SOA Exam FAM Sample Question 4.12

Study guide: Exam FAM

For three fully discrete insurance products on the same $(x)$ , you are given:

(i) $Z_{1}$ is the present value random variable for a 20-year term insurance of 50

(ii) $Z_{2}$ is the present value random variable for a 20-year deferred whole life insurance of 100

(iii) $Z_{3}$ is the present value random variable for a whole life insurance of 100.

(iv) $E[Z_{1}] = 1.65$ and $E[Z_{2}] = 10.75$

(v) $Var(Z_{1}) = 46.75$ and $Var(Z_{2}) = 50.78$

Calculate $Var(Z_{3})$ .

[Question 4 on the Fall 2015 exam]

Concepts tested