flour, worth $10.50 a barrel. The premium paid was $2887.50: what was the rate per cent. of the insurance?

11. Paid $120 for insurance on $7500 what was the rate per cent.?

my dwelling, valued at

12. A merchant imported 225 pieces of broadcloth, each piece containing 40 yards, at $3.50 a yard: he paid $1323 for insurance: what was the rate per cent.?

13. A merchant paid $1320 insurance on his vessel and cargo, which was 51 per cent. on the amount insured ; how

much did he insure?

14. A man pays $51 a year for insurance on his storehouse, at 11 per cent., and $126.45 on the contents, at 24 per cent: what amount of property does he get insured?

15. A person shipped 15 pianos, valued at $275 each. He insures them at 3 per cent., and also insures the premium at the same rate: what insurance must he pay?

16. A store and its contents are valued at $16750. The owner insures them at 1 per cent., and then insures the premium at the same rate: what insurance must he pay?

LIFE INSURANCE.

310. LIFE INSURANCE is an agreement to pay, in consideration of a premium, a specified amount to parties named in the agreement, in case of death, or other specified contingency.

311. To enable the company to fix their premiums at such rates as shall be both fair to the insured and safe to the association, they must know the average duration of life from any given time to its probable close. This average is called the "Expectation of Life," and is determined by collecting

310. What is life insurance?-311. What is necessary to enable a company to fix their premiums? How is the expectation determined 1 What do you understand by the expectation of life?

from many sources the most authentic information in regard to the average duration of life from any period named.

If we take 100 infants, some will die in infancy, some in childhood, and some in old age. It has been found, from careful observation, that if the sum of their ages, after the last shall have died, be divided by 100, the quotient will be 38.72 very nearly: hence 38.72 is said to be the "Expectation of Life" at infancy.

The Carlisle Tables of England, which differ but little from those used in this country, show the "Expectation of Life" from 1 to 100 years. At 10 years old it is found to be 48.82; at 20, 41.46; at 30, it is 34.34; at 40, 27.61; at 50, it is 21.11; at 60, 14 years; at 70, 9.19; at 80, 5.51; at 90, 3.28; and at 100, it is

2.28 years.

If we wish the expectation of life, between the periods named in the table, we can readily find it by the rules of proportion. Thus, if we wished the expectation of life at 16 years, we should observe that, at 10 years, it has been found to be 48.82; at 20 years, it has been found to be 41.46; hence, for 10 years it varies 48.82 41.467.36 years:

Then, 10 : 6 :: 7.36 : 4.416;

which number being subtracted from 48.82, leaves 44.40, the expectation of life at 16 years of age.

312. From the above facts, and the value of money (which is shown by the rate of interest), a company can calculate with great exactness the amount which they should receive annually for an insurance on a life for any number of years, or during its entire continuance.

313. The Mutual Life Insurance Company, of New York, has made a valuable collection of statistics, and its actuary, Shephard Homans, has constructed therefrom, a set of Tables, differing slightly from the Carlisle Tables. These changes have been adopted by several other Companies; but, as no settled standard has yet been fixed, the examples, as before, are wrought from the Carlisle

Tables. Tables are also published, showing the quarterly, semiannual, and annual premiums that must be paid on each $100, or $1000 insured.

NOTE.-Experience has demonstrated that the risks are about equal on all ages between 14 and 25 years. Persons under the age of 25 years are charged for whole life policies, the rate at that age; though dividends are based on the true age. An extra charge, on the above rates, of one-half per cent. on the amount insured, is made for insuring the lives of women under the age of 48 years.

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 4 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 ambas sador, 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.

314. 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.

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 of 21 years. The table is calculated under the hypothesis that money is worth 6 per cent. interest.

TABLE OF ENDOWMENTS,

Showing the sum to be paid at 21 years, if alive.

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 pur chase 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?

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 pnt 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 30 years, at different rates of interest.