The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

561

CHAPTER 13

SUMMARY

Topic Key Ideas, Formulas, and Techniques Example(s)

Pure Premium and the Law of

Large Numbers, p. 525

• The pure premium of an insurance policy is
  the predicted amount of claims divided by the
  number of policies.


• Over a large number of policies, the average
  claims per policy should be very close to the
  pure premium.

An insurance company

offers a policy that pays a

fl at $5,000 if a policyholder

is a victim of identity theft.

The company believes that

on average 1 out of every

287 policyholders will have

a claim on its policies each

year. Calculate the pure

premium for this policy.

(Example 13.1.1)

Calculating Auto Liability

Premiums from a Rate Table,

p. 528

• Use the rate table to fi nd the appropriate rate
  based on the insured’s information.


• If there are adjustment factors (such as for
  age/sex), obtain these from the factor table and
  multiply by the table rate.

Using a given rate table

above, determine the

semiannual rate for a policy

for a 17-year-old male with

no driver training who lives

in Region A and commutes

4 miles per day.

(Example 13.1.2)

Deductibles, p. 529 • A deductible is the amount that must be paid

by the insured for a covered event before the

insurance makes any payment.

• Subtract the deductible from the amount of the
  claim.


• If the deductible is larger than the claim, the
  insurer pays nothing.

Adam has comprehensive

coverage on his car. The

deductible is $500. The car’s

value is $13,200, and it is

stolen. How much will the

insurer pay on this claim?

(Example 13.1.4)

Coverage Limits, p. 530 • A coverage limit is the maximum amount the

insurer will pay for claims on a policy.

• Auto insurance liability policies often state their
  limits as a maximum per person followed by an
  overall maximum for liability.


• There may also be a third limit that applies to
  damage to property.

Kelsi has a 25/75/50 motor

vehicle liability policy. Kelsi

caused a car accident in

which she injured two people

and caused $18,500 in

property damage. A court

awarded one of the victims

a $35,000 judgment, and

$15,000 to the other. How

much will her insurance

company pay?

(Example 13.1.8)

Coinsurance Clauses, p. 531 • If the percent of the property’s value that is

insured falls below the coinsurance percent, the

amount of the claim to be paid is reduced.

• Divide the insured value by the actual value, and
  multiply the results by the amount of the claim.


• If the insured percent is more than the
  coinsurance percent, the claim is covered in full
  up to the insured amount.

Your warehouse and

its contents are worth

$2,500,000. You insure the

property for $1,500,000. Your

policy contains a coinsurance

clause. There is a fi re, and

you incur a $1,200,000

loss. How much will your

insurance pay?

(Example 13.1.9)

(Continued)