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# tut03s - UNSW ACTL1001 Actuarial Studies and Commerce...

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UNSW ACTL1001 Actuarial Studies and Commerce Sample Solutions Exercises 3 Exercise 1 For s ( x ) = q ° 1 ° x 100 ± for 0 ± x < 100 we have 1. Pr [ a life aged 15 survives to 45 ] = s (45) s (15) = q ° 1 ° 45 100 ± q ° 1 ° 15 100 ± = r 0 : 55 0 : 85 = 0 : 8044 2. 45 p 20 = s (65) s (20) = q ° 1 ° 65 100 ± q ° 1 ° 20 100 ± = r 0 : 35 0 : 8 = 0 : 6614 1

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3. Pr [ a life aged 20 will not survive to age 40 ] = 20 q 20 = 1 ° 20 p 20 = 1 ° s (40) s (20) = 1 ° q ° 1 ° 40 100 ± q ° 1 ° 20 100 ± = 1 ° r 0 : 6 0 : 8 = 0 : 13397 4. Pr [ a life aged 20 will die between age 50 and 65 ] = 30 j 15 q 20 = s (50) ° s (65) s (20) = q ° 1 ° 50 100 ± ° q ° 1 ° 65 100 ± q ° 1 ° 20 100 ± = p 0 : 5 ° p 0 : 35 p 0 : 8 = 0 : 1291 5. q 40 = 1 ° p 40 = 1 ° s (41) s (40) = 1 ° s 1 ° 41 100 1 ° 40 100 = 0 : 00837 Exercise 2 For s ( x ) = ° 1 ° x 100 ± 3 for 0 ± x < 100 we have 2
1. 10 p 20 = s (30) s (20) = ² 0 : 7 0 : 8 ³ 3 = 0 : 6699 2. 5 j 30 q 35 = s (40) ° s (70) s (35) = ° 1 ° 40 100 ± 3 ° ° 1 ° 70 100 ± 3 ° 1 ° 35 100 ± 3 = 0 : 216 ° 0 : 027 0 : 274625 = 0 : 6882 Exercise 3 The IA64-70 Table is available on Page 48 of the text for ages 10 to 50. 1. the expected age at death of a life aged 20 is 20 + 53 : 71 = 73 : 71 2. the expected age at death of a life aged 25 25 + 49 : 12 = 74 : 12 3. the probability that a life age 20 will survive to age 50

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tut03s - UNSW ACTL1001 Actuarial Studies and Commerce...

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