Page 227 - Probability Demystified

216 CHAPTER 12 Actuarial Science

EXAMPLE: If a 21-year-old healthy female takes a 20-year term life
insurance policy for $100,000, how much would she pay in premiums if she
lived at least 20 years?

SOLUTION:
Her premium would be $96 per year, so she would pay $96 20 years ¼ $1920.

EXAMPLE: If a healthy 30-year-old male takes a 20-year term life insurance
policy for $25,000, how much would he pay if he lives for at least 20 years?

SOLUTION:
The premium for a healthy 30-year-old male for a 20-year term policy of
$100,000 is $147. So for a $25,000 policy, the premium can be found by
making a ratio equal to

face value of insurance policy
and multiplying it by the premium:
$100,000

$25,000
$147 ¼ $36:75: Then multiply by 20 years:
$100,000
$36:75 20 ¼ $735:

EXAMPLE: If the life insurance company insures 100 healthy females age
40 for 20-year, $100,000 term life insurance policies, find the approximate
amount the company will have to pay out.

SOLUTION:

First use the mortality table to find the probability that a female aged 40
will die before she reaches age 60. At age 40, there are 97,512 females out
of 100,000 living. At age 60, there are 90,867 living. So, in twenty years,
97,512 90,867 ¼ 6645 have died during the 20-year period. Hence, the prob-
ability of dying is

number who have died 6645
P(dying) ¼ ¼ ¼ 0:068
number living at age 40 97,512