Actuary Certification Actuary Certification Life Contingencies 2

Question 1

A life annuity-due of 1 per year pays at the beginning of each year while a life (x) survives. Its APV is denoted:

Accepted Answer

äx

Answer

äx (a-umlaut-x) is the actuarial present value of a life annuity-due, with payments at the start of each year the life survives.

Question 2

The complete expectation of life e°x is defined as:

Accepted Answer

E[T(x)]

Answer

The complete expectation of life e°x equals E[T(x)], the expected value of the complete future lifetime T(x).

Question 3

For a select-and-ultimate life table, the select period represents:

Accepted Answer

The first years after underwriting when mortality differs from the ultimate table

Answer

The select period is the duration immediately following underwriting during which recently selected lives have different (usually lower) mortality than the ultimate rates.

Question 4

The variance of the present value of a whole life insurance Āx can be expressed using the second moment as:

Accepted Answer

²Āx − (Āx)²

Answer

Var(Z) = E[Z²] − (E[Z])² = ²Āx − (Āx)², where ²Āx is evaluated at double the force of interest.

Question 5

A term life insurance pays a death benefit only if the insured dies within n years. Its APV for (x) is written as:

Accepted Answer

A¹x:n|

Answer

A¹x:n| (with superscript 1 over x) denotes the n-year term insurance APV, where the superscript 1 indicates the benefit is paid only on the life's death within n years.

Actuary Certification Practice Test

Actuary Certification Practice Test

Actuary Certification Actuary Certification Life Contingencies 2