This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 imageQ <’ :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 ...
View
Full Document
 Fall '11
 NA

Click to edit the document details