The Mathematics of Money

(Darren Dugan) #1

552 Chapter 13 Insurance and Risk Management


Example 13.3.2 If the annual premium for a term insurance policy is $413.00, what
would the premium be from the table above if the premium is paid (a) semiannually,
(b) quarterly, and (c) monthly.

(a) (0.52)($413.00)  $214.76 semiannually

(b) (0.265)($413.00)  $109.45 quarterly

(c) (0.135)($413.00)  $55.76 monthly

The semiannual rate is not exactly half the annual rate, nor is the quarterly rate a quar-
ter, nor the monthly rate one-twelfth. This difference reflects the insurance company’s
higher costs of processing multiple payments, the fact that the insurance company loses the
opportunity to earn as much interest when the entire premium is not paid up front, and the
possibility that, if a claim is filed during the year, the insurer will not collect any premium
after the claim is filed.
As mentioned previously, if an applicant for life insurance does not meet the insurer’s usual
underwriting criteria, the insurer may still offer to issue a “substandard” policy at an increased
rate. The amount of the increase is indicated by an underwriting classification called a sub-
standard rating or table rating. Insurers do not all use the same terminology to indicate table
ratings. The rating is often expressed as a percent of the standard premium. Another common
method is to use letters of the alphabet, with each successive letter representing a 25% increase
over the standard premium.^5 For example, a “Table C” rating would mean a rate that is 75%
over the standard premium. This rating could also be expressed as a “175% table rating.”
Normally, the increase applies only to the portion of the rate which is based on policy
size; it does not apply to the flat per policy fee.

Example 13.3.3 Amy is a 38-year-old smoker who has applied for a $180,000
annually renewable term policy with Trustworthy Mutual. Because of her high cholesterol,
the company’s underwriter has rated her at Table B. What would the quarterly premium
be for this policy?

Table B means 150% of the usual premium (not including the policy fee). So Amy’s annual
premium would be (1.50)(180)($1.70)  $25  $484.00. Her quarterly premium would
then be (0.265)($484.00)  $128.26.

The rates shown in the examples above are intended to illustrate the general method of cal-
culating term insurance premiums; they should not be taken as an indication of the actual
rates that anyone might be expected to pay. As with other types of insurance, rates can vary
considerably from one company to another.

Whole Life Insurance


Term insurance is intended primarily to provide life insurance coverage for a limited period
of time, particularly for times of life when death is unlikely. Though many term policies
can be renewed annually, as the insured gets older the costs become prohibitively high.
The risk of a 35-year-old who has passed underwriting standards dying in the near term is
remote. The risk of a 75-year-old who passed underwriting 40 years ago dying in the near
term is not nearly so remote. If the life insurance is bought as protection against premature
death during one’s working years, or until children are grown, or until the mortgage is paid
off, then term may be the best fit. Though most such policies expire without ever paying
their death benefits, they provide enormous peace of mind while they are in force. How-
ever, for someone who wants a policy that will remain in force until death, and pay a death
benefit regardless of when death occurs, term insurance may be poor fit.
Whole life insurance policies are policies that are intended to remain in force for the
insured’s entire remaining life. With a whole life policy, the premium is set when the policy

(^5) The 25% per letter increment is common, but not always used. “Table A” normally means 25% above the usual
premium, but for another insurer it may mean 50% or some other percent. In this text we will assume the 25% per
letter increment, but the reader should be aware that this cannot always be assumed in practice.

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