INSURANCE.

263. INSURANCE is security given to reimburse losses of property by fire, storms at sea, and other casualties.

OBS. This security is usually effected by contract with Insurance Companies, who, for a stipulated sum, agree to restore to the owners the amount insured on their houses, ships, and other property, if destroyed or injured during the specified time of insurance.

The written instrument or contract containing the terms of insurance, is called the Policy.

The sum paid for insurance, is called the Premium.

The premium is usually reckoned at a certain per cent. on the amount of property insured for 1 year, or during a voyage, or other specified time of risk.

Note-1. Insurance on ships and other property, is sometimes effected by contract with individuals. It is then called out-door insurance.

2 The insurers, whether an incorporated company or individuals, are called Underwriters.

CASE I. To find the PREMIUM, the sum insured, the rate per cent., and the time being given.

Ex. 1. How much premium must a mechanic pay annually for the insurance of his shop and tools worth $350, at 11 per cent.?

Suggestion. This example is similar to the ordinary examples in interest, and is solved in the same manner. That is, we multiply the sum insured by the rate per cent., and the result $5.25, is the premium. Hence,

Operation.

$350

.015

1750

350

$5.250

264. To find the premium, when the sum insured, the rate per cent., and the time are given.

Multiply the sum insured by the given rate per cent. expressed in decimals, and the product will be the premium.

Note. This Case is the same as finding the interest on a given sum, at an given rate, when the time is 1 year.

QUEST.-263. What is Insurance? What is a policy? The premium? Note. When insurance is effected with individuals, what is it called? What are the insurers sometimes called? 264. How find the premium, when the sum insured, the rate, and time are given?

2. What premium must be paid annually for insuring a house worth $875, at 3 per cent.?

3. Shipped a box of books valued at $1000, from New York to New Orleans, and paid 14 per cent. insurance: what was the premium?

4. A powder mill worth $925, was insured at 15 per cent.: what was the premium?

5. A merchant shipped a lot of goods worth $1560, from Boston to Natchez, and paid 13 per cent. insurance: what premium did he pay?

6. A gentleman obtained a poliey of insurance on his house and furniture to the amouut of $2500, at 31 per cent. per annum: what premium did he pay a year?

7. A man owning a sixteenth of a whale ship, which cost him $2750, got it insured, at 7 per cent. for the voyage: how much did he pay ?

8. A man owning a schooner worth $3800, obtained insurance upon it, at 5 per cent. for the season: what premium did he pay?

9. A crockery merchant having a stock of goods valued at $7500, paid 2 per cent. for insurance: how much premium did he pay a year? Ans. $150.

10. A merchant shipped $3765 worth of flour from Cincinnati to New York, and paid 14 per cent. insurance: how much premium did he pay?

11. What is the annual premium for insuring a store worth $7350, at per cent.?

12. An importer effected insurance on a cargo of tea worth $65000, from Canton to Philadelphia, at 3 per cent.: how much did his insurance cost him?

13. A manufacturer obtained insurance to the amount of $76500 on his stock and buildings, at 3 per cent.: how much premium did he pay annually?

14. A policy was obtained on a cargo of goods valued at $95600, shipped from Liverpool to New York, at 21 per cent.: what was the premium?

15. The owners of the whale ship George Washington obtained a policy of $58000 on the ship and cargo, at 74 per cent. for the voyage: what was the premium?

CASE II. To find the SUM INSURED, the premium and rate per cent. being given.

16. A gentleman paid $60 annually for insurance on his house and furniture, which was 2 per cent. on its value: what amount of property was covered by the policy?

Operation.

.02)$60.00 Ans. $3000

Suggestion. Since the rate is 2 per cent., 2 cents is the premium on $1; consequently, $60 must be the premium on as many dollars as 2 cents are contained times in $60. We therefore divide $60 by .02, and the result is the sum insured. Hence, 264.a. To find the sum insured, when the premium and the rate per cent. are given.

Divide the premium by the rate per cent., expressed in decimals, and the quotient will be the sum insured.

Note.-This Case is similar in principle to Problem III. in Interest.

17. If I pay $250 premium on silks, from Havre to New York, at 1 per cent., what amount does my policy cover?

18. A merchant paid $1200 premium, at 2 per cent., on a ship and cargo from London to Baltimore, which was lost on the voyage: what amount of insurance should he recover?

