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Unformatted text preview: ACTUARIAL SCIENCE 232
TERM TEST # 2
SPRING 2006 Student Name: UW Student ID Number: AIDS: Calculator only
TIME: 50 minutes
INSTRUCTOR: H.H. Panjer 1. (a) t 0» [2] 1. (21) Assuming the deMoivre law of mortality a;
= 1 — —— < < 100,
8(I) 100 . 0 _ a: _
calculate A 1_l, the expected present value (net single premium) of $1000 paid on (50)’s death
50le
within 10 years, if the rate of interest is 6% per year compounded continuously. t 77,: Ken tam/4m q/M/rJJW/w; 6 71,7 77w)
Aw 4 61/050) dumlmmw Wm M; frwygt ,— 7°
7 a “.051. 51)
“£7 ’ 6 _/~ 05" 4— /0~ .L 014'
0 SD ,0 {'0 s 5:
.2 J 5=oé
C0
,o,é
.. "
" e’ r. o./§o’$9é
60006) f AMW 1;: $19240 ,4“.
[3] (b) Calculate the corresponding standard deviation. 5 (i) = OJrosﬂ, ’° .41 f '
E(=z”>= f e ’“ Law : fﬂdchon
5'0
0 go
..I.’L
; 1‘1» _. .//44’/é71> ___.—— non.)
VH0!) : .wvné ~/./g03%)L—.— 0739/54 0(7): 3&53‘2’7 m [2] 2‘ If MI) 2 .02, :5 2 20, and 6 = ,06, ﬁnd the net single premium of a whole life insurance of $1000 00 ‘79 ‘— f ’7 ’.06£
74 , V (2H. a” S J‘dzt
2. o eﬂ’u J 06 .2 inf l\ .. 02. ( [x .08 M .07. / or w x: =»~ 3 ’76 2;
7» M+g _,0‘Z+' / 3, A 3year term insurance policy issued to (50) provides death beneﬁts of bk payable at the end of the
year 16. If [)1 = $100,000 , b2 = $150, 000 and [)3 = $200, 000 ,
i: 0.06 and qw = .01 , qﬁ1 = .02 and q52 = .03, for this policy: [2] (a) Write the present value function Z. [00 000 L: C)
1.04, 2’ ll 18v 000 3 K51 M 1.067” ’
960 0°C’ ) K: 2.
/v06 3 0 127/3 [2] (b) Calculate the net single premium, E(Z). [2] (C) Calculate the standard deviation of Z. .41 V D  ‘1 [a
C(‘l ) ‘ lo) «iii—r "5 (meg) 4 (“mama ala‘ﬂlﬂo L FF“ 9"
"°6 L06” ““"“‘ [04" I) I
1/0413: .I\4L£‘x'°  “$1.131; /_/90f)</0ﬁ :1“
0'6?) ‘ W?) 3" 34993.07 [2] (d) How much would the net single premium increase if payments were assumed at the moment of
death? State any assumptions used, . ~
«we I L iv" ';L\ “6 v/0297
D M9? ‘3 A y . = ’— *’ ~
Total 15 wab’v ) bl 8 ANN") Alias) NJP = I10??? x (HM2! = mural;
gavaL , 47¢ Ash/«w cleLo: «X Ml?er 1W 4, a; (3474.»5)‘ M73 wchﬁ
n ‘ a
115—0. 3’3
’7 lW be) / ...
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 Summer '08
 MATTHEWTILL
 Standard Deviation, Trigraph, Term life insurance, net single premium

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