Illinois real estate exam math guide

Short answer: The broker national outline assigns 7% to Real Estate Calculations. PSI names five transaction calculations and four general concepts. Expect seller proceeds, buyer funds, prorations, transfer fees, PITI, equity, cap rate or rate of return, LTV, and points or origination fees.

The official source is the PSI Illinois Candidate Information Booklet dated June 24, 2026. Its calculation list is shorter and more focused than some older exam-prep formula sheets.

Start with the requested quantity. Then choose the matching row. A formula is useful only after you know what each number represents and whether it is a debit, credit, annual amount, monthly amount, percentage, or dollar figure.

Percentage answers use a percent form. Dollar calculations use a decimal form. For example, 8% becomes 0.08 before multiplication or division.

Seller’s net proceeds

Begin with the sale price. Add any seller credits, then subtract every seller debit named in the question. Common debits include a loan payoff, brokerage fee, seller-paid closing cost, repair allowance, tax charge, and buyer concession.

Trap: A loan payoff reduces seller proceeds. It does not reduce the contract price.

Buyer funds needed at closing

Add the buyer’s debits, then subtract the buyer’s credits. Purchase price and closing costs are debits. Loan proceeds, earnest money already paid, and an allowed seller credit reduce the amount still due.

Trap: Earnest money already deposited is a buyer credit at closing. Do not add it a second time.

A proration allocates an expense or income item between parties for the time each is responsible. Use the period and day-count method stated in the question. Count the closing day for the party the prompt assigns it to.

1. Identify the full-period amount.
2. Divide by the number of units in that period.
3. Count the responsible days or months.
4. Multiply the unit amount by the responsible units.
5. Decide who receives the debit and who receives the credit.

If the tax is unpaid and the buyer will later pay the bill, the seller’s share is generally a seller debit and buyer credit. The Illinois Department of Revenue’s closing guidance says sellers of existing homes generally cover outstanding bills and credit buyers for the seller’s ownership period, subject to the contract.

Trap: Never choose 360 or 365 from habit. Use the convention supplied in the question.

For an Illinois state-tax problem, divide the taxable consideration by $500, round any fraction to the next whole unit, and multiply by $0.50. The state rate is $0.50 for each $500 of value or fraction. Counties may impose $0.25 per $500, and a home-rule municipality may impose an additional tax.

The Illinois Department of Revenue transfer-tax page explains the governing law and declaration process. On the exam, use the taxable amount, rate, responsible party, and rounding rule given. Do not silently add a Chicago or other local rate.

Trap: “Per $500 or fraction” means 624.5 units becomes 625, not 624.

PITI means principal, interest, taxes, and insurance. Add the monthly principal-and-interest payment to monthly property taxes and monthly homeowners insurance. Convert annual taxes and annual insurance to monthly amounts before adding.

A question may supply the principal-and-interest payment, a payment factor, or enough loan facts to estimate it. Use the information provided. Do not replace the stated payment with a guessed amount.

Trap: PITI is not simply the loan payment. Property taxes and homeowners insurance must be converted to the same monthly period.

Equity and LTV

Equity is property value minus debt secured by the property. LTV compares the loan with the property value. On a $300,000 property with a $225,000 balance, equity is $75,000 and LTV is 75%.

If value and LTV are known, loan amount equals value multiplied by LTV. If price and loan are known, the down-payment amount equals price minus loan.

Discount points and origination fees

One point is 1% of the loan amount. Two points are 2%. Discount points and origination fees may serve different lending purposes, but the exam calculation uses the loan as the base unless the question says otherwise.

Trap: Apply points to the loan amount, not the purchase price, unless the problem explicitly defines another base.

The capitalization-rate triangle contains annual net operating income, value, and cap rate:

• Cap rate = NOI ÷ value
• Value = NOI ÷ cap rate
• NOI = value × cap rate

NOI is property income after operating expenses but before debt service and income taxes. Do not subtract a mortgage payment when the question asks for cap rate from NOI.

A general rate-of-return problem divides annual return by the investment base stated. For example, $24,000 annual cash flow on $200,000 cash invested is a 12% cash return. Keep that setup separate from a capitalization-rate question using NOI and property value.

Trap: A percentage must become a decimal before you use it to solve for value. A 7.5% cap rate is 0.075.

PSI places some number-based concepts outside the seven-question calculation heading. Property Ownership includes linear, square-foot, and land measurement. Financing includes interest, down payments, loan terms, and qualification concepts. Learn these compact relationships:

The current calculation heading does not name commission splits as a standalone family. A brokerage fee can still appear as a seller debit, so know the basic percentage setup without giving it more study time than PSI’s nine named families.

1. Name the target. Write “seller net,” “LTV,” “seller tax share,” or the exact quantity requested.
2. Label every fact. Mark dollars, percentages, annual amounts, monthly amounts, days, and debits or credits.
3. Write the setup before calculating. This catches the wrong base, reversed division, and mixed time periods.
4. Estimate and check units. An 80% loan on $300,000 should be near $240,000, not $24,000 or $2.4 million.

PSI permits physical calculators at test centers but not during remote-proctored exams. Test-center candidates receive scratch paper and a pencil and must return them. Remote candidates may not use scratch paper.

Follow the booking instructions and use only the tools PSI authorizes for your format. Do not bring a phone, smartwatch, or another electronic device as a calculator. Use the pre-exam computer tutorial to become familiar with any controls PSI provides.

Practice at least a few problems without handwritten scratch work if you plan to test remotely. That exposes whether your setup is too dependent on a full page of notes.

These are original practice questions, not copied or reconstructed live exam items. Solve each one before opening the explanation.

• PSI Illinois Candidate Information Booklet
• Illinois Department of Revenue tax-rate table
• Illinois Department of Revenue real estate transfer-tax guidance
• Illinois Department of Revenue property-tax closing guidance

Pass Illinois is independent exam prep. It is not affiliated with PSI or IDFPR, does not replace required education, and does not provide legal, tax, lending, or investment advice. Examples are simplified for exam study.