ANALYSIS.-The gain or loss will be equal to the difference between the cost and the amount received from the sale. If this difference be divided by the cost, the quotient will

OPERATION.

$200 170 = $30

$30 $200 = .15. Ans. 15 per cent.

denote the per cent on the cost; if it be divided by the amount of the sale, the quotient will denote the per cent on the sale.

RULE.-Divide the gain or loss by the number on which the per cent is reckoned.

EXAMPLES.

1. Bought a quantity of goods for $348,50, and sold the same for $425: what per cent did I make on the amount received?

2. Bought a piece of cotton goods for 6 cents a yard, and sold it for 7 cents a yard: what was my gain per cent?

3. If I buy rye for 90 cents a bushel, and sell it for $1,20, and wheat for $1,123 a bushel, and sell it for $1,50 a bushel, upon which do I make the most per cent?

4. If paper that cost $2 a ream, be sold for 18 cents a quire, what is gained per cent?

5. How much per cent would be made upon a hogshead of sugar weighing 13cwt. 3qr. 14lb., that cost $8 per cwt. if sold at 10 cents per pound?

6. A hardware merchant bought 45 T. 16cwt. 25lb. of iron, at $75 per ton, and sold it for $78,50 per ton: what was his whole gain, and how much per cent did he make?

7. If 25 per cent be gained on flour when sold at $10 a barrel, what per cent would be gained when sold at $11,60 a barrel?

NOTE. In this class of examples, first find the cost, as in Art. 246: then find the gain, or loss, and then divide by the number on which the per cent is reckoned.

8. A lumber dealer sold 25650 feet of lumber at $19,20 a thousand, and gained 20 per cent: how much would he have gained or lost had he sold it at $15 a thousand?

9. A man sold his farm for $3881,25, by which he gained 121 per cent on its cost: what was its cost, and what would he have gained or lost per cent if he had sold it for $3277,50 ?

10. If a merchant sell tea at 66 cents a pound, and gain 20 per cent, how much would he gain per cent if he sold it at 77 cents a pound?

11. Sold 5520 bushels of corn at 50 cents a bushel, and lost 8 per cent: how much per cent would have been gained had it been sold at 60 cents a bushel?

12. A grocer bought 3 hogsheads of sugar, each weighing 1412 pounds; he sold it at 11 cents a pound, and gained 371 per cent what was its cost, and for how much must he sell it to gain 50 per cent on the cost?

INSURANCE.

249. INSURANCE is an agreement, generally in writing, by which individuals or companies bind themselves to exempt the owners of certain property, such as ships, goods, houses, &c., from loss or hazard.

The POLICY is the written agreement måde by the parties. 250. The BASE of insurance is the value of the property insured.

251. PREMIUM is the amount paid by him who owns the property to those who insure it, as a compensation for their risk. The premium is generally so much per cent on the property insured.

252. There are four cases which may arise in questions of Insurance. The principles on which these cases depend have already been considered, and reference is made to the articles.

249. What is insurance? What is a policy?

250. What is the base of insurance?

251. What is a premium ?

252. How many cases are there which arise in insurance? What are they?

1. To find the Premium (Art. 216).

2. To find the Rate (Art. 217).

3. To find the base, or sum insured (Art. 218).

4. To insure on both the base and premium.

253. To find the premium:

1. What would be the premium on a cargo of goods, valued at $39854, the insurance being made at 4 per cent?

ANALYSIS. This is simply a case of finding the percentage when the base and rate are given (Art. 216).

OPERATION.
39854

.045

$1793,430

EXAMPLES.

1. What would be the premium for insuring a ship and cargo, valued at $147674, at 3 per cent?

2. What would be the insurance on a ship, valued at $47520, at per cent? At per cent?

3. What would be the insurance on a house, valued at $16800, at 14 per cent? At 3 per cent?

4. A merchant owns of of a ship, valued at $24000, and insures his interest at 2 per cent: what does he pay for his policy? 5. What will it cost to insure a store worth $5640, at 3 per cent, and the stock worth $7560, at per cent?

6. A carriage maker shipped 15 carriages worth $425 each: what must he pay to obtain an insurance upon them at 75 cents on a hundred dollars?

7. A merchant imported 150hhd. of molasses, at 35 cents a gallon: he gets it insured for 3 per cent on the selling price of 50 cents a gallon: if the whole should be destroyed, and he get the amount of insurance, how much would he gain?

8. If I get my house and furniture, valued at $3640, insured at.4 per cent, what would be my actual loss if they were destroyed?

253. How do you find the premium?

9. The ship Astoria is valued at $20450, and her cargo at $25600; being bound on a voyage from New York to Canton, insured $12000 on the vessel, at the St. Nicholas Office, at 23 per cent, and $18500 on the cargo, at the Howard Office, at 31 per cent if the vessel founder at sea, what will be the loss to the owner?

10. Shipped from New York to the Crimea 5000 barrels of 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 my dwelling, valued at $7500: what was the rate per cent.?

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 5 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 21 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. If a store and its contents are valued at $16750, and they are insured at 13 per cent, how much must be paid to cover the base of insurance and the premium?

LIFE INSURANCE.

254. INSURANCE for a term of years, or for the entire continuance of life, is a contract on the part of an authorized association to pay a certain sum, specified in the policy of insurance, on the happening of an event named therein, and for which the association receives a certain premium, generally in the form of an annual payment.

254. What is a life insurance ?

66

255. 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 its commencement to its extreme limit. This average is called the Expectation of Life," and this is determined by collecting from many sources the most authentic information in regard to births and deaths. The " Carlisle Table" shows the expectation of life from birth to 100 years, and is considered the most accurate. It is much used in England, and is in general use in this country. By the "Expectation of Life," must be understood the average age of any number of individuals. Thus, if 100 infants be taken, some dying in infancy, some in childhood, some in youth, some in middle life, and some in old age; the average ages of all is found to be 38.72 years. At 10 years of age, the average age is 48.82 years; at 20, it is 41.46 years; at 30, it is 34.34 years; at 40, it is 27.61 years; at 50, it is 21.11 years; at 60, it is 14 years; at 70, it is 9.19 years; at 80, it is 5.51 years; at 90, it is 3.28 years; and at 100, it is 2.28 years.

256. 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.

Among the principal life insurance companies in the United States, are the New York Life Insurance and Trust Company, the Girard Life Insurance, Annuity and Trust Company of Philadelphia, and the Massachusetts Hospital Life Insurance and Trust Company of Boston. The rates of insurance, in these companies, differ but little.

The PREMIUM for life insurance is generally at so much per annum on $100; and is always paid in advance.

255. What is necessary to enable a company to fix their premiums ? How is the expectation determined? What do you understand by the expectation of life?

256 What may be calculated from the necessary facts?