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EXAMPLE. Find the sum to which $ 700 will amount in 15 years if put at interest at 4 %, compounded annually.
$ 1.800944 Amount of $ 1 at 4 % for 15 years
Exercise Using the table on page 87, find the amount in each of the following examples if the interest is compounded annually:
1. $ 200 for 4 yr. at 4 % 6. $ 100 for 8 yr. at 5% 2. $ 250 for 6 yr. at 5% 7. $ 780 for 14 yr. at 6 % 3. $ 300 for 5 yr. at 6 % 8. $ 275 for 15 yr. at 5 % 4. $ 400 for 8 yr. at 7 % 9. $ 1000 for 20 yr. at 4 % 5. $ 650 for 10 yr, at 4 % 10. $ 50 for 20 yr. at 7 %
Insurance is security against damage or loss, and is of two general kinds, property and personal.
The former includes insurance against fire, flood, marine disaster, burglary, default, theft, etc. The latter includes life insurance, insurance against accident, illness, libel, etc. Of these, only property and life insurance will be discussed here.
The policy is the written or printed contract between the insurance company and the person insured.
The premium is the sum paid by the insured at stated periods, usually annually, for his insurance.
The rate is the specified number of cents or dollars paid for each $100 of insurance.
Property Insurance. - Property may be insured against damage by fire, flood, marine disaster, collision, and the like. In property insurance the premium is usually stated as so much per $100, or as so many per cent.
EXAMPLE. If a house is insured for $ 3000 for 1 year at 1%, what is the premium ?
$ 3000 Amount of insurance
1. A merchant insures his stock of goods for $ 4000 at 1%. What premium does he pay?
2. A factory worth $ 36,000 is insured for å of its value at 2%. What is the premium?
3. A man insured his dwelling valued at $ 75,000 for of its value at 11%. In case of total loss how much would the owner lose, including the premium paid ?
4. A dealer insured his stock of goods valued at $ 16,000 for } of their value at 14%. In case of total destruction by fire what would be the owner's loss, including the premium ?
5. A professor insured his library for its full value, $ 8000, at 18%. What premium did he pay ?
6. A stock of goods worth $ 39,000 is insured for 1 of their value at $.95. What is the amount of the premium ?
7. What will it cost to insure a building for $ 3000 at 1 % and the contents for $ 2200 at 11% for one year?
8. A dwelling valued at $ 15,000 was insured for sof its value at i % and contents valued at $ 50,000 for of their value at 1%. What premium was paid ?
9. If the three-year rate is twice the rate for one year, find the cost of insuring a dwelling for $ 7200 for three years if the annual rate is 1 %.
10. If insurance on inflammable and explosive materials is 7 % per year, how frequently can a manufacturer of such goods afford to have his plant destroyed by fire in order to save the cost of insurance ?
Personal Insurance. There are many varieties of insurance policies. Only the simplest form will be treated here.
In life insurance the premium is usually stated as so much on $ 1000 of insurance. Thus, a premium of $ 26.72 means $ 26.72 on each $ 1000.
The rate of insurance increases as the age of the applicant increases, as indicated in the following table.
In the following examples use the rates given in the above table :
1. What is the annual premium on an ordinary life policy of $ 2000 at the age of 25 ?
2. What is the annual premium on a 20-payment life policy of $ 4000 at the age of 40 ?
3. A man at the age of 30 takes out a $ 2000 ordinary life policy and dies 15 years later. What per cent of the face of the policy has he paid in premiums?
4. A man at 45 took out a $10,000 ordinary life policy. At the age of 60 how much had he paid in premiums ? What fractional part of the face of the policy had he paid ?
5. The day he was 25 a man took out a 20-payment policy for $ 4000 ; when he was 30 he took out a 20-payment policy for $ 6000; when he was 40 an ordinary life policy for $ 10,000. If he died when he was between 44 and 45 years old, how much more did his estate receive than he had paid for insurance ?