EXAMPLES.

1. A person, 20 years of age, finds that the premium, per annum, is $1.36 on $100: what must he pay to insure his life for 1 year for $8950?

2. A man, aged 40 years, wishes to insure his life for 5 years, and finds that the annual rate is $1.86 for $100: how much premium must he pay per annum on $12500?

3. A person, 38 years of age, obtains an insurance on his life for 5 years, at the rate of $1,75 per annum on $100: how much is the annual premium on $15000?

4 A person going to Europe, expecting to return in 2 years, effects an insurance on his life at of per cent. premium on $100; he insures for $5000: what is the annual premium?

5. What will be the annual premium for insuring a person's life, who is 60 years of age, for $2000, at the rate of $4,91 on $100 ?

6. A person, at the age of 50 years, obtained an insurance at 43 per cent. per annum on each $100; he insured for $1500, and died at the age of 70. How much more was the insurance than the payments, without reckoning interest?

7. A gentleman, 47 years of age, going to China as ambassador, obtains an insurance on his life for $10000, by paying a premium of $2.71 per annum on every $100, and dies at the middle of the third year: reckoning simple interest on his payments at 7 per cent, what is gained by the insurance?

ENDOWMENTS.

257. AN ENDOWMENT is a certain sum to be paid at the expiration of a given time, in case the person on whose life it is taken shall live till the expiration of the time named.

257. What is an endowment? What does the table of endowments show? What may be found from the table?

The following table shows the value of an endowment purchased for $100, at the several periods mentioned in the column of ages, the endowment to be paid if the person attains the age

This table shows that if $100 be paid at the birth of a child, he will be entitled to receive $376,84, if he lives to attain the age of 21 years. If $100 be paid when he is ten years old, he will be entitled to receive $164,46, if he lives to attain the age of 21 years. And similarly for other ages. We can easily find by proportion

1st. How much must be paid, at any age under 21, to purchase a given endowment at 21; and

2d. What endowment a sum paid at any age under 21, will purchase?

EXAMPLES.

1. What endowment, at 21, can be purchased for $250, paid at the age of 10 years?

2. What endowment, at 21, can be purchased for $360, paid at the age of 5 years?

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?

4. If, at the birth of a daughter, I purchase an endowment for $350, what will she receive if she attain the age of 21 years?

ANNUITIES.

258. AN ANNUITY is a fixed sum of money to be paid at regular periods, 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 present value; for the seller cannot afford to take the money of the purchaser, invest it, re-invest 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 30 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

258. What is an annuity? What is the present value of an annuity? How do you find the present value of an annuity for a given rate and time? How do you find what annuity a given sum will produce, at a given rate and for a given time ?

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 x 600 = $3725.8764; that is,

pres. val. of $1 x annuity pres. val., hence,

annuity =

=

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

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.

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

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 cost of an annuity of $860 a year, for

16 years, compound interest, and charged 25 dollars a year for doing the business?

if the company borrowed the money at 5 per cent.

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

4. For what sum could Mr. Jones purchase an annuity for 28 years, of $1250, if he paid 30 dollars a year for investing his money and paying over the interest; the money yielding per cent?

6

the

5. What annuity would $27560 purchase for 24 years, purchaser to pay $35 a year for loaning the money and collecting the interest, which is reckoned at 6 per cent?

6. Mr. Jones having a small fortune of $25000, and calculating that he will live about 20 years, purchases an annuity at six per cent, with an agreement that he will pay $20 a year for

doing the business: what was his annual income from the investment?

ASSESSING TAXES.

259. A TAX is a certain sum required to be paid by the inhabitants of a town, county, or state, for the support of government. It 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.

260. 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. Having done this, divide the whole tax to be raised by the amount of taxable property, and the quotient will be the tax on $1. Then multiply this quotient by the inventory of each individual, and the product will be the tax on his property.

EXAMPLES.

1. 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,

259. What is tax? How is it generally collected? What is a poll-tax? 260. 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?