Page 229 - Probability Demystified

218 CHAPTER 12 Actuarial Science

ANSWERS

1. $151 20 ¼ $3020
$40,000
2. 96 20 ¼ $768
$100,000

3. At age 35, there are 98,067 females out of 100,000 alive. At age 55,
there are 93,672 females alive. Therefore, 98,067 93,672 ¼ 4395
females will die.

number who will die 4395
P(dying in 20 yearsÞ¼ ¼ ¼ 0:0448
number alive at 35 98,067

Out of 100 females, 100 0.0448 ¼ 4.48 or about 5 will die. Hence,
5 $100,000 ¼ $500,000 will have to be paid out.
4. At age 35, there are 98,067 females out of 100,000 alive;
98,067 … 2 ¼ 49,033.5. At age 83, there are 48,848 females alive. So,
83 35 ¼ 48 is the median future lifetime.

5. At age 50, there are 91,865 males out of 100,000 alive; 91,865 … 2 ¼
45,932.5. At age 79, there are 45,459 males alive. Hence, the median
future lifetime of a male age 50 is 79 50 ¼ 29 years.

Summary

This chapter introduces some of the concepts used in actuarial science. An
actuary is a person who uses mathematics in order to determine insurance
rates, investment strategies, retirement accounts and other situations
involving future payouts.
Actuaries use mortality tables to determine the probabilities of people
living to certain ages. A mortality table shows the number of people out
of 1,000, 10,000, or 100,000 living at certain ages. It can also show the
probability of dying at any given age. Barring unforeseen catastrophic events
such as wars, plagues, and such, the number of people dying at a specific age
is relatively constant for certain groups of people.
In addition to life insurance, mortality tables are used in other areas. Some
of these include Social Security and retirement accounts.