Free real estate math reference

Set up Illinois real estate math before touching the calculator

Formula memory helps only when the right number goes in the right place. This printable pairs each formula with the unit, setup warning, and a worked exam-style check.

Last updated: August 1, 2026

The resource first

Direct answer: The current national broker outline assigns 7 percent to real estate calculations, while the Illinois outline also includes real property transfer fees and taxes. The free three-page PDF covers square footage and acreage, commission and split math, seller and buyer closing equations, prorations, LTV, down payment, points, simple interest, PITI, NOI, capitalization rate, GRM, appreciation, and the current Illinois state transfer-tax unit of $0.50 per $500 of taxable value or fraction. It also shows why points use the loan amount, debt service is excluded from cap-rate NOI, and proration conventions must come from the question.

Download the Illinois math formula sheet

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Land conversion

1 acre = 43,560 sq ft

Point

1% of the loan amount

Cap-rate core

Value = NOI / rate

Illinois state transfer tax

$0.50 per $500 or fraction

Use the four-line setup

Write the unknown with its unit, list the given values with compatible units, choose the formula that connects them, and test whether the result has the right direction and size. This short setup prevents many errors that calculator fluency cannot repair.

Percentages should become decimals before multiplication or division. Time periods, income periods, and area units must match. Delay rounding until the stated instruction or final money result unless a tax unit specifically requires rounding up.

Keep the denominator honest

LTV divides the loan by value, point cost multiplies the loan by the point rate, capitalization rate divides NOI by value, and GRM divides sale price by gross monthly rent. The most tempting wrong answers often use a familiar but incorrect base, such as sale price for points or gross income for a capitalization calculation.

For NOI, subtract operating expenses from effective gross income. Do not subtract mortgage debt service in the standard cap-rate setup. For a proration, identify the annual or periodic amount, the day convention, chargeable days, responsible party, and advance-or-arrears timing before labeling a debit or credit.

Loan = value x LTV.
Down payment = purchase price - loan.
Value = NOI / capitalization rate.
Value by GRM = gross monthly rent x market GRM.

Apply the Illinois transfer-tax unit carefully

For the state tax, divide the taxable value by $500, round any fraction up to the next whole unit, and multiply by $0.50. The PDF works $327,250 into 655 units and $327.50 of state tax.

A county may impose $0.25 per $500, and home-rule municipalities may add their own tax. An exam question should supply the relevant local rate or scope. Do not treat the state-only number as the universal transaction total.

Quick questions

How much math is on the national broker exam?

Real Estate Calculations is 7 percent of the current 100-question national broker outline, or about seven scored questions by weight.

Are mortgage payments an NOI operating expense?

No in the standard capitalization setup. NOI subtracts operating expenses from effective gross income before debt service.

Are points based on price or loan?

Points are a percentage of the loan amount. One point equals 1 percent of the loan.

Should I use 360 or 365 days for a proration?

Use the convention stated in the question. Do not assume one when the problem supplies another.

What is the Illinois state real estate transfer-tax rate?

The current state rate is $0.50 for each $500 of taxable value or fraction of $500. County and municipal taxes may also apply.

Primary sources and review status

Checked through August 1, 2026. The downloadable resource also displays its source and review date. The current official source controls if a rule, outline, or procedure changes.