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ACTS 4301
Instructor: Natalia A. Humphreys
HOMEWORK 5
Lesson 8. Survival Distributions: Select Mortality.
Lesson 9. Insurance: Continuous - Moments - Part I.
Due: March 5, 2015 (Thurs)
Sufficient work must be shown to get credit for a correct answer. Partial credit may be given for
incorrect answers which have some positive work.
Problem 1
You are given the following information from a 2-year select and ultimate mortality table:
x
qx
80 0.09
81 0.11
82 0.12
83 0.14
84 0.15
In addition, you are given that
(i) q[x] = 0.4qx
(ii) q[x]+1 = 0.8qx+1
(iii) l[81] = 9000
Calculate l[80] .
(A) 9890
(B) 10,053
(C) 9915
(D) 10,028
(E) 9968
Problem 2
You are given the following extract from a 2-year select and ultimate mortality table:
x
l[x]
l[x]+1 lx+2 x + 2
70 1200
1000
71
950
72
In addition, you are given that q[70]+1 = q[71]+1
Calculate 1| q[70]+1
920
72
73
850
74
ACTS 4301. SP 2015. HOMEWORK 5.
Problem 3
You are given the following extract from a 3-year select and ultimate mortality table:
x
l[x]
l[x]+1 l[x]+2
60
61
lx+3
x+3
7500
63
7934
62 7966
64
7540
65
Assume:
(i) The ultimate table follows de Moivre’s law
(ii) d[x] = d[x]+1 = d[x]+2 , x = 60, 61, 62, where d[x]+t = l[x]+t − l[x]+t+1
Calculate 8000 2|2 q[61] .
Problem 4
For a 2-year select and ultimate mortality table, you are given:
(i) Ultimate mortality follows the Illustrative Life Table.
(ii) q[x] = 0.75qx
(iii) q[x]+1 = 0.8qx+1
(iv) l[54] = 15,000
Calculate l[55] .
Problem 5
You are given the following extract from a 2-year select and ultimate mortality table:
x
l[x]
l[x]+1
lx+2
x+2
40 70,525 69,325 67,518
42
41 68,234 67,404 65,330
43
42 67,124 64,566 63,870
44
Assume that deaths are uniformly distributed between integral ages.
Calculate 0.6 q[40]+0.7 .
Problem 6
An n-year term insurance payable at the moment of death has actuarial present value of 0.06273.
You are given:
(i) µx (t) = 0.008, t > 0
(ii) δ = 0.06
Determine n.
Copyright ©Natalia A. Humphreys, 2015
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ACTS 4301. SP 2015. HOMEWORK 5.
Problem 7
For a whole life insurance of 1000 on (x) with benefits payable at the moment of death:
(i)
0.05 0 ≤ t ≤ 12
µx (t) =
0.06 t > 12
(ii)
0.03 0 ≤ t ≤ 12
δt =
0.04 t > 12
Calculate the single benefit premium for this insurance.
Problem 8
Ann wants to purchase a 6-year pure endowment with a single benefit premium. The amount of the
endowment is $2000. Her insurance agent convinces her instead to use the same money to purchase
a 6-year endowment insurance policy which pays at the moment of death or at the end of six years,
whichever comes first. You are given that µ = 0.05 and δ = 0.07.
Calculate the benefit amount for this 6-year endowment.
(A) 1238.32
(B) 4552.21
(C) 1389.52
(D) 1077.58
(E) 973.50
Problem 9
John, a nonactuary, estimates the single benefit premium for a continuous whole life policy with a
benefit of $9000 on (40) by calculating the present value of $9000 paid at the expected time of death.
(40) is subject to a constant force of mortality µx = 0.055, and the force of interest is δ = 0.075.
Determine the absolute value of the error of John’ s estimate.
Problem 10
Given:
(i) i = 4.5%
(ii) The force of mortality is constant.
(iii) ˚
ex = 15
Calculate 30,00018| A¯x .
Copyright ©Natalia A. Humphreys, 2015
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