STAT 490 F11 Test 1 Solutions

# STAT 490 F11 Test 1 Solutions - STAT 490 Test 1 October 4...

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Unformatted text preview: STAT 490 Test 1 October 4, 2011 v? o" 1- You are given: a. Mortality follows the Illustrative Life Table. [3- Deaths occur uniformly between integer ages. c. 2': 6% @7 Calculate 10004113 \ MW) (/14): 7:7 T A ml i7) g? Maggi 5>< A977: :77 /@@@ Eva/A477; W lg” 5%, #65?) "77’ 7s: Kw Mm f/(a 91W§[WQW>W ( 57%??? 777W (.smag +— < 53 496% 7/9/7g \t ugaﬂg at» a 2. Mortality follows Mortality Table A. Deaths are uniformly distributed between integer ages. The interest rate is 8%. Calculate 100,000 (:2). A”; w 4;: gag/Q AW :03) A7r§ #30 A73 3: glam «is» lax/out .. «y. rm. ... is. ”75" .. 510% 0,99%i77?/a X {02:} m (a . é? \$8 W7? 9’5?) ”E & '9’ L“ (9 5 (8 D (90? l Lila); )DNK l . Qﬁjlaﬂw a c O .077ngﬁlal; €13 ﬁt 3. Assume that a constant force of mortality occurs between integer ages. Using Mortality Table A, calculate ”p775 . 03 4. You are given [p0 =1—0.0045t—0.OOOlt2 for 0 s t s 80. 0 Calculate €50. Wm . 30 5 S 1“” 6215+ await) wgﬂta5+ 2245. t +mm g5 J5? ﬂit; l 5. A whole insurance on (25) pays a death benefit immediately upon death. The death benefit at time t is (1.05)". l E You are given: a. Mortality follows Gompertz Law with B = 0.0002 and c = 1.1025. b. i: 0.05 C. 825 = 53.06 Calculate the Expected Present Value of this insurance benefit. (Hint — The answer should be i numeric and should be between 0.100 and 0.200.) 0 Mb @ 990%)[//©2§> if? “if 69 mega image-Q <’ :53 @QW Oil 01E 6. You are given: a. Mortality follows Mortality Table B. b. i: 7% Calculate 1000(M)[514]§l :fptlt Efﬁwmj‘” Numbgéwm QC? 631 535 7. Z is the present value random variable for a whole life on (77) with a death benefit of 1000 payable at the end of the year of death. You are given: a. Mortality follows Table A. b. v = 0.9 Calculate Var[Z]. 55552555 3 (/@@3§3€3A55 W<A 35> 9590 55577 “E 555:5:5> 5(555Cf>5 5E3 5155;553 {5% 5 W. W 5.. 555 8’76 /l 5 555 o. « ‘5 {W (7100 3577 I 590 (555(55555555 {55555.53 595755252 .3 5.. W Um {5:7 rX/ 0069310, 775575553 {0‘3 548735] 5 3955.55 W W (ﬁg 8. Complete the following table. Be sure to show your work. x L (L T [x 50 0.050 A | 40:2 0% 51 ‘9"0 L99 82259 :5; 52 O "7 78,660.00 53 0.200 M137» g .g 54 I 021" “52,230.24 mm W 0.95” 593/ 9. You are given: a. Mortality follow the Illustrative Life Table except at age 90 where qgo = 0.1. b. 2': 6% c. Z is the present value random variable for a whole life insurance on (90) with a death benefit 1 paid at the end of the year of death; Calculate Var[Z]. 52 l 10. You are given: a. SEX = 0.7200 b. 10EX=0.4480 c. 20Ex20.2048 d. 10px=0.7000 Calculate 5usqx. :- 19; ~} 5" ij + 2&9 ...
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