439.. To find the sum insured when the premium an rate per cent. are given.

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

Note. This case is similar in principle to Problem III. in Interest.

19. An importer paid $650 premium on goods from Hamb to New York, which was 14 per cent. on the amount ins how much did he insure?

20. A merchant paid $1640 premium on goods from Phil piia to Constantinople, which was 24 per cent. on the wor the goods insured: how much did he insure?

21. A premium of $487.50 was paid on a cargo of cotton New Orleans to Liverpool, which was per cent. on its v what amount was insured on the cargo ?

22. When the rate of insurance is 1 per cent., what sur you get insured for $860 premium ?

23. At per cent. per annum, what amount can a man g sured on his house and furniture for $20.50 per annum?

CASE IV.

To find what sum must be insured on any given proper that, if destroyed, its value and the premium may both be r ered.

24. If a man owns a vessel worth $1920, what sum must h insured on it, at 4 per cent., so that if wrecked, he may re both the value of the vessel and the premium?

Analysis. It is plain, when the rate of insurance is 4 per on a policy of $1, or 100 cents, the owner would receive b cents towards his loss; for, he has paid 4 cents for insu Since therefore the recovery of 96 cents requires $1 to be ins the recovery of $1920 will require as many dollars to be in as 96 cents is contained times in $1920; and $1920÷ $2000. Ans.

PROOF.-$2000X.04 $80, the premium paid, and $20 $80 $1920, the value of the vessel.

440. Hence, 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 may 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.

25. What sum must be insured on property worth $8240, at 1 per cent., so that the owner may suffer no loss if the property is destroyed?

26. What sum must be insured on $13460, at 3 per cent., in order to cover both the premium and property insured ?

27. If I send an adventure to the Sandwich Islands worth $25000, what sum must I get insured, at 7 per cent., that I may sustain no loss in case of a total wreck?

LIFE INSURANCE.

441. A LIFE INSURANCE is a contract for the payment of a certain sum of money on the death of an individual, in consideration of a stipulated sum paid down, or, more commonly, of an annual premium, to be continued during the life of the assured.

The average duration of human life is often called the Expectation of Life. This is different in different countries, but it may be determined with great accuracy in any given country, by calculations founded on the register of births and deaths in that country.

OBS. At birth, the expectation of life, according to the Carlisle Table, is 38.72 y.; at 5, it is 51.25 y.; at 10, it is 48.82 y.; at 15, it is 45 y.; at 20, it is 41.46 y.; at 25, it is 37.86 y. ; at 30, it is 34.34 y.; at 35, it is 31 y.; at 40, it is 27.61 y.; at 45, it is 24.46 y.; at 50, it is 21.11 y.; at 55, it is 17.58 y.; at 60, it is 14.34 y.; at 65, it is 11.79 y.; at 70, it is 9.19 y. ; at 75, it is 7.01 y.; at 80, it is 5.51 y.; at 85, it is 4.12 y.; at 90, it is 3.28 y.; at 100, it is 2.28 y.

442. The premium paid for life insurance, like that for other insurance, is calculated at a certain per cent. on the amount insured. The per cent. varies according to the age and employment of the assured, and the time embraced in the policy.

QUEST.-441. What is Life Insurance? What is meant by the expectation of life? 442. How is Life insurance calculated?

*See Registers of London, Breslau, Northampton, &c.

OBS. 1. At the age of 21 years, the per cent. on a policy for life is from 1to 24 per cent. per annum on the sum insured; for 7 years, it is from

1 per cent. per annum; for 1 year, from to 13 per cent.

to

to 2 per cent. per annum; for

2

At 30, on a policy for life, it is from 2 7 years, from 1 to 18 per cent.; for 1 year, At 40, on a policy for life, it is from 32 to 3 1 to 2 per cent.; for 1 year, from 13 to 2 At 50, on a policy for life, it is from 4 to 46 2 to 3 per cent.; for 1 year, from 1 to 2 At 60, on a policy for life, it is from 63 43 to 5 per cent.; for 1 year, from 32 to 4

from 13 to 17 per cent.

per cent.; for 7 years, from per cent.

per cent.; for 7 years, from

per cent.

to 7 per cent.; for 7 years, from per cent.

