SOA Exam ALTAM Sample Question 35

Study guide: Exam ALTAM

XYZ Insurance Company sells three-year term policies with a death benefit of 1,000,000 payable at the end of the year of death, to lives age $x$ . Premiums are payable annually.

The insurer holds reserves for the policy equal to net premium policy values, based on an interest rate $i = 0.05$ and mortality of $q_{x+t} = 0.10 + 0.10t$ for $t = 0, 1, 2$ .

The net premium for this policy is 177,313.20. The net premium policy value at the end of the first year, ${}_1V^n$ , is 95,754.

The assumptions used for profit testing this policy are:

(i) The pre-contract underwriting expense is 4,000 per policy.

(ii) Commissions are 20% of premium in year 1 and 5% of premium each year thereafter. The extra 15% of premium in commissions in the first year is treated as a pre-contract cash flow for profit testing purposes.

(iii) Maintenance expense is 100 per policy at the beginning of every year including the first year.

(iv) The earned interest rate is 7%.

(v) Mortality is equal to the policy value mortality.

(vi) At the end of each of the first two years, 10% of the surviving policyholders withdraw.

(vii) There are no cash values.

Part a (1 point)

List four ways that profit tests are applied in practice.

Part b (1 point)

Show that the net premium policy value at the end of the second year is 108,400 to the nearest 10. You should calculate the value to the nearest 1.

Part c (2 points)

XYZ uses a gross premium of 210,000 in its first profit test for this three-year term policy. Using this premium, $\Pr_2 = 37{,}766$ and $\Pr_3 = 29{,}347$ .

(i) Determine $\Pr_0$ .

(ii) Determine $\Pr_1$ .

Part d (3 points)

(i) Determine the profit signature for this policy.

(ii) Calculate the NPV for this policy using a risk discount rate of 12%.

(iii) Calculate the profit margin for this policy.

Part e (3 points)

XYZ wants to achieve a profit margin of 10% on this policy. Calculate the gross premium that XYZ should charge to meet that objective.

(This is Question 2 from the Fall 2021 Form B Written Answer exam.)

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