SOA Exam FAM Sample Question 5.4

Study guide: Exam FAM

(40) wins the SOA lottery and will receive both:

A deferred life annuity of $K$ per year, payable continuously, starting at age $40 + \mathring{e}_{40}$ and
An annuity certain of $K$ per year, payable continuously, for $\mathring{e}_{40}$ years

You are given:

(i) $\mu = 0.02$

(ii) $\delta = 0.01$

(iii) The actuarial present value of the payments is 10,000

Calculate $K$ .

[A modified version of Question 5 on the Fall 2013 exam]

Concepts tested