28. A young man, at the age of 21 years, effected an insurance for $1500 for life, at 2 per cent.: what was the annual premium? Ans. $31.50.

29. A man, at the age of 30, effected a life insurance for $2700, for 7 years, at 1 per cent.: what was the premium?

30. At 60 years of age, a man effected a life insurance for 1 year for $5750, at 62 per cent.: how much premium did he pay?

31. At 40 years of age, a man effected an insurance for $10000 for life, at 34 per cent. per annum; he lived till he was 75 years old: which was the larger, the sum paid for insurance, or the sum insured?

PROFIT AND LOSS.

443. 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 AMOUNT of profit or loss, the purchase price and rate per cent. being given.

Ex. 1. A grocer bought a lot of flour for $84, and sold it for 7 per cent. profit: how much did he make by his bargain?

QUEST.-443. What is meant by profit and loss? How are they reckoned? 444. How is the amount of profit or loss found, when the cost and rate per cent. are given?

Analysis. Since he gained 7 per cent. on the cost of the flour, he must have gained 17 of 84. Now of $34 is, and is 7 times as much, which is $5.88. Ans.

Or thus: If $1 (100 cents) gain 7 cents, $84 will gain 84 times as much; and $84X.07-$5.88, the same as before. Hence,

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

Multiply the purchase price by the given per cent, as in percentage; and the product will be the amount gained or lost by the transuction. (Art. 388.)

OES. In order to obtain the exact profit and loss in mercantile operations, it is manifest that the interest on the cost or purchase price of the goods, during the time they have been on hand, also for the time before payment is received should be taken into consideration.

2. If I buy a piece of broadcloth for $120, and after keeping it 6 months, sell it at 8 per cent. advance on 6 months credit, how much shall I gain if I pay 7 per cent. for the money invested? Ans. $1.20.

3. If I buv a farm for $1740, and sell it 8 per cent. less than cost, how much do I lose? Ans. $139.20. 4. If you buy a house for $2180, and sell it at 10 per cent. advance, how much will you gain by your bargain?

5. A merchant bought goods amounting to $3400, and retailed them at 20 per cent. profit: how much did he make?

6. A grocer bought a lot of flour for $6235, and sold it 15 per cent. less than cost: what was his loss?

7. A speculator bought a quantity of cotton for $24850, and sold it at 5 per cent. advance: how much did he make by the operation?

8. A man bought a block of stores for $58246, and sold them at 118 per cent. advance: how much did he gain?

9. A man bought wild land amounting to $125000, and after keeping it 10 years, sold it at 50 per cent. advance: allowing money to be worth 6 per cent., did he raake or lose by the operation; and how much?

CASE II.

To find how an article must be sold to gain or lose a specified per cent., the cost being given.

10. A man bought a building lot for $625, and afterwards sold it so as to gain 10 per cent.: how much did he sell it for?

Operation.

$625 purchase price. .10 per cent. profit. $62.50 profit. $687.50 selling price.

Since he gained 10 per cent., it is obvious he sold it for the purchase price together with 10 per cent. of that price. We therefore find 10

per cent. on the cost, and add it to itself. (Art. 388.)

11. A man bought a small house for $840, and afterwards sold it so as to lose 10 per cent.: how much did he get for it?

Operation.

$840 purchase price.

.10 per cent. loss.

$84.00 sum lost.

$756.00 selling price.

Having found the sum lost, (Art. 388,) subtract it from the cost, and

the remainder is obviously the selling price. Hence,

445. To find how any article must be sold, in order to gain or lose a given rate per cent. when the cost is given.

First find the amount of profit or loss on the purchase price at the given rate, as in the last Case; then the amount thus found added to, or subtracted from the purchase price, as the case may be, will give the selling price required.

12. A grocer bought a quantity of cheese for $130.67: for how much must he sell it, to gain 20 per cent. ?

13. Bought a stock of goods for $3460: for how much must they be sold, to gain 22 per cent.?

14. Bought a quantity of flour for $5245: for how much must it be sold, to gain 13 per cent.?

15. Bought 2500 bales of cotton for $30575, which were sold at a loss of 34 per cent.: what did they fetch?

QUEST. 445. What is the method of finding how any article must be sold, in order to gain or lose a given per cent.? 446. How is the rate per cent. of profit or loss found, when the cost and selling price are given ?