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ACTSC-232-1065-Test2_solutions

# ACTSC-232-1065-Test2_solutions - ACTUARIAL SCIENCE 232 TERM...

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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 6-0006) 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 (2-H. 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 3-year 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” ’ 9-60 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 (HM-2! = mural; gavaL , 47¢ Ash/«w cleLo: «X Ml?er 1W 4, a; (3474.»5)‘ M73 wch-ﬁ n ‘ a 115—0. 3’3 ’7 lW be) / ...
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