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A. Pure Premium and the Law of Large Numbers- An insurance policy will pay a lump sum of $500,000 in the event that a policyholder becomes permanently disabled.
The insurer believes that on average one out of every 2,500 people buying this policy will have a claim. What is the
pure premium for this policy? - An insurance policy will pay a business a lump sum of $2,800,000 in the event that its chief executive dies in the next
year. The insurer believes that there is a 1 in 375 chance that this will happen. Calculate the pure premium for this
policy. - An auto insurance company has determined from past experience that it can expect 1 out of every 189 policyholders
to have a liability claim in the next year, and that the average claim size will amount to $87,532. Calculate the pure
premium for this liability policy. - From past experience, an insurance company believes that the average claim on a $1 million umbrella liability policy
will be $436,000, and that on average 1 out of every 7,350 policy holders will fi le a claim in the next year. What would
be the pure premium for this policy? - A group of 37 business owners in Cascadilla Falls is considering forming a cooperative insurance company to
provide themselves with liability insurance. The likelihood of any of these business owners having a liability claim
in any given year is very small, but if a claim is made, it could be for a very large amount of money. Is their plan
reasonable?
B. Underwriting and Premium CalculationsFor Exercises 6 to 18, use the Affi liated Benevolent Mutual automobile liability insurance rate table and demographic factors
table given on page 528 of this section. Note that the premiums listed in the table are semiannual rates.- Calculate the semiannual premium for a 35-year-old unmarried man who lives in Region A and commutes 10 miles
to work. - Calculate the semiannual premium for a 43-year-old married woman who lives in Region C, and commutes 8 miles
to work. - Calculate the semiannual premium for a 17-year-old male who has not taken driver training, lives in Region B, and
commutes 3 miles. - Calculate the semiannual premium for a 21-year-old married woman who lives in Region A and has no daily
commute.
EXERCISES 13.1
Exercises 13.1 533