Illinois real estate math formula sheet: set up the problem first

Page 1 is the cover. Page 2 covers area, units and transaction math; page 3 covers financing and valuation. Page 4 gives commission, capitalization and LTV triangles with all three algebraic directions. Page 5 works loan and points, capitalization, proration and Illinois state transfer tax examples.

The triangles are memory aids. Cover the quantity you need, multiply the two bottom quantities or divide the top by the known bottom quantity. A diagram does not decide which value or rate belongs in a question.

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.

LTV divides the loan by the stated property value. Point cost uses the loan amount, while capitalization rate uses annual NOI divided by value. The PDF uses monthly GRM: sale price divided by gross monthly rent. If a question supplies an annual multiplier, use annual rent instead. Match the rent period to the multiplier.

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.

PITI combines monthly principal, interest, taxes and insurance. It does not automatically include mortgage insurance or association dues. Down payment is price minus loan; closing cash can include additional debits and credits.

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.

Start with taxable value rather than automatically using contract price. When the transferring document states that the property transfers subject to an existing mortgage, the outstanding mortgage is excluded from the Illinois state tax basis. Check the condition before subtracting a mortgage.

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.