By the assistance of the following tables, questions in annuities may be easily performed.

TABLE I.

Showing the amount of $1 annuity from 1 year to 40.

Showing the present value of an annuity of $1 from 1 year to 40.

Years.

10. What is the present worth of an annuity of $200, at 5 per cent. compound interest, for 7 years? Ans. $1157.27+. 11. What is the present worth of an annuity of $ 300, to continue 8 years, at 6 per cent. compound interest?

Ans. $1862.93,8+. 12. What is the present value of an annuity of $100, at 6 per cent. for 9 years? Ans. $ 680.16,9+.

6

Questions to be performed by the preceding tables.

13. What will an annuity of $30 amount to in 11 years, at cent.?

per

By Table I., the amount of $1 for 11 years is $14.971643; therefore, $14.971643 × 30 = $449.14,9+ Answer.

14. What is the present worth of an annuity of $80 for 30 years, at 5 per cent.?

By Table II., the present worth of $1 for 30 years is $15.372451, therefore $15.372451 × 80 = $1229.79,6-+ Ans. 15. What will an annuity of $800 amount to in 25 years, at

5 per cent. ?

16. What will an annuity of $40 6 per cent. ?

Ans. $38181.67,9+. amount to in 30 years, at Ans. $3162.32,7+.

17. Required the present worth of an annuity of $ 500, to continue 40 years, at 6 per cent. Ans. $7523.14,8+. 18. A certain parish in the town of B., having neglected for 6 years to pay their minister's salary of $700, what in justice, provided he has preached the truth, should he receive? Ans. $4882.72,3.

SECTION LXVIII.

ASSESSMENT OF TAXES.

A TAX is a duty laid by government, for public purposes, on the property of the inhabitants of a town, county, or State, 2 and also on the polls* of the male citizens liable by law to as

sessment.

A tax may be either general or particular; that is, it may affect all classes indiscriminately, or only one or more classes.

* Poll is said to be a Saxon word, meaning head. In the constitution it means a person; that is, a person who is liable to taxation.

Taxes may be either direct or indirect; that is, they may either be imposed on the incomes or property of individuals, or on the articles on which these incomes or property are expended.

The method of assessing town taxes is not precisely the same in all the States, yet the principle is virtually the same.

In some of the States the poll tax is more than in others. The following is the law regulating taxation in Massachusetts (see Revised Statutes, page 79): —

"The assessors shall assess upon the polls, as nearly as the same can be conveniently done, one sixth part of the whole sum to be raised; provided the whole poll tax assessed in any one year upon any individual for town and county purposes, except highway taxes, shall not exceed one dollar and fifty cents; and the residue of said whole sum to be raised shall be apportioned upon property "; that is, on the real and personal estate of individuals which is taxable.

RULE FOR ASSESSING TAXES. First take an inventory of all the taxable property, real and personal, in the town or county, and then the number of polls liable to taxation. Multiply the sum assessed on each poll by the number of taxable polls in the town. Subtract this amount from the sum to be raised by the town. Then as the whole valuation of the town is to the sum to be raised, after having deducted the amount to be paid by the polls, so is the amount of each man's real and personal estate to his tax. Or, if the sum to be raised on property be divided by the valuation of the town, the quotient will be the sum to be paid on each dollar of an individual's real or personal estate. Multiply each man's property by this sum, and the product will be the amount of his taxes. The town of B. is to be taxed $4109. The real estate of the town is valued at $493,000, and the personal property at $177,000. There are 506 polls, each of which is taxed $1.50. What is John Smith's tax, whose real estate is valued at $3700 and his personal at $2300, he paying for 6 polls? And what will be the tax on $1.00?

OPERATION.

$1.50 × 506 = $759, amount assessed on the polls.

$493,000 +$177,000 $670,000, amount of taxable property. $4109 $759 $3350, amount to be assessed on property. $670,000 $3350::$1: $.005, to be assessed on each dollar. $3700 x .005 $18.50, tax on Smith's real estate.

$2300 x .005

$1.50 x 6

$11.50, tax on Smith's personal estate.

$9.00, tax on 6 polls.

$18.50 +$11.50 +$9.00 $39.00, amount of Smith's tax.

What will be the amount of taxation on each of the following individuals of the above town, their taxable property being as annexed to their names?

Form of a tax-list committed to the collector, containing the answers to the above questions.

Having found the amount to be raised on the dollar, the operation of assessing taxes will be much facilitated by the use of

By the aid of the above table the amount of any person's tax may be found.

Required the amount of James Dow's tax, his real estate being $4780, his personal $ 1720, and he paying for 3 polls.

$4780 $23.90 Amount of Dow's tax on real

2. To find the amount on his personal estate.

Dow's whole tax,

NOTE. It will be necessary to construct a different table, although on the same principle, when a different per cent. is paid on the dollar.

$37.00

SECTION LXIX.

ALLIGATION.

ALLIGATION teaches how to compound or mix together several simples of different qualities, so that the composition may be of some intermediate quality or rate. It is of two kinds, Alligation Medial and Alligation Alternate.

ALLIGATION MEDIAL.

Alligation Medial teaches how to find the mean price of several articles mixed, the quantity and value of each being given. RULE. As the sum of the quantities to be mixed is to their value, so is any part of the composition to its mean price.

EXAMPLES.

1. A grocer mixed 2cwt. of sugar at $9.00 per cwt., and 1cwt. at $7.00 per cwt., and 2cwt. at $10.00 per cwt.; what is the value of lcwt. of this mixture?