The Mathematics of Money

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

factoring in agent commissions, expenses, profit, and other costs, this low likelihood of a

claim can produce surprisingly low premiums.

Rates are typically expressed per $1,000 of coverage, sometimes varying depending on

the size of the policy. There may also be a flat amount added to all policies, regardless of

the policy size. The following is a typical example of a portion of a term insurance rate

book. (Only a few ages are shown.)

TRUSTWORTHY MUTUAL LIFE INSURANCE COMPANY

ANNUAL RATES PER $1,000 PLUS $25 ANNUAL POLICY CHARGE

RATES FOR MINIMUM $100,000 MAXIMUM $249,999

PER $1,000 RATES REDUCED BY 3% FOR ISSUE AMOUNTS $250,000 TO $500,000

ANNUALLY RENEWABLE TERM

MALE FEMALE

Age Preferred Standard Smoker Preferred Standard Smoker

35 $0.89 $1.02 $1.85 $0.78 $0.89 $1.62

36 $0.89 $1.04 $1.88 $0.78 $0.91 $1.64

37 $0.92 $1.05 $1.90 $0.80 $0.92 $1.66

38 $0.93 $1.06 $1.94 $0.81 $0.93 $1.70

39 $0.95 $1.06 $1.96 $0.83 $0.93 $1.71

40 $0.95 $1.08 $2.01 $0.83 $0.94 $1.76

20-YEAR LEVEL TERM

MALE FEMALE

Age Preferred Standard Smoker Preferred Standard Smoker

35 $1.26 $1.45 $2.63 $1.11 $1.26 $2.30

36 $1.26 $1.48 $2.67 $1.11 $1.29 $2.33

37 $1.31 $1.49 $2.70 $1.14 $1.31 $2.36

38 $1.32 $1.51 $2.75 $1.15 $1.32 $2.41

39 $1.35 $1.51 $2.78 $1.18 $1.32 $2.43

40 $1.35 $1.53 $2.85 $1.18 $1.33 $2.50

Example 13.3.1 Using the table above, determine the annual premium for

(a) a $200,000 annually renewable term policy for a male smoker aged 38 and

(b) a $350,000 20-year level term policy for a female preferred age 35.

(a) The rate per $1,000 is $1.94, plus a fl at policy charge of $25. So the premium would be

(200)($1.94)  $25 
 $388.00  $25.00 
 $413.00.

(b) The rate per $1,000 is $1.11. Since the table states that there is a 3% discount for death

benefi ts above $250,000, the actual rate would only be 97% of this however. The premium

would then be (350)(0.97)($1.11)  $25 
 $376.85  $25 
 $401.85.

Insurance premiums may be paid annually, or may be paid at other common frequencies such as

semiannually, quarterly, or monthly. Insurance rate books may contain factors that can be multi-

plied by the annual rate to determine premiums for other payment frequencies. For example:

TRUSTWORTHY MUTUAL LIFE INSURANCE COMPANY

PERIODIC PAYMENT FACTORS

If premium is paid: Annually Semiannually Quarterly Monthly

Multiply annual rate by: 1 0.52 0.265 0.135

13.3 Life Insurance 551