SOA Exam ALTAM Sample Question 49

Study guide: Exam ALTAM

A life insurance company issues a Type B universal life policy with an Additional Death Benefit of 150,000 to a life age 35.

You are given:

Policy Year	Annual Premium	% Premium Charge	Annual Cost of Insurance Rate Per Thousand	Credited Interest Rate	Account Value at End of Year	Surrender Charge
1	4800	20%	2.31	4%	3647	2500
2	4800	5%	2.46	4%	8166	1500
3	4800	5%	2.62	4%	-	0

Part a (2 points)

Show that the total death benefit at the end of the third year is 162,800 to the nearest 100. You should calculate the value to the nearest 1.

Now the company wants to carry out a profit test of this contract using the following assumptions:

(i) At the end of the first year, 10% of the in-force policyholders surrender.
(ii) At the end of the second year, 20% of the in-force policyholders surrender.
(iii) At the end of the third year, all remaining in-force policyholders surrender.
(iv) There are no reserves held other than the account value.
(v) The interest earned on all insurer's funds is 8% per year.
(vi) Mortality experience is $q_{35+t} = 0.0015$ for $t = 0, 1$ and 2.
(vii) Pre-contract expenses are 800.
(viii) Percent of premium expenses are 25% in the first year and 7% for years 2 and 3.
(ix) Expenses on death are 500.
(x) The hurdle rate is 10% per year.

Calculate the profit vector.

Calculate the NPV.

Calculate the profit margin.

(This is Question 2 from the Fall 2017 Written Answer exam.)