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

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

Years.

5 per cent. 6 per cent. ll Years. | 5 per cent. 6 per cent. 1.000000 1.000000

35.719252 39.992727 2.050000 2.060000

38.505214 43.392290 3.152500 3.183600

41.430475 46.995828 4.310125 4.374616

44.501999 50.815577 5.525631 5.637093

47.727099 54.864512 6.801913 6.975319

51.113454 59.156383 8.142008 8.393838

54.669126 63.705766 9.549109 9.897468

58.402583 68.528112 11.026564 11.491316

62.322712 73.639798 12.577893 13.180795

66.438847

79.058186 14.206787 14.971643

70.760790 84.801677 15.917127 16.869941

75.298829 90.889778 17.712983 18.882138

80.063771 97.343165 19.598632 21.015066

85.066959 104.183755 21.578564 23.275970

90.220307 111.434780 23.657492 25.672528

95.836323 119.120867 25.840366 28.212880

101.628139 127.268119 28.132385 30.905653

107.709546 135.904206 30.539004 33.759992

114.095023 145.058458 33.065954 | 36.785591 | 40 l 120.799774 | 154.761966

TABLE II. Showing the present value of an annuity of $ 1 from 1 year to 40. Years. 5 per cent. 6 per cent. Years. 5 per cent. 6 per cent. 0 952381 0.943396

12.821153 11.764077 1.859410 1.833393

13.163003 12.041582 2.723248 2.673012

13.488574 12.303379 3.545950 3.465106

13.798642 12.550358 4.329477 4.212364

14.093945 12.783356 5.075692 4.917324

14.375185 13.003166 5.786373 5.582381

14.643034 13.210534 6.463213 6.209794

14.898127 13.406164 7.107822 6.801692

15.141074 13.590721 7.721735 7.360087

15.372451 13.764831 8.306414 7.886875

15.592810 13.929086 8.863252 8.388844

15.802677 14.084043 9.393573 8.852683

16.002549 14.230230 9.898641 9.294984

16.192904 14.368141 10.379658 9.712249

16.374194 14.498246 10.837770 10.105895

16.546852 14.620987 11.274066 10 477260

16.711287 14.736780 11.689587 10.827603

16.867893 14.846019 12.085321 11.158116

17.017041 14.949075 12.4622161 11.469921

17.159086 | 15.046297

10. What is the present worth of an annuity of $ 200, at 5 per cent. compound interest, for 7 years ? Ans. $ i 157.27+.

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+. Questions to be performed by the preceding tables. 13. What will an annuity of $ 30 amount to in 11 years, at 6 per cent. ?

By Table I., the amount of $ 1 for 11 years is $14.971643; therefore, $ 14.971643 x 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 X 80 = $ 1229.79,6-t Ans.

15. What will an annuity of $ 800 amount to in 25 years, at 5 per cent. ?

Ans. $ 38181.67,9+. 16. What will an annuity of $ 40 amount to in 30 years, at 6 per cent. ?

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 assessment.

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 Laxable property, real and personal, in the town or county, and then the number of polls liable to taration. Multiply the sum assessed on each poll by the number of taxable polls in the lown. 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 X 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 = $ 11.50, tax on Smith's personal estate. $ 1.50 X 6= $ 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 ? Persons

Real Estate. Personal Estate. No. of Polls. James Dow,

$ 4780

$ 1720 John Brown,

7500

2120 Samuel Foster,

1135

175 James Emerson,

8960

5000 - 2 A. C. Hasseltine, 7140

3720 Form of a tax-list committed to the collector, containing the answers to the above questions.

Tax on | Tax on

Time
No. of Poll Taxel

Real Personal
Polls.

when

Total.

Estate. Estate.
James Dow, 3 $ 4.50 $ 23.90 $ 8.60 $ 37.00
John Brown, 11 1.50 1 37.50 | 10.60 | 49.601
Samuel Foster, 1 g | 10.50 / 5.674 .8711 17.05
James Emerson,! 2 3.00 | 44.80" 25.00 72.80
A.C. Hasseltine,! O 0.00 35.70 / 18.60 54.30
John Smith, 16 9.00 | 18.50 | 11.50 39.00

Names.

11 Tax.

paid.

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

TABLE.

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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.

1. To find the amount on his real estate.

OPERATION. Dow's tax on $ 4000 is $ 20.00

700 66 3.50 66 80 4 .40

[estate. $ 4780 $23.90 Amount of Dow's tax on real 2. To find the amount on his personal estate.

OPERATION.
Dow's tax on $ 1000 is $5.00

70066 3.50
20 “ .10

(sonal estate.
$ 1720 $ 8.60 Amount of Dow's tax on per-
Tax on real estate, $ 23.90
Tax on personal estate, 8.60
Tax on 3 polls,

4.50 Dow's whole tax, $37.00 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.

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 lcwt. at $ 7.00 per cwt., and 2cwt. at $ 10.00 per cwt. ; what is the value of lcwt, of this mixture ?

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