SOA Exam FAM Sample Question 5.5

Study guide: Exam FAM

For an annuity-due that pays 100 at the beginning of each year that (45) is alive, you are given:

(i) Mortality for standard lives follows the Standard Ultimate Life Table

(ii) The force of mortality for standard lives age $45+t$ is represented as $\mu_{45+t}^{SULT}$

(iii) The force of mortality for substandard lives age $45+t$ , $\mu_{45+t}^{S}$ , is defined as:

$\mu_{45+t}^{S} = \begin{cases} \mu_{45+t}^{SULT} + 0.05, & \text{for } 0 \le t < 1 \\ \mu_{45+t}^{SULT}, & \text{for } t \ge 1 \end{cases}$

(iv) $i = 0.05$

Calculate the actuarial present value of this annuity for a substandard life age 45.

[A modified version of Question 4 on the Fall 2017 exam]

Concepts tested