SOA Exam ALTAM Sample Question 31

Study guide: Exam ALTAM

A life insurer issues a single premium whole life annuity-immediate, payable annually, with a 10-year guarantee, to B who is age 65.

The basis for calculating the premium and policy values is as follows:

(i) Mortality follows the Standard Ultimate Life Table.

(ii) $i = 0.05$

(iii) Commission is 2000 at issue.

(iv) Other acquisition expenses are 500.

(v) Maintenance expenses of 25 per year are payable with the annuity payments.

(vi) The premium is determined using the equivalence principle.

The single premium is 100,000.

Part a (2 points)

Show that B's annuity payment is 7550 to the nearest 10. You should calculate the payment amount to the nearest 0.1.

Part b (1 point)

The insurer conducts a profit test of this contract using the following three states:

State 0: Payments in progress; annuitant alive
State 1: Payments in progress; annuitant dead
State 2: Payments ceased; annuitant dead

You are also given the following assumptions for a profit test of the contract.

Interest on insurer's funds: 6%
All other assumptions follow the premium and policy value basis.
Reserves are gross premium policy values.

Write down values for the following probabilities:

(i) $p^{01}_{73}$

(ii) $p^{02}_{73}$

(iii) $p^{12}_{73}$

Part c (2 points)

Show that the reserve at time 8 for a policy in State 0 is ${}_8V^{(0)} = 76{,}100$ to the nearest 100. You should calculate the value to the nearest 1.

Part d (1 point)

Show that the reserve at time 8 for a policy in State 1 is ${}_8V^{(1)} = 14{,}100$ to the nearest 100. You should calculate the value to the nearest 1.

Part e (4 points)

(i) Show that $\Pr_9^{(0)} = 760$ to the nearest 10. You should calculate the value to the nearest 0.1.

(ii) Show that $\Pr_9^{(1)} = 140$ to the nearest 10. You should calculate the value to the nearest 0.1.

(iii) Calculate $\Pi_9$ .

(This is Question 5 from the Spring 2020 Written Answer exam.) (Part (a) is covered by the FAM-L exam.)

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