Utah Real Estate Math
Practice Questions & Answers (2026)
Real estate math questions appear on every Utah 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 Utah 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. Utah 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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Utah Real Estate Math — Practice Questions & Answers
210 questions on Real Estate Math from the Utah real estate question bank. First 10 are free — sign up to unlock all 210.
Q1. A Utah investment property has an annual gross rental income of $42,000. The vacancy rate is 5% and operating expenses total $16,000. What is the net operating income (NOI)?
Explanation
EGI = $42,000 × (1 − 0.05) = $42,000 × 0.95 = $39,900. NOI = EGI − Operating Expenses = $39,900 − $16,000 = $23,900.
Q2. A home originally purchased for $280,000 is sold 4 years later for $336,000. What is the percentage increase in value?
Explanation
Increase = $336,000 − $280,000 = $56,000. Percentage increase = $56,000 ÷ $280,000 = 0.20 = 20%.
Q3. A buyer obtains a $240,000 mortgage at 7% annual interest. What is the first month's interest payment?
Explanation
Monthly interest = Loan balance × (Annual rate ÷ 12) = $240,000 × (0.07 ÷ 12) = $240,000 × 0.005833 = $1,400.
Q4. A commercial property is valued at $875,000 using a cap rate of 7%. If the NOI increases by $5,000 per year, what is the new estimated value at the same 7% cap rate?
Explanation
Original NOI = $875,000 × 0.07 = $61,250. New NOI = $61,250 + $5,000 = $66,250. New value = $66,250 ÷ 0.07 = $946,428.57 ≈ $946,429.
Q5. A property is listed at $425,000 and sells for 96% of the listing price. What is the sale price?
Explanation
Sale price = $425,000 x 0.96 = $408,000.
Q6. A lot measures 150 feet wide and 200 feet deep. How many square feet is the lot?
Explanation
Area = Length x Width = 150 x 200 = 30,000 square feet.
Q7. A real estate agent earns a 6% commission on a $350,000 sale. The listing and selling commissions are split 50/50 between two brokers and the agent earns 60% of their broker's side. How much does the agent receive?
Explanation
Total commission = $350,000 x 6% = $21,000. Each broker's side = $21,000 / 2 = $10,500. Agent's share = $10,500 x 60% = $6,300.
Q8. A property has a market value of $380,000. The county assesses it at 55% of market value and applies a tax rate of $12 per $1,000 of assessed value. What are the annual property taxes?
Explanation
Assessed value = $380,000 x 0.55 = $209,000. Annual taxes = ($209,000 / $1,000) x $12 = 209 x $12 = $2,508.
Q9. A property manager charges 9% of collected rents. If a property collects $3,200 in rent during a month, what is the management fee?
Explanation
Management fee = $3,200 x 9% = $3,200 x 0.09 = $288.
Q10. An investor purchases a property for $500,000 with a 25% down payment. What is the loan amount?
Explanation
Down payment = $500,000 x 25% = $125,000. Loan amount = $500,000 - $125,000 = $375,000.
Q11. A rectangular acre of land contains 43,560 square feet. If a lot is 1.5 acres, how many square feet does it contain?
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