AS 5102 Study Guide - Midterm Guide: Term Life Insurance, Life Insurance, Life Table

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Published on 23 Nov 2019
EXAM 2, 2:00-2:50 PM, MARCH 28, 2018
For undergraduate students, there are 4 problems and 35 points in total. For graduate students, there
are 5 problems and 40 points in total.
You must show your work in the blue book. No credit will be given for unsupported answers.
Clearly mark all final answers.
1. (10 points) You are given the following select life table:
x l[x]l[x]+1 lx+2 x+ 2
60 96568.13 96287.48 95940.60 62
61 96232.34 95920.27 95534.43 63
62 95858.91 95511.80 95082.53 64
63 95443.51 95057.36 94579.73 65
64 94981.34 94551.72 94020.33 66
If i= 0.05, calculate
(a) 1000A[60]:2
(b) 1000(DA)1
(c) Under the UDD fractional age assumption, determine 1000A(2) 1
2. (7 points) You are given that
Z=(1,000vT40 , T40 30
1,000v30, T40 >30
(a) Describe in words the insurance benefits with the present value random variable given above.
(b) Find an expression in terms of standard actuarial notations for the expected value of Z.
(c) If the force of interest δ= 0.06, and the force of mortality is a constant µx= 0.04 for all x > 0,
calculate the expected value of Z.
3. (8 points) For a special discrete whole life insurance issued to a person aged 30, a benefit of $10,000
will be paid at the end of the death year if the insured dies within the first 10 years; and a benefit of
$20,000 will be paid at the end of the death year if the insured dies after 10 years. The annual effective
rate of interest is i= 0.06. You are given that the force of mortality satisfies De Moivre’s law with
ωx,0x < ω.
The complete expectation of future lifetime for (30) is ˚e30 = 35.
(a) Write down the present value random variable, Z, of the benefit in this insurance.
(b) Calculate the actuarial present value of this insurance.
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