SOA Exam FAM Sample Question 6.4

Study guide: Exam FAM

For whole life annuities-due of 15 per month on each of 200 lives age 62 with independent future lifetimes, you are given:

(i) $i = 0.06$

(ii) $A_{62}^{(12)} = 0.4075$ and ${}^{2}A_{62}^{(12)} = 0.2105$

(iii) $\pi$ is the single premium to be paid by each of the 200 lives

(iv) $S$ is the present value random variable at time 0 of total payments made to the 200 lives

Using the normal approximation, calculate $\pi$ such that $\Pr(200\pi > S) = 0.90$ .

[Question 19 on the Fall 2012 exam]

Concepts tested