The Mathematics of Money

(Darren Dugan) #1

556 Chapter 13 Insurance and Risk Management


than the surrender charge, so the policy will contain a provision that as long as a certain
minimum amount of premium is paid the policy will remain in force during the first few
years.

Example 13.3.6 For the universal life insurance policy used in Example 13.3.5, the
surrender charge is $5,000 in the fi rst year, declining by $500 per year until it reaches
$0 after 10 years. (a) If the policy is surrendered after 3 months, how much will the
policyholder receive? (b) If the policy’s balance has grown to $4,843.25 after 4 years,
how much would the policyholder receive if he surrendered at that point?

(a) After 3 months, the surrender charge is $5,000, which is more than the account value.
If the policy lapses or is surrendered, the policyholder would receive nothing, and the entire
account value would be forfeited to the insurance company.

(b) After 4 years, the surrender charge will have declined to $5,000  4($500)  $3,000.
If the policy is surrendered, the policyholder would receive $4,843.25  $3,000 
$1,843.25.

The interest rate paid, and the mortality costs charged, change over time. At issue, the
insurer provides a guaranteed minimum interest rate to be paid, and a table of guaranteed
maximum mortality cost rates (based on age) to be charged. These rates will usually be
extremely conservative. During the course of the policy, the insurer will set the actual rate
to be paid based on the insurer’s investment performance and prevailing interest rates in
the market, and a mortality cost rate based on a realistic but less overcautious assessment of
rates of death. The insurer will provide an illustration of the future cash values of the policy
both based on the guaranteed rates and on the rates that are actually being used when the
policy is issued. (Both are based on an assumed rate of premium payment.)
Universal life policies tend to be popular when interest rates are high. With high rates,
the “current rates” illustrations look very attractive, as high interest on the policy com-
pounds, keeping the interest above the insurance costs and leading to large projected future
values. When interest rates are lower, though, the projections don’t look nearly as appeal-
ing. Over the 1990s and early 2000s, interest rates were quite low, and universal life did not
rouse as much interest as it did in earlier, higher interest rate periods. However, as interest
rates rise, universal life may come back into prominence. In considering this product it is
important to understand how things actually work. Many people who bought universal life
policies in the 1980s when interest rates were high and “current rate” projections looked
wonderful were very disappointed in how their policies actually performed in the 1990s
when interest rates dropped.
An alternative form of this type of policy is variable universal life. Variable universal
life works much like regular universal life, except that instead of the account value earning
interest, it is invested in portfolios similar to mutual funds. Though the investment choices
usually include a wide range of options, variable universal life tends to attract more atten-
tion when the stock market is performing well.
Universal life policies are most commonly sold on the individual market. Group offer-
ings, while not unheard of, are not very common.

Other Types of Life Insurance


While the types of life insurance described thus far represent the vast majority of the mar-
ket, there are some variations. There are whole life policies that are intended to be paid
with a limited number of premiums; for example, a variant of a whole life policy might
require premium payments for 20 years, and then be considered paid up thereafter. Many
other variations exist.
Life insurance policies, whether term, whole life, or universal, commonly offer a waiver
of premium rider. For an additional premium, a waiver of premium rider provides that if
the policyholder becomes disabled, the life insurance policy will continue in force without
the premium being paid.
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