599. Arithmetic of Taxation. When it is decided that a certain sum is to be raised by means of a property tax, then the arithmetic problem of taxation consists in apportioning this tax among the various persons in proportion to the assessed value of their property.

600. Rate of Taxation. The rate of taxation is expressed as so many mills per dollar, cents per hundred dollars, or as a rate per cent of the assessed valuation.

Thus 12 mills, 120 cents, or 13%, all express the same rate.

601. Problem. Given the Assessed Valuation and the Amount to be Raised, to Find the Rate.

Solution. Find what per cent of the assessed valuation is equal to the amount to be raised.

602. Problem. Given the Assessed Valuation and the Rate, to Find the Tax.

Solution. Multiply the assessed valuation by the rate.

EXERCISES

Find the rate of taxation in each of the following:

603. Spreading the Tax. After the assessor has made his list of assessed valuations the work of determining how much tax each person shall pay is called spreading the tax. This work consists in solving the two problems just given: (1) to find the rate, and (2) to find each person's tax, using this rate.

604. Tax Table.

The actual work of spreading a tax is greatly facilitated by what is called a tax table. This consists of a table giving the tax at the required rate on every dollar from $10 to $100. The tax on any valuation may then be obtained by properly placing the decimal point and adding.

7830 7965

6

8100 8235 8370

8505

7

8910 9045 9180 9215 9450 9585 9720 9855 9990 10125 10260 10395 10530 10665 8 10800 10935 11070 11205 11340 11475 11610 11745 11880 12015 9 12150 12285 12420 12555 12690 12825 12960 13095 13230 13365

8640 8775

The numbers in the first line of the table give the tax on amounts from $10 to $19, in the second line on amounts from $20 to $29, etc. Thus to find the tax on $67, we go down the left column to 6, and then along this line until we get to the column under 7, finding $.9045 as the required tax.

To find the tax on $37000 find the tax on $37 and multiply by 1000 (move the decimal point three places to the right). To find the tax on $860, find the tax on $86 and multiply by 10.

The method of using the table is shown in the following.

Example. By means of the above tax table find the tax on an assessed valuation of $37,860 at 13.5 mills.

By means of the above tax table find the tax at 13.5 mills on each of the following assessed valuations:

Example. Make a tax table if the rate is 11.7 mills.

Suggestions. The tax on $10, is $.117 and on $1 is .0117. To find the tax on $11 add .0117 to .117, obtaining .1287. To find the tax on $12 add .0117 to .1287, obtaining .1404, etc. When the tax on amounts from $10 to $20 has been obtained in this way, check by multiplying .0117 by 20. This checks all amounts between $10 and $20. Similarly check the tax on $30, $40, etc. In this way we are certain we are right as we go along.

WRITTEN EXERCISES

From the tax table made in the preceding example find the tax at 11.7 mills on each of the following assessed valuations.

1. What is the value of my property, if I pay $648.125 taxes at 15 mills on a dollar, the assessment being of the real value?

2. The tax rate of a city is 12% upon the assessed value of the property. If this value is 75% of the actual value, how much tax does a man pay upon property the actual value of which is $24,000 ?

3. A city made the following appropriation for its public schools: supervision, $70,000; instruction, $2,756,344.15; debt service, $335,855; contingent fund, $1,475,108. The assessed valuation is $898,204,300. What is the tax rate for school purposes?

4. In a town 2550 persons were subject to poll tax: the assessed valuation of the real estate was $3,450,200 and of personal property $350,000. The poll tax was $1.50 each. The tax to be collected was $55,000. What was the tax rate? What is a man's tax who has real estate to the value of $5000, and personal property to the value of $2500, and who pays for 2 polls?

5. A certain city spent $64,519.08 for supervision, $2,548,833.52 for teachers' salaries, $1,878,471.51 for another purpose. If the total valuation is $1,750,421,250, what is the rate of school tax?

6. The tax rate on' a certain property is 1.71% of its cash value; in how many years will the tax equal the cash value?

CHAPTER XLII

INCOME TAX

605. On January 1, 1914, a law went into effect levying a tax on all persons in the United States having an income above a certain amount. This law was amended by an act of September 8, 1916, and on October 3, 1917, a law was enacted imposing special war income taxes.

606. Exemption under the Law of 1916. Under the act of 1916 all net incomes above $3000 per annum are taxable in the case of persons not having a family, while all net incomes above $4000 are taxable in the case of married persons living with their families.

Thus, under the act of 1916, a single man having a net income of $10,000 has a taxable income of $7000, while a married man having a $10,000 income has a taxable income of $6000.

607. Exemptions under the Law of 1917. - Under the act of 1917 an additional tax is imposed on all net incomes above $1000 per annum in the case of single persons and on all net incomes above $2000 in the case of married persons and heads of families. The amount of $200 is added to the $2000 of exempted income for each dependent child.

Thus under the act of 1917 an unmarried person having an income of $5000 pays tax on $4000 and a married person with an income of $5000 and with no dependent children pays tax on $3000.

A married person with three dependent children and an income of $5000 pays tax on $5000 $2600 $2400.

=

608. The War Tax an Additional Tax.

The act of 1917 does not

repeal the act of 1916 but imposes an additional tax.

That is, to compute the tax on a certain income under these two acts, compute the tax under each act separately and add the results. Thus a single person having an income of $5000 pays tax on $2000 under the act of 1916 and also a tax on $4000 under the act of 1917.

A combined rate for the two acts may be computed, thus making it possible to find the combined tax directly.

609. Normal Taxes under the Act of 1916 and of 1917. — The act of 1916 imposes a normal tax of 2% on all incomes above the exempted amounts, and the act of 1917 imposes an additional normal tax of 2% on all incomes above the exempted amounts.

provided for in each act are called supertaxes or surtaxes.

The rates of taxation imposed by these two acts and also the combined rate are shown in the following table: