Page 228 - Probability Demystified

CHAPTER 12 Actuarial Science 217

Hence about 6.8 or 7% (rounded) of the females have died during the
20-year period. If the company has insured 100 females, then about
7% 100 ¼ 7 will die in the 20-year period. The company will have to pay
out 7 $100,000 ¼ $700,000 in the 20-year period.
Notice that knowing this information, the insurance company can estimate
its costs (overhead) and calculate premiums to determine its profit.
Another statistic that insurance companies use is called the median future
lifetime of a group of individuals at a given age. The median future lifetime
for people living at a certain age is the number of years that approximately
one-half of those individuals will still be alive.

EXAMPLE: Find the median future lifetime for a male who is 30 years old.

SOLUTION:
Using the mortality table, find the number of males living at age 30. It is
97,129 out of 100,000. Then divide this number by 2 to get 97,129 … 2 ¼
48,564.5. Next, using the closest value, find the age of the males that
corresponds to 48,564.5. That is 48,514. The age is 78. In other words, at
age 78, about one-half of the males are still living. Subtract 78 30 ¼ 48.
The median future lifetime of a 30-year-old male is 48 years.

PRACTICE

1. If a healthy 40-year-old male takes a 20-year, $100,000 term life
insurance policy, how much would he pay in premiums if he lived
to age 60?
2. If a healthy female age 21 takes a 20-year, $40,000 term life insurance
policy, about how much would she pay in premiums if she lived to age
41?
3. If a life insurance company insures 100 healthy females age 35 for
$50,000, 20-year term policies, how much would they expect to
pay out?
4. Find the median future lifetime of a female who is age 35.
5. Find the median future lifetime of a male who is age 50.