), loan-to-value ratios, appreciation and depreciation, and area calculations. The Montana Board of Realty Regulation does not provide a calculator — but the math is designed to be workable without one if you know the right formulas. Montana candidates consistently lose points on proration questions because they apply the wrong day-count convention (360-day vs. 365-day year) or miscalculate the seller's vs. buyer's share. Work through every problem in this section until you can solve each type without hesitation.
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Montana Real Estate Math — Practice Questions & Answers
130 questions on Real Estate Math from the Montana real estate question bank. First 10 are free — sign up to unlock all 130.
Q1. A home sells for $285,000. The listing agent's brokerage charges a 6% commission, split equally between listing and selling brokerages. What does each brokerage receive?
Explanation
Total commission: $285,000 × 0.06 = $17,100. Split equally: $17,100 ÷ 2 = $8,550 per brokerage.
Q2. A rectangular lot measures 150 feet by 200 feet. What is the lot's area in acres? (1 acre = 43,560 sq ft)
Explanation
Area = 150 × 200 = 30,000 sq ft. Acres = 30,000 ÷ 43,560 ≈ 0.689 acres, which rounds to approximately 0.69 acres.
Q3. A property sells for $320,000. The seller's net after paying a 5.5% commission is:
Explanation
Commission = $320,000 × 0.055 = $17,600. Seller's net = $320,000 − $17,600 = $302,400.
Q4. A buyer purchases a home for $250,000 with a 10% down payment. The lender charges 2 discount points. How much will the buyer pay in discount points?
Explanation
Down payment = $250,000 × 0.10 = $25,000. Loan amount = $250,000 − $25,000 = $225,000. Each point = 1% of the loan. 2 points = $225,000 × 0.02 = $4,500.
Q5. A property has a gross monthly rent of $2,400. Using a GRM of 110, what is the estimated property value?
Explanation
GRM × Monthly Rent = Value. Annual rent = $2,400 × 12 = $28,800. If GRM 110 is applied to annual rent: $28,800 × 110 = $3,168,000 — but for monthly GRM: $2,400 × 110 = $264,000.
Q6. A salesperson earns 60% of the commission from a sale. The total commission was $15,600. How much did the salesperson earn?
Explanation
Salesperson earnings = $15,600 × 0.60 = $9,360.
Q7. A property sells for $410,000. The county transfer tax is $1 per $500 of the sale price. What is the transfer tax due?
Explanation
Transfer tax = ($410,000 ÷ $500) × $1 = 820 × $1 = $820.
Q8. An investor buys a property for $180,000 and sells it 3 years later for $225,000. What is the percentage gain?
Explanation
Gain = $225,000 − $180,000 = $45,000. Percentage gain = $45,000 ÷ $180,000 = 0.25 = 25%.
Q9. A listing agent charges a 6% commission on the first $200,000 and 4% on any amount above $200,000. A property sells for $350,000. What is the total commission?
Explanation
Commission on first $200,000: $200,000 × 0.06 = $12,000. Commission on remaining $150,000: $150,000 × 0.04 = $6,000. Total: $12,000 + $6,000 = $18,000. Wait — recalculating: $12,000 + $6,000 = $18,000, which is answer B. Correct answer is 1 ($18,000).
Q10. A property has an annual NOI of $36,000 and a cap rate of 8%. What is its estimated value using the income approach?
Explanation
Value = NOI ÷ Cap Rate = $36,000 ÷ 0.08 = $450,000.
Q11. A buyer makes a 20% down payment on a $375,000 home. What is the loan amount?
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