ACT348 December 2003 Final Exam
Questions 1 to 4 relate to
a fully discrete whole life insurance policy of face amount 1 issued at
age 40.
A level annual benefit (equivalence principle) premium
is payable for life.
Mortality
T
is based on the Illustrative Life Table at
(from the Actuarial Math Text).
3œÞ!'
1.
Find
#&
%!
ZÞ
(A)
.29
(B)
.31
(C)
.33
(D)
.35
(E)
.37
2.
Find
(variance of the 25th year terminal prospective loss given that
Z +<Ò PlOÐ%!Ñ #&Ó
#&
the insured is still alive).
(A)
Less than .060
(B)
At least .060, but less than .062
(C)
At least .062, but less than .064
(D)
At least .064, but less than .066
(E)
At least .066
3.
How many of the following are correct formulations for
?
#&
%!
Z
I.
II.
III.
IV.
E
T†
+
"
Ò
T
TÓ
†
+
ÞÞ
ÞÞ
'&
'&
'&
'&
%!
'&
+
ÞÞ
+T
ÞÞ
T
'&
%!
%!
%!À#&l
"
%!À#&l
(A)
None
(B)
1
(C)
2
(D)
3
(E)
4
4.
Find the conditional expectation of the 25th year Net Cash Loss
(for the period age 64 to
G
#%
65) given that insured is still alive at age 64.
(A)
.0075
(B)
.0085
(C)
.0095
(D)
.0105
(E)
.0115
5.
A fully continuous whole life insurance issued at age
has a death benefit of 2 if death
B
occurs within 10 years, and a death benefit of 1 if death occurs after 10 years.
The force of
mortality is constant at .04 for all ages, and the force of interest is .06.
The level benefit
premium payable for life is
.
Find the 5th year terminal reserve for this policy.
T œ Þ!!'&#)&
(A)
Less than
(B)
At least
, but less than
Þ$
Þ#
(C)
At least
, but less than
(D)
At least
, but less than
Þ"
!
(E)
At least
!
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View Full DocumentQuestions 6 and 7 relate to
two separate 3year fully discrete insurance policies issued at age
B
with level benefit premiums for which the death benefit is equal to
1000
terminal reserve in
the year of death
(
,
and
).
, œ "!!! Z
, œ "!!! Z
, œ "!!! Z
""
##
$$
You are given:
,
3œÞ"!
; œÞ#& ß ;
œÞ&! ß ;
œÞ)!
BB
"B
#
Policy 1 is a term insurance and policy 2 is an endowment insurance with an endowment
amount of 1000.
The annual benefit premium for Policy 1 is
and for Policy 2 it is
.
TT
"#
6.
Find first year terminal benefit reserve for Policy 2 (nearest 10).
(A)
510
(B)
520
(C)
530
(D)
540
(E)
550
7.
Which of the following is a correct expression for
?
TT
#"
(A)
(B)
(C)
(D)
(E)
"!!!
"!!!
=+
ÞÞ
ÞÞ
$lÞ"
$lÞ"
"!!!=
"!!!+
$$$Þ$$
ÞÞ
ÞÞ
$lÞ"
$lÞ"
Questions 8 to 10 relate to
the following information.
Smith is now 70 years old and Jones is
now 80 years old and their future lifetimes are independent.
Mortality for both of them is based
on the Illustrative Life Table (at the end of this exam paper), and
.
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 Fall '04
 Broverman
 Actuarial Science, Demography, Life table, ÞÞ ÞÞ

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