Illinois Real Estate Math
Practice Questions & Answers (2026)
Real estate math questions appear on every Illinois 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 Illinois Department of Financial & Professional Regulation (IDFPR) does not provide a calculator — but the math is designed to be workable without one if you know the right formulas. Illinois 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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Illinois Real Estate Math — Practice Questions & Answers
119 questions on Real Estate Math from the Illinois real estate question bank. First 10 are free — sign up to unlock all 119.
Q1. A buyer in Illinois purchases a home for $320,000. The transfer tax is $1.50 per $500 of purchase price (or fraction thereof). What is the total transfer tax?
Explanation
Number of $500 increments = $320,000 ÷ $500 = 640. Transfer tax = 640 × $1.50 = $960.
Q2. A broker lists a home for $275,000 and earns a 6% commission. The listing broker and selling broker split the commission 50/50. How much does each broker receive?
Explanation
Total commission = $275,000 × 6% = $16,500. Each broker's share = $16,500 ÷ 2 = $8,250.
Q3. A property was purchased for $180,000 and later sold for $225,000. What was the percentage increase in value?
Explanation
Percentage increase = (Selling Price − Purchase Price) ÷ Purchase Price × 100. ($225,000 − $180,000) ÷ $180,000 = $45,000 ÷ $180,000 = 0.25 = 25%.
Q4. A lender requires a borrower to maintain a debt-to-income ratio of no more than 43%. If the borrower's gross monthly income is $6,500, what is the maximum allowable total monthly debt payment?
Explanation
Maximum monthly debt = Gross Monthly Income × DTI limit. $6,500 × 43% = $6,500 × 0.43 = $2,795.
Q5. A property sells for $415,000. The Illinois state transfer tax is $0.50 per $500 of purchase price. The county transfer tax is $0.25 per $500, and the city transfer tax is $3.00 per $500. What is the total transfer tax?
Explanation
Total rate per $500 = $0.50 + $0.25 + $3.00 = $3.75. Number of $500 increments = $415,000 ÷ $500 = 830. Total transfer tax = 830 × $3.75 = $3,112.50. Note: actual rates vary by municipality; in this question the answer closest to $3,113 would be selected. With the given options, $3,735 ($4.50/500 × 830) or the question uses $3.00 combined: 830 × $3.00 = $2,490.
Q6. A rectangular lot measures 150 feet by 220 feet. What is the lot size in acres? (1 acre = 43,560 sq ft)
Explanation
Area = 150 × 220 = 33,000 sq ft. Acres = 33,000 ÷ 43,560 = 0.758 acres, approximately 0.76 acres.
Q7. A buyer obtains a $300,000 mortgage at 5% annual interest. What is the first month's interest payment?
Explanation
Monthly interest = Principal × Annual Rate ÷ 12. $300,000 × 5% ÷ 12 = $300,000 × 0.05 ÷ 12 = $15,000 ÷ 12 = $1,250.
Q8. A property generates $3,200 per month in gross rental income. Annual operating expenses total $14,400. What is the annual net operating income (NOI)?
Explanation
Annual gross income = $3,200 × 12 = $38,400. NOI = Gross Income − Operating Expenses = $38,400 − $14,400 = $24,000. Wait — $38,400 − $14,400 = $24,000, which matches option B. Annual NOI = $24,000.
Q9. An appraiser estimates land value at $80,000 and the depreciated value of improvements at $195,000. What is the estimated property value using the cost approach?
Explanation
Cost approach value = Land Value + Depreciated Improvement Value = $80,000 + $195,000 = $275,000.
Q10. A home purchased for $250,000 appreciates at 4% per year. What is its value after 2 years?
Explanation
Year 1: $250,000 × 1.04 = $260,000. Year 2: $260,000 × 1.04 = $270,400. Compound appreciation over 2 years at 4% yields $270,400.
Q11. A rental property has an annual gross income of $60,000, a vacancy and credit loss of 5%, and operating expenses of $18,000. What is the net operating income (NOI)?
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