The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

The assessed value of the property is $75,372, this is 75,372/1,000  75.372 thousands.

We will consider the county rate, expressed in mills, as a rate per thousand.

County tax: ($14 per thousand)(75.372 thousands)  $1,055.21.

Town tax: ($8.57 per thousand)(75.372 thousands)  $645.94

For the school district, it is most convenient to read $1.35 per hundred as 1.35%. So:

School tax: (1.35%)($75,372)  $1,017.52.

Overall, Josh’s real estate taxes total $1,055.21 
 $645.94 
 $1,017.52  $2,718.67.

Setting Property Tax Rates

Property tax rates are normally set by first determining the total amount of tax to be collect-

ed (called the tax levy) and then dividing it by the total assessed value of taxable property.

This result is then put in terms of a rate per thousand, or percent, or whatever the desired

form to express the rate may be. The following example will illustrate this.

Example 9.3.4 The Bloome County legislature has set the overall property tax levy

for 2008 to be $39,600,000. The total assessed value of taxable property in the county

is $4,873,595,000. Determine the 2008 real estate tax rate for the county. Express

the result as (a) a percent (to four decimal places), (b) a rate per hundred (to three

decimal places), (c) a rate per thousand (to two decimal places), and (d) mills (to two

decimal places).

Dividing this tax levy by the taxable property gives a percent rate of:

Rate 

$39,600,000

_______________

$4,873,595,000

 0.0081254354

(a) Moving the decimal place, we can express this as a 0.8125% rate.

(b) A rate per hundred is essentially the same as a percent, except expressed in dollars.

Therefore the rate is $0.813 per hundred.

(c) To fi nd the rate per $1,000, we can apply our original percent to a $1,000 assessed

value. Then (0.0081254354)($1,000)  $8.13 per thousand.

(d) Mills are essentially the same as a rate per thousand. So the rate is 8.13 mills.

The table below summarizes the ideas used in this example:

If the Rate is Expressed as: Divide the Total Levy by the Assessed Value and:

Rate per thousand • Multiply the result by $1,000

Mills • Multiply the result by 1,000

Percent • Move the decimal two places to the left (as usual)

Rate per hundred • Rewrite the percent rate as a dollar amount

Rounding can be an issue with tax rates. To get the exact $39,600,000 tax levy, the rate

would have to be applied without any rounding, or at least carried out to quite a few decimal

places. Any reasonable degree of rounding may cause the actual taxes charged to work out

to more, or less, than the intended levy. This is why the instructions to Example 9.3.4 asked

for the percent to more than the two decimal places that we have been customarily using

with percents; the more decimal places, the less rounding, and hence the less difference

due to rounding.

Example 9.3.5 Suppose that the county sets the tax rate to be $8.13 per thousand.

How much will the actual taxes total?

(4,873,595 thousands)($8.13 per thousand)  $39,622,327.35

9.3 Property Taxes 401