Illinois Real Estate Exam Math: Practice Problems With Solutions

Math questions appear throughout the Illinois real estate exam. The Illinois transfer tax calculation is state-specific and will likely appear. Here are all the core formulas with worked examples.

Illinois Transfer Tax

Illinois state transfer tax: $0.50 per $500 of purchase price (paid by the seller) Chicago municipal transfer tax: $5.25 per $500 of purchase price

Formula: Transfer Tax = (Purchase Price ÷ 500) × Tax Rate per $500

Example 1 — Statewide: A property sells for $350,000 outside Chicago. What is the Illinois state transfer tax?

• $350,000 ÷ 500 = 700 units
• 700 × $0.50 = $350 (seller pays)

Example 2 — Chicago: A property sells for $500,000 in Chicago. What is the total transfer tax?

• State: (500,000 ÷ 500) × $0.50 = $500
• Chicago: (500,000 ÷ 500) × $5.25 = $5,250
• Total: $500 + $5,250 = $5,750

Commission Calculations

Formula: Commission = Sale Price × Commission Rate

Example: A property in Springfield sells for $285,000 with a 5.5% total commission split 50/50 between listing and buyer's broker. The listing broker's salesperson (actually "broker" in IL) earns 55% of the listing broker's share. What does the Illinois broker earn?

• Total commission: $285,000 × 0.055 = $15,675
• Listing broker's share: $15,675 ÷ 2 = $7,837.50
• IL broker's share: $7,837.50 × 0.55 = $4,310.63

Loan-to-Value Ratio

Formula: LTV = Loan Amount ÷ Purchase Price

Example: A buyer purchases a Chicago condo for $420,000 and makes a 15% down payment. What is the LTV?

• Down payment: $420,000 × 0.15 = $63,000
• Loan: $420,000 − $63,000 = $357,000
• LTV: $357,000 ÷ $420,000 = 85%

Proration (360-Day Year — "Banker's Method")

Note: Many Illinois exam questions use a 30-day month / 360-day year (banker's method). Confirm the method specified in the question.

Example (360-day year): Annual property taxes are $5,400. Closing is on March 15. How much does the buyer owe the seller for taxes (Jan 1 – March 15 = 2 months + 15 days = 75 days)?

• Daily rate (360-day year): $5,400 ÷ 360 = $15.00/day
• Buyer owes: $15.00 × 75 = $1,125 (debit to buyer, credit to seller)

Capitalization Rate

Formula: Value = NOI ÷ Cap Rate

Example: A Chicago apartment building has a Net Operating Income of $96,000. Market cap rates are 6%. What is the estimated value?

- Value: $96,000 ÷ 0.06 = $1,600,000

Reverse: A building is listed at $1,200,000 with an NOI of $72,000. What is the cap rate?

- Cap Rate: $72,000 ÷ $1,200,000 = 6%

Gross Rent Multiplier

Formula: GRM = Price ÷ Gross Annual Rent

Example: A property sells for $540,000 and generates $45,000 in annual gross rents. What is the GRM?

- GRM: $540,000 ÷ $45,000 = 12

Points

Formula: 1 point = 1% of the loan amount

Example: A buyer borrows $320,000 and pays 2 discount points. What do the points cost?

- $320,000 × 0.02 = $6,400

Area Calculations

Example: A rectangular building is 60 feet wide and 80 feet long. What is the square footage?

- 60 × 80 = 4,800 sq ft

Study Tips for Illinois Math

• Know both transfer tax rates: state ($0.50 per $500) and Chicago ($5.25 per $500)
• Practice proration with both 360-day and 365-day methods — know which one the question specifies
• Write all key formulas on scratch paper immediately when your exam begins

For more Illinois math practice and full exams, visit [CARealestate.com/states/illinois](https://carealestate.com/states/illinois).