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Chapter_7_-_Question_Set

# Chapter_7_-_Question_Set - ACTSC 331 Life contingencies 1...

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ACTSC 331 - Life contingencies 1 Exercises (Chapter 7) 1. A fully continuous 20 -year payment, 30 -year term insurance of \$2000 is issued to (35) . We assume that the force of interest of 6%, and the force of mortality is such that t p x = exp & 0 : 0005246 ± 1 : 1 x ± 1 : 1 t 1 ²³ , t;x ² 0 . Under these assumptions, n A 1 35+ n : 30 n j a 35+ n : 20 n j 0 0 : 06873 11 : 39534 10 0 : 09710 7 : 35175 25 0 : 07952 12 : 063 ) j L for j = 10 ; 25 . Plot roughly the curves of j L in function of T for j = 10 ; 25 . (c) Find the value of 10 L if T = 12 : 3 and the one of 25 L if T = 27 : 4 . (Answers: 1716 : 3 and 1731 : 8 ) (d) Compute the policy value j V = E [ j L j T > j ] for j = 10 and 25 . (Answers: 105 : 52 and 159 : 04 ) (e) Given that T > 10 10 L is less than or equal to 1800 . (Answer: 0 : 99377 ) 2. A fully continuous 20 -year deferred whole life insurance of \$4000 is issued to (45) is payable as long as the insured is alive without exceeding the deferred period. We assume a force of interest of 6% , and the force of mortality is such that t p x = exp & 0 : 0005246 ± 1 : 1 x ± 1 : 1 t 1 ²³ , t;x ² 0 . Under these assumptions, n 20 n j A 45+ n A 45+ n a 45+ n : 20 n j 0 0 : 11630 0 : 21341 11 : 01577 10 0 : 22524 0 : 33092 7 : 09581 25 & 0 : 56246 42 : 23 ) j L for j = 10 ; 25 . Plot roughly the curves of j L in function of T for j = 10 ; 25 . (c) Find the value of 10 L if T = 12 : 3 and the one of 25 L if T = 27 : 4 . (Answers: 90 : 725 and 3463 : 6 ) (d) Compute the policy value j V = E [ j L j T > j ] for j = 10 and 25 . (Answers: 601 : 3 and 2249 : 8 ) (e) Given that T > 10 10 L is less than or equal to 0 . (Answer: 0 : 15051 ) 3. A fully continuous 35 -year payment, whole life insurance of \$1000 is issued to (30) . For calculation purposes, we assume (1) ( x ) = 1 100 x , 20 ³ x < 100 ; (2) ± = 6% ; Under the equivalence principle, the premium was found to be P = 19 : 28043 . Find 10 such that Pr( 10 L > 10 j T > 10) = 5% . (Answer: 782 : 34 ) 1

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4. A fully discrete 15 -year payment, 40 -year endowment insurance of \$3000 is issued to ( x ) . We assume that the force of interest of 6%, and the force of mortality is such that t p x = exp & 0 : 0005246 ± 1 : 1 x ± 1 : 1 t 1 ²³ , t;x ² 0 . Under these assumptions, n A x + n : 40 n j a x + n : 15 n j 0 0 : 06532 10 : 10623 10 0 : 10211 4 : 42878 25 0 : 15924 19 : 39 ) j L for j = 10 ; 25 . (c) Find the value of
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Chapter_7_-_Question_Set - ACTSC 331 Life contingencies 1...

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