(D) 0.27(E) 0.30
Exam M: Fall 2005 -3- GO ON TO NEXT PAGE
3. A special whole life insurance of 100,000 payable at the moment of death of (x) includes a
double indemnity provision. This provision pays during the first ten years an additional
benefit of 100,000 at the moment of death for death by accidental means.
You are given:
(i) µ τ
x t t b gb g= ≥ 0 001 0 . ,
(ii) µx t t 1 0 0002 0 b gb g= ≥ . , , where µx
1 b g is the force of decrement due to death by
accidental means.
(iii) δ= 006 .
Calculate the single benefit premium for this insurance.
(A) 1640
(B) 1710
(C) 1790
(D) 1870
(E) 1970
Exam M: Fall 2005 -4- GO ON TO NEXT PAGE
4. Kevin and Kira are modeling the future lifetime of (60).
(i) Kevin uses a double decrement model:
x ( )
x l τ ( ) 1
x d ( ) 2
x d
60 1000 120 80
61 800 160 80
62 560 − −
(ii) Kira uses a non-homogeneous Markov model:
(a) The states are 0 (alive), 1 (death due to cause 1), 2 (death due to cause 2).
(b) 60 Q is the transition matrix from age 60 to 61; 61 Q is the transition matrix
from age 61 to 62.
(iii) The two models produce equal probabilities of decrement.
Calculate 61 Q .
(A)
1.00 0.12 0.08
0 1.00 0
0 0 1.00
⎛ ⎞
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎝ ⎠
(B)
0.80 0.12 0.08
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