Arizona Real Estate Math
Practice Questions & Answers (2026)
Real estate math questions appear on every Arizona 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 Arizona Department of Real Estate (ADRE) does not provide a calculator — but the math is designed to be workable without one if you know the right formulas. Arizona 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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Arizona Real Estate Math — Practice Questions & Answers
142 questions on Real Estate Math from the Arizona real estate question bank. First 10 are free — sign up to unlock all 142.
Q1. A buyer in Arizona purchases a home for $420,000 with a 20% down payment. What is the amount of the buyer's mortgage loan?
Explanation
Down payment = $420,000 × 20% = $84,000. Loan amount = $420,000 − $84,000 = $336,000.
Q2. An Arizona property sold for $350,000. The total commission rate is 6%. The listing broker and buyer's broker split the commission 50/50. How much does each broker receive?
Explanation
Total commission = $350,000 × 6% = $21,000. Each broker receives $21,000 ÷ 2 = $10,500.
Q3. An Arizona homeowner wants to net $280,000 after paying a 6% commission. What is the minimum sale price needed?
Explanation
If the commission is 6%, the seller nets 94% of the sale price. Sale price = $280,000 ÷ 0.94 ≈ $297,872.
Q4. A rectangular Arizona lot measures 150 feet wide by 200 feet deep. What is the area in square feet?
Explanation
Area = length × width = 150 ft × 200 ft = 30,000 square feet.
Q5. An Arizona investor paid $500,000 for a rental property. After one year, the property has appreciated 4%. What is the new value of the property?
Explanation
Appreciation = $500,000 × 4% = $20,000. New value = $500,000 + $20,000 = $520,000.
Q6. An Arizona property has an annual property tax bill of $3,600. The tax is paid in two installments. The seller is closing on October 1. Using a 365-day proration, how many days of taxes has the seller already 'used' (January 1 through September 30)?
Explanation
January (31) + February (28) + March (31) + April (30) + May (31) + June (30) + July (31) + August (31) + September (30) = 273 days. The seller owes 273/365 × $3,600 ≈ $2,692 in taxes as a credit to the buyer at closing.
Q7. A seller wants to net $275,000 after paying a 6% commission. What must the property sell for?
Explanation
The seller nets 100% − 6% = 94% of the sale price. Required sale price = $275,000 ÷ 0.94 = $292,553 (rounded to the nearest dollar).
Q8. A 1-acre lot sells for $87,120. What is the price per square foot? (1 acre = 43,560 sq ft)
Explanation
Price per sq ft = $87,120 ÷ 43,560 = $2.00 per square foot.
Q9. A property is assessed at 10% of its $420,000 market value. The tax rate is $8.50 per $100 of assessed value. What is the annual property tax?
Explanation
Assessed value = $420,000 × 10% = $42,000. Tax = $42,000 ÷ $100 × $8.50 = 420 × $8.50 = $3,570.
Q10. A buyer purchases a home for $310,000. The lender requires a 5% down payment. The buyer also pays 1.5 discount points. What is the total amount the buyer pays in points?
Explanation
Loan amount = $310,000 − (5% × $310,000) = $310,000 − $15,500 = $294,500. Points = 1.5% × $294,500 = $4,417.50.
Q11. A rectangular lot measures 150 feet wide and 200 feet deep. A buyer pays $12 per square foot. What is the purchase price?
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