I found this little article on the Chicago Bar Association website regarding how Cook County Property Taxes are calculated.
Your Cook County real estate tax bill is the result of the assessed valuation of your real estate multiplied by an equalization factor and then multiplied by the tax rate.

The assessed valuation of your real estate is determined by the Office of the Assessor of Cook County. For tax purposes, there are 38 townships in Cook County, eight of which are within the City of Chicago. The Office of the Assessor reappraises the market value of properties in one-third of the townships each year. Thus, each property is reappraised every three years. In addition, the Assessor has the authority to reappraise a property at any time. In the latter case, notice must be sent to you by the Assessor’s Office if your assessment is increased.

Under an ordinance of the Cook County Board of Commissioners, real estate must be assessed at the following percentages of fair market value:

16 percent for farm land or real estate improved with residential buildings of less than seven units, including individual condominium and co-operative apartments;
22 percent for unimproved real estate;
33 percent for properties improved with residential buildings of more than six units;
38 or 36 percent for properties improved with commercial or industrial buildings.
The ordinance also provides in limited situations for lower assessments as incentives to build or rehabilitate commercial or industrial structures and to rehabilitate low and moderate income apartment buildings having more than six units.

Improvements worth up to $30,000 made to a single family residence, condominium apartment or apartment building of less than seven units may be made without increasing the assessed value of the real estate for four years after the improvement was made.

If you believe your real estate taxes are disproportionately high you may file a complaint about the assessed valuation of your real estate with the Office of the Assessor. The main office is located on the third floor of the County Building at 118 North Clark Street, Chicago. The Assessor also has offices in Circuit Court Buildings at: 16501 South Kedzie Parkway, Markham, Illinois 60426; Maywood Civic Center, 1500 Maybrook Square, Maywood, Illinois 60153; 5600 Old Orchard Rd., Room 149, Skokie, Illinois; 10200 76th Ave., Room 237, Bridgeview, Illinois; and 2121 Euclid Ave., Room 237, Rolling Meadows, Illinois.

The Assessor’s Office has a Taxpayer’s Assistance Department. If you have a question about your real estate taxes, you can meet with a Hearing Officer in the Taxpayer’s Assistance Department. The Hearing Officer will check your real estate tax records and explain how the Assessed Valuation was made on your home. If you still feel that the assessment is too high, a Hearing Officer will help you prepare and file a complaint.

When you file a complaint, you will be asked to bring at least one of the following forms of documentation with you, although it is NOT REQUIRED:

A copy of the signed contract of purchase and sale of the property, if the property was purchased within the last three years; or
Evidence of sale prices of homes recently sold similar to those in your neighborhood; or
Information regarding the assessment on homes similar to yours in your neighborhood; or
An appraisal of the property made by a reputable and equitable appraiser.
This documentation, again, is not required but would be helpful to your complaint. If you cannot bring in any of this information, you will be requested, if possible, to bring recent photographs of your home. As soon as possible, a letter stating and explaining the results of the complaint will be mailed to you. If you are dissatisfied with the results, you may contact the Taxpayer’s Advocate in the Assessor’s Office. The Taxpayer’s Advocate will explain how and why the Assessor reached his decision. If you have any new or additional information, you should give it to the Taxpayer’s Advocate.

If warranted, the Advocate will see that the complaint is reviewed again. The Taxpayer’s Advocate has only one responsibility: to see that your rights are protected.

If you are not satisfied with the decision of the Taxpayer’s Advocate, you may have the assessed valuation of your property reviewed by the Board of Appeals of Cook County. This process starts when you file a complaint with the Board. The office of the Board is on the sixth floor of the County Building, at 118 North Clark Street. The Board accepts and hears complaints only during a limited time each year. You must call or write the office of the Board to ask when complaints for your area will be accepted.

If you are not satisfied with the decision of the Board of Appeals, you may pursue a further challenge to your taxes by filing a complaint with the Property Tax Appeal Board, or by filing a Tax Objection Complaint in the circuit Court of Cook County. A prerequisite to either challenge is (1) that you have sought relief from the Board of Appeals, and in order to file a Tax Objection Complaint in the Circuit Court (2) that you have paid the second installment of your taxes within 60 days of the due date. The procedures for challenging real estate taxes in court require careful attention and you should consult a lawyer concerning this remedy.

After the assessed valuation of your real estate is determined by the Office of the Assessor and reviewed by the Boards of Appeals, the Illinois Department of Revenue has the authority to increase the valuation of all properties(except farmland) in the County by an equal percentage. In recent years, that increase has been by multiple of about 2. The purpose of such action is to bring the assessments of Cook County to the aggregate level of one-third of market value. This increase factor is called the “multiplier” or equalization rate.

Senior Citizens, 65 or over, may obtain a Homestead Exemption of $2,500 as a reduction in the equalized assessment of real estate which they occupy as a residence. If they qualify for the Senior Citizen Exemption and have household income of $35,000 or less, they may qualify for the Senior Citizen Assessment freeze, which freezes the assessed value of the property. They must make application to the Office of the Assessor to obtain these reductions. Also, all owners regardless of age who occupy their residential property are entitled to an annual homestead exemption of up to $4,500 in deduction from their equalized valuation.

After the equalized valuation is established the amount of your real estate tax bill is determined by applying the tax rate to the equalized assessed valuation of your property. The tax rate is set equal to the amount sufficient to produce, with other forms of taxes, enough money to operate the various governmental agencies and bodies in the municipalities and county.

Although it is possible to challenge the tax rate, unless your real estate is improved with a large structure and your real estate tax bill is very substantial, significant reductions in your bill will most likely result from successfully protesting the amount of the assessed valuation of your property and not the tax rate. Challenging the assessed valuation must be done in the Office of the Assessor and/or before the Board of Appeals prior to the issuance of your real estate tax bill. The various filing deadlines are very important in challenging real estate taxes. The Assessor’s Office does have a “Certificate of Error” procedure to permit relief after deadlines have passed, but the availability of relief under that process is limited.

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