Colorado Real Estate Math
Practice Questions & Answers (2026)
Real estate math questions appear on every Colorado 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 Colorado Division of Real Estate does not provide a calculator — but the math is designed to be workable without one if you know the right formulas. Colorado 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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Colorado Real Estate Math — Practice Questions & Answers
142 questions on Real Estate Math from the Colorado real estate question bank. First 10 are free — sign up to unlock all 142.
Q1. A Colorado property sells for $485,000. The listing broker charges a 6% commission, split equally with the buyer's broker. How much does each broker's office receive?
Explanation
Total commission = $485,000 × 6% = $29,100. Each broker's office receives $29,100 ÷ 2 = $14,550.
Q2. A rectangular lot measures 150 feet by 200 feet. What is the area in acres? (1 acre = 43,560 sq ft)
Explanation
Area = 150 ft × 200 ft = 30,000 sq ft. Acres = 30,000 ÷ 43,560 = approximately 0.69 acres.
Q3. A Colorado home is assessed at 7.15% of its actual value. The actual value is $400,000 and the mill levy is 85 mills. What is the annual property tax?
Explanation
Assessed value = $400,000 × 7.15% = $28,600. Property tax = $28,600 × 85 mills = $28,600 × 0.085 = $2,431.
Q4. A buyer purchases a property for $560,000 and sells it 3 years later for $672,000. What is the percentage increase in value?
Explanation
Increase = $672,000 − $560,000 = $112,000. Percentage increase = ($112,000 ÷ $560,000) × 100 = 20.00%.
Q5. A Colorado broker's office has a total annual commission income of $1,200,000. The employing broker receives 30% and the remaining 70% is split equally among 10 associate brokers. How much does each associate broker earn annually?
Explanation
Amount for associates = $1,200,000 × 70% = $840,000. Each associate's share = $840,000 ÷ 10 = $84,000.
Q6. A Colorado property is sold for $525,000 with a 5.5% commission. The listing broker and buyer's broker split the commission 50/50. The listing associate receives 60% of their office's share. How much does the listing associate earn?
Explanation
Total commission = $525,000 × 5.5% = $28,875. Each office receives $28,875 ÷ 2 = $14,437.50. Listing associate receives $14,437.50 × 60% = $8,662.50.
Q7. An investor buys a Colorado rental property for $380,000 and rents it for $2,200 per month. What is the gross rent multiplier (GRM)?
Explanation
Monthly GRM = Sale Price ÷ Monthly Rent = $380,000 ÷ $2,200 = 172.7. Annual GRM would be $380,000 ÷ ($2,200 × 12) = $380,000 ÷ $26,400 = 14.4.
Q8. A Colorado property assessed at $35,000 with a mill levy of 92 mills. What is the annual property tax?
Explanation
Property tax = Assessed value × Mill levy = $35,000 × 92 mills = $35,000 × 0.092 = $3,220.
Q9. A Colorado home has a market value of $500,000. The residential assessment rate is 7.15%. What is the assessed value?
Explanation
Assessed value = Market value × Assessment rate = $500,000 × 7.15% = $500,000 × 0.0715 = $35,750.
Q10. A Colorado seller wants to net $400,000 after paying a 6% broker commission. What must the property sell for?
Explanation
The seller keeps 94% of the sale price after a 6% commission. Required sale price = $400,000 ÷ 0.94 = $425,531.91.
Q11. A buyer's monthly principal and interest payment is $1,850. Annual property taxes are $3,600 and homeowners insurance is $1,200 annually. What is the total monthly PITI payment?
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