The Mathematics of Money

(Darren Dugan) #1

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


is issued, and does not increase as the insured gets older. The premium in the early years of
a whole life policy is much higher than the rate for a comparable death benefit term policy,
but in the later years that premium will be much lower than what a comparable term policy
would cost. The basic idea is that the extra premium paid in the early years is used to “save
up” to subsidize the cost of coverage in the policy’s later years.
Determining the appropriate rate for a whole life policy is a challenge, requiring the
insurer to take into account the probability of death at different ages, as well as the future
rate of investment return on the “extra” premium paid in the early years. Insurance compa-
nies employ financial professionals know as actuaries to perform these calculations. Once
an actuary has determined the appropriate rates, though, whole life insurance rates may be
given in tables similar to those used for term insurance.
Whole life policies require the policyholder to pay the required premium throughout the
insured’s life. For typical life expectancies, a whole life policy bought on, say, a 25 year
old insured may run for 50 years or more before paying its death benefit. A lot can happen
over the course of 50 years. Regardless of the policyholder’s intent when the policy was
purchased, it is not unusual for a whole life policy to not remain in force until the insured’s
death. If the policy premium is not paid, the policy will not remain in force, in which case
it is said to lapse. If the policy owner decides that he no longer wants to continue the policy,
we say that he surrenders the policy.
This poses a question, though. If a whole life policy lapses, what happens to the “sav-
ings” that were building up to subsidize the policy in later years? It does not seem quite
fair that these should be entirely forfeited, and in fact they are not. A distinctive feature of
a whole life policy is that it accumulates a cash value. If the insurance policy lapses, the
policy owner is entitled to receive the policy’s cash value. In the early years of a whole life
policy the cash value will be quite small, but over time the cash value grows as additional
premiums are paid and invested by the insurer. When a policy is first issued, the policy-
holder is provided with a table of the policy’s cash value over the course of its life.
Whole life policies offer their policyholders alternatives to taking the cash value in
cash. Since these represent the alternatives to simple forfeiting the built-up policy values,
these are referred to as nonforfeiture options. The policyholder may select reduced paid
up (RPU) insurance, a life insurance policy with a reduced death benefit that is considered
paid in full by the cash value. An RPU policy cannot lapse as a result of nonpayment of pre-
mium, since there is no premium due. Another common option is extended term coverage.
With extended term, the whole life policy is replaced with a term policy having the same
death benefit. The cash value is used to pay for this term policy for a set period of time.
Extended term is often the default option in the event that a policy lapses and the insurance
company is unable to contact the policyholder. (It happens.) A table of reduced paid up and
extended term rates for a whole life contract will be provided when the policy is issued. An
example of a typical table is shown below:

End of
Contract Year

Cash Value
(per $1,000)

RPU (per
$1,000)

EXTENDED TERM


Ye ars Days
1$0$0 00
2$0$0 00
3$ 9 $25 3 104
4 $23 $61 8 82
5 $36 $94 11 263
6 $50 $127 14 148
7 $65 $162 16 189
8 $80 $195 18 21
9 $95 $226 19 66
10 $110 $256 20 7
Age 65 $610 $819 15 265

13.3 Life Insurance 553
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