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MATH 471: Actuarial Theory I
Homework #9: Fall 2010
Assigned October 27, due November 3
1. Assume mortality follows de Moivre’s Law with
ω
= 110 and
d
= 0.05.
Calculate:
(a) ¨
a
45
.
(14.36)
(b) ¨
a
45:
15
.
(9.73)
(c)
15

¨
a
45
.
(4.63)
(d) ¨
a
45:
15
.
(15.36)
2. Allen, age 15, has been cursed by the dreaded Hattendorf. Consequently,
he now has the following survival probabilities:
p
15
= 0.95,
p
16
= 0.80,
p
17
= 0.50,
p
18
= 0.
Assuming
i
= 0.06, calculate:
(a) ¨
a
15
.
(2.89)
(b)
a
15
.
(1.89)
(c)
a
15:
2
.
(1.57)
3. Consider a special whole life annuity on (x) which pays
R
at the beginning
of the ﬁrst year, 2
R
at the beginning of the second year, and 3
R
at the
beginning of each year thereafter. You are also given:
(i) The actuarial present value of this annuity is 3333.
(ii)
i
= 0.05
(iii)
p
x
= 0.98 and
p
x
+1
= 0.97
(iv) ¨
a
x
+2
= 31.105
Calculate:
R
.
(40)
4. Suppose
Z
is the present value random variable for a 2year pure endow
ment of 1 on (x). You are given:
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This note was uploaded on 02/02/2011 for the course MATH 471 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Staff
 Math

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