Actuarial Science Study Note - Life Annuity

AS2053 Feb. 2012 Lecture Notes-AM Note-Chapter 2

Chapter 2:

(Contingent) Life Annuities

2.1 Annuity Certain Review 2.2 Net Single Premium(NSP) 2.3 Pure Endowment 2.4 Whole Life annuities 2.5 Temporary Life Annuities 2.6 Deferred Life Annuities 2.7 Varying Life Annuities
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AS2053 Feb. 2012 Lecture Notes-AM Note-Chapter 2

Chapter 2- Life Annuities
Note: There are copies of the text tables at the end of the lecture note handout. You should print them off and bring them to class (for examples)

2.1 Annuity Certain Review • most of this material you have seen before • the following additional notation/formulas(to Zima material) is and/or will be referenced in the Actuarial Mathematics note; Define v=(1+i) -1 then d= 1 – v
&& Also, a n
|i

(d= 1- 1/(1+i)= i/(1+i))
&& (an
|i

= (1-vn)/d

=

a

n|i (1+i)
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AS2053 Feb. 2012 Lecture Notes-AM Note-Chapter 2

Example 1 Find the present value of an annuity certain with payments of $1,000 per year for 10 years, first payment made immediately. You are given that d=5%.

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AS2053 Feb. 2012 Lecture Notes-AM Note-Chapter 2

2.2

Net Single Premiums(NSP)

NSP is the single sum of money paid at time 0 for a benefit • NSP is the net amount and therefore excludes expenses, profit loadings and taxes o the customer would actually pay a gross single premium(GSP) as opposed to a NSP o GSP calculations are similar in approach to NSP calculations (expenses are considered in Ch. 4 of the AM note) • Life annuities and Life Insurance benefits are not guaranteed to

be paid , so NSP for these benefits depends on probability of receiving the benefit
• NSP and APV (Actuarial Present Value) mean the same

thing. APV terminology often used to denote that probabilities and interest are involved.
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AS2053 Feb. 2012 Lecture Notes-AM Note-Chapter 2

Example 1 If j1=8%, compare the net single premiums of two products both paying $1,000 at the end of 3 years to a person currently age 30. The