SOA Exam FAM Sample Question 4.11

Study guide: Exam FAM

You are given:

(i) $Z_{1}$ is the present value random variable for an $n$ -year term insurance of 1000 issued to $(x)$

(ii) $Z_{2}$ is the present value random variable for an $n$ -year endowment insurance of 1000 issued to $(x)$

(iii) For both $Z_{1}$ and $Z_{2}$ the death benefit is payable at the end of the year of death

(iv) $E[Z_{1}] = 528$

(v) $Var(Z_{2}) = 15{,}000$

(vi) $A_{x:\overline{n}|}^{\phantom{x:}1} = 0.209$

(vii) ${}^{2}A_{x:\overline{n}|}^{\phantom{x:}1} = 0.136$

Calculate $Var(Z_{1})$ .

[Question 5 on the Spring 2015 exam]

Concepts tested