The Mathematics of Money

(Darren Dugan) #1

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


Example 13.1.2 Using the tables above, determine the semiannual rate for a policy for:

(a) A 17-year-old male with no driver training who lives in region A and
commutes 4 miles per day

(b) A 27-year-old married female living in Region C with a 17-mile daily commute

(c) A 67-year-old single man who lives in Region B with a 12-mile commute who
qualifi es for the long-term rate

(a) From the basic rate table, we fi nd a basic rate of $182.50. From the multiplier table, we
see a multiple of 2.55. So the rate would be ($182.50)(2.55)  $465.38.

(b) The basic rate is $192.05, the multiplier is 1.35. Rate  ($192.05)(1.35)  $259.27.

(c) The basic rate is $230.15, the multiplier is 1.10. (The fact that he is single is irrelevant in
this company’s rate book for ages 65.) Rate  $230.15(1.10)  $253.17.

The multipliers function in the same way as a percent increase or decrease applied to the
basic premium. This provides an alternative way of stating the effect of rating classifica-
tions, and they are sometimes expressed in that way.

Example 13.1.3 What percent over the basic rate does a 26-year-old married man
pay? What percent below the basic rate does a 54-year-old-woman pay?

The man’s multiplier is 1.45, so he would pay 145% of the basic rate. So he pays 45% over
the basic rate.

The woman’s multiplier is 0.85, so she would pay 85% of the basic rate. She pays 15% below
the basic rate.

The rate book and examples used above are intended to represent a typical rate book and
its use; it should be clearly understood though that the example is completely hypothetical,
and any given insurance company may set its tables up differently. For example, the lower
“long-term client” rate might be given as a percent discount instead of a separate rate in
the book, the workday commute might be dealt with as a multiplier instead of a separate
rate, or separate rates might be given by gender rather than have multipliers to deal with
genders. The company may also charge a higher premium for customers who have been
involved in traffic accidents. (See Exercises 15-18 for more on this.) While the specifics
might differ, though, this is illustrative of the general way a rate book might be set up.

Deductibles, Coinsurance, and Coverage Limits


Insurance policies seldom provide complete and unlimited coverage of a claim, regardless
of its size. A deductible is the amount of expense that the policyholder must pay herself
before the insurer will pay any benefits.

Example 13.1.4 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?

Adam is responsible for the $500 deductible; the insurer pays the claim beyond that. So the
insurer will pay $13,200  $500  $12,700.

Example 13.1.5 Kyle and Sara’s homeowner’s insurance policy has a $1,000
deductible. Some of the house’s siding is blown off in a windstorm, costing $735.22 to
repair. How much will the insurer pay on this claim?

Kyle and Sara are responsible for the fi rst $1,000 in claims. Since the siding damage was less
than this, the insurance company will pay nothing.

Coverage limits specify a maximum amount that the insurer will pay for claims on a policy. For
example, a business should carry liability insurance to financially protect itself against lawsuits,

13.1 Property, Casualty, and Liability Insurance 529
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