3. If my child is 7 years old, and I purchase an endowment for $650, what will he receive if he attains the age of 21 years ?

ANNUITIES.

315. AN ANNUITY is a fixed sum of money to be paid at regular periods, generally, yearly, either for a limited time, or forever, in consideration of a given sum paid in hand.

THE PRESENT VALUE of an annuity is that sum which, being put at compound interest, would produce the sums necessary to pay the annuity.

The purchaser of an annuity should pay more than the compound interest; for the seller cannot afford to take the money of the purchaser, invest it, reinvest the interest, and pay over the entire proceeds.

Knowing the rate of interest on money, and the present value of an annuity, a close estimate may be made of the price it ought to sell for.

Table,

Showing the PRESENT VALUE OF AN ANNUITY OF $1, from 1 to 80 years, at different rates of interest.

To find the present value of an annuity for any rate, and for any time, we simply multiply the present value of an annuity of $1 for the same rate and time, by the annuity, and the product will be its present value.

Thus, the present value of an annuity of $600 for 8 years, at 6 per cent.,

is

$6.209794 × 600 = $3725.8764; that is,

pres. val. of $1 × annuity

annuity =

pres. val.; hence,

316. To find what sum will produce a certain annuity at a given rate and for a given time.

Rule.-Multiply the present value of an annuity of $1, at the given rate and for the given time, by the given annuity; the product will be that sum.

317. To find what annuity a given sum will produce at a given rate, and for a given time.

Rule.-Divide the given sum, or present value, by the present value of $1, for the given rate and time, and the quotient will be the annuity.

Examples.

1. What is the present value of an annuity of $550, at 5 per cent., for 21 years?

2. What would be the value of an annuity that should yield eight hundred and thirty-five dollars a year for sixteen years, the interest being compound, and at the rate of 5 per cent. per annum?

3. What is the present value of an annuity of $1500 a year, for 30 years, the compound interest being reckoned at 5 per cent.?

314. What is an endowment? What does the table of endowments show? What may be found from the table?-315. What is an annu ity? What is the present value of an annuity?-316. How do you find the present value of an annuity for a given rate and time?

4. What annuity, for twenty-four years, could be purchased for the sum of twenty-seven thousand five hundred and sixty dollars, the compound interest being reckoned at 6 per cent.?

5. Mr. Jones having a small fortune of $25000, and calculating that he would live about 20 years, purchased an annuity at 6 per cent., with an agreement that he would pay $20 a year to an invalid sister: what was his annual income from the investment after making that payment?

ASSESSING TAXES.

318. A TAX is a certain sum required to be paid by the inhabitants of a town, county, or State, for the support of govIt is generally collected from each individual, in proportion to the amount of his property.

In some States, however, every white male citizen, over the age of twenty-one years, is required to pay a certain tax. This tax is called a poll-tax; and each person so taxed is called a poll.

319. In assessing taxes, the first thing to be done is to make a complete inventory of all the property in the town, on which the tax is to be laid. If there is a poll-tax, make a full list of the polls, and multiply the number by the tax on each poll, and subtract the product from the whole tax to be raised by the town; the remainder will be the amount to be raised on the property. This remainder is the percentage or tax to be raised. The value of the property taxed is the base; hence this remainder, divided by the value of the property,

317. How do you find what annuity a given sum will produce, at a given rate and for a given time?-318. What is tax? How is it generally collected? What is a poll-tax?-319. What is the first thing to be done in assessing a tax? If there is a poll-tax, how do you find the amount? How, then, do you find the per cent. of tax to be levied on a dollar? How do you find the tax to be raised on each individual?

gives the rate. Each man's property, multiplied by the rate, gives his tax or percentage.

Examples.

A certain town is to be taxed $4280; the property on which the tax is to be levied is valued at $1000000. Now there are 200 polls, each taxed $1.40. The property of A is valued at $2800, and he pays 4 polls,

What will be the tax on one dollar, and what will be A's tax; and, also, that of each on the list?

First, $1.40 × 200 = $280, amount of poll-tax.

$280 = $4000, amount to be levied on property.

$4280

Then, $4000 $1000000 = .004

=

10%

4 mills on $1.

Now, to find the tax of each, as A's, for example :

In the same manner, the tax of each person in the township may be found.

Examples.

1. In a county embracing 350 polls, the amount of property on the tax-list is $318200; the amount to be raised is as follows for State purposes, $1465.50; for county purposes, $350.25; and for town purposes, $200.25. By a vote of the county, a tax is levied on each poll of $1.50: how much per cent. will be laid upon the property?

2. In a county embracing a population of 98415 persons, a

tax is levied for town, county, and State purposes, amounting to $100406. Of this sum, a part is raised by a tax of 25 cents on each poll, and the remainder by a tax of two mills on the dollar what is the amount of property taxed?

3. In a county, embracing a population of 56450 persons, a tax is levied for town, county, and State purposes, amounting to $87467; the personal and real estate is valued at $4890300. Each poll is taxed 25 cents: what per cent. is the tax, and how much will a man's tax be, who pays for five polls, and whose property is valued at $5400?

What is B's tax, who is assessed for 2 polls, and whose property is valued at $3760.50?

4. A banking corporation, consisting of 40 persons, was taxed $957.50; their property was valued at $125000, and each poll was assessed 50 cents: what per cent. was their tax, and what was a man's tax, who paid for 1 poll, and whose share was assessed for $2000 ?

5. What sum must be assessed to raise a net amount of $5674.50, allowing 2 per cent. commission on the money collected?

6. Allowing 4 per cent. for collection, what sum must be assessed to raise $21346.75 net?

7. In a certain township, it becomes necessary to levy a tax of $4423.2475, to build a public hall. The taxable property is valued at $916210, and the town contains 150 polls, each of which is assessed 50 cents. What amount of tax must be raised to build the hall, and pay 5 per cent. for collection, and what is the tax on a dollar?

What is a person's tax who pays for 3 polls, and whose personal property is valued at $2100, and his real estate at $3000?

What is G's tax, who is assessed for 1 poll, and $1275.50? What is H's tax, who is assessed for 1 poll, and $2456 ?