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

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Published on 23 Nov 2019

School

Department

Course

Professor

TEMPLE UNIVERSITY

AS 3501/5102 ACTUARIAL MODELING I, SPRING 2018

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

[61]+1:2

(c) Under the UDD fractional age assumption, determine 1000A(2) 1

[61]:2

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

µx=1

ω−x,0≤x < 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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