CASE III.-To find the RATE PER CENT., the sum insured, and the annual premium being given.

19. If a man pays $60 premium annually for the insurance of his house, which is worth $3000, what rate per cent. does he pay?

Analysis. If $3000 cost $60 premium, $1 will cost 1 three thousandth part of $60. We therefore divide $60 by $3000, and the quotient is .02 or 2 per cent. Hence,

Operation. $3000)$60.00(.02

6000 Ans. 2 per cent.

265. To find the rate per cent. when the sum insured and the annual premium are given.

Divide the given premium by the sum insured, and the quotient will be the rate per cent. required.

Note. This Case is similar in principle to Problem II. in Interest.

QUEST.-264.a. How find the sum insured, when the premium and the rate per cent. are given?

20. A merchant paid $40 premium for insuring $5000 on his stock what rate per cent. did he pay?

21. If a man pays $75 for insuring $15000, what rate per cent. does he pay?

22. If the owner pays $2800 for insuring a ship worth $40000, what rate per cent. does he pay?

CASE IV.-To find what sum must be insured on a given amount of property, so that if the property is destroyed, its value and the premium may both be recovered.

23. A blacksmith owns a shop worth $720: what amount must he get insured annually, at 10 per cent., so that in case of loss, both the value of the shop and the premium may be repaid?

Operation. $.90)$720.00 Ans. $800

Analysis. Since the rate of insurance is 10 per cent., on a policy of $100, the owner would actually receive but $90; for he pays $10 for insurance. Now, if the recovery of $.90 requires $1 to be insured, the recovery of $720 will require as many dollars to be insured as 90 cents is contained times in $720. We therefore divide $720 by $.90, and the quotient is the answer required. Hence,

265.a. To find what sum must be insured on a given amount of property, so that if destroyed, both the value of the property and the premium inay be recovered.

Subtract the rate per cent. from $1, then divide the value of the property insured, by the remainder, and the quotient will be the sum to be insured.

24. If I send an adventure to China worth $6250, what amount of insurance, at 8 per cent. must I obtain, that in case of a total wreck I may sustain no loss by the operation?

25. What amount of insurance must be effected on $11250, at 5 per cent., in order to cover both the premium and property insured?

QUEST.-265. How find the rate per cent., when the sum insured and the annual premium are given? 265.a. How find what sum must be insured on a given amount of property, so that if destroyed, its value and the premium may be recovered?

PROFIT AND LOSS.

266. Profit and Loss in commerce, signify the sum gained or lost in ordinary business transactions.

They are reckoned at a certain per cent. on the purchase price, or sum paid for the articles under consideration.

CASE I. To find the PROFIT or Loss, the purchase price and rate per cent. being given.

Ex. 1. A merchant bought a quantity of grain for $375, and sold it for 8 per cent. profit: how much did he gain?

Suggestion.-8 per cent. is 8 cents on 100 cents

Operation. $375

.08

or $1. Now, if $1 gains 8 cents, $375 will gain 375 times as much. We therefore multiply the cost and the per cent. profit together, and the Ans. $30.00 result $30, is the amount gained. Hence,

267. To find the profit or loss, when the purchase price and rate per cent. are given.

Multiply the purchase price by the given per cent. expressed in decimals, and the product will be the profit or loss.

OBS. If the rate per cent. is an aliquot part of 100, the profit or loss may be found by taking a like part of the cost. Thus, for 25 per cent. take ; for 20, take ; for 334, take, &c.

2. A man bought a sleigh for $60, and afterwards sold it for 10 per cent. less than cost: how much did he lose?

3. A grocer bought a cask of oil for $96.50, and retailed it at a profit of 6 per cent.: how much did he make on his oil? 4. A pedlar bought a lot of goods for $215, and retailed them at 20 per cent. advance: how much was his profit?

5. A merchant bought a cargo of coal for $450, which he sold for 12 per cent. less than cost: what was his loss?

6. A manufacturer bought $1000 worth of wool, and after making it up, sold the cloth for 25 per cent. more than the cost of the materials: what did he receive for his labor?

QUEST.-266. What is meant by profit and loss? How are they reckoned? 267. How do you find the profit or loss, when the cost and rate per cent. are given?