ct010s10 - UNSW ACTL1001 Actuarial Studies and Commerce...

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UNSW ACTL1001 Actuarial Studies and Commerce Sample Solutions Exercises 10 NOTE: the following questions can be computed either by hand or by excel. You should ensure that you are able to use both methods. Exercise 1 We have 1. Expected present value of claim payments using actuarial notation is 100000 A 1 30: 5 where A 1 30: 5 = 4 X k =0 v k +1 ( k p 30 q 30+ k ) Age qx px k kp30 kp30q30+ v^(k+1) Product 30 0.00131 0.99869 0 1.000000 0.001310 0.952381 0.0012476 31 0.00132 0.99868 1 0.998690 0.001318 0.907029 0.0011957 32 0.00133 0.99867 2 0.997372 0.001327 0.863838 0.0011459 33 0.00135 0.99865 3 0.996045 0.001345 0.822702 0.0011063 We then have A 1 30: 5 = 0 : 005771 at 5% 2. The expected present value of the premiums of $1 p.a. payable in ad- vance for 5 years on a life aged 30 using actuarial notation is & a 30 : 5 where & a 30 : 5 = 4 X k =0 v k ( k p 30 ) Age k kp30 v^k kp30v^k 30 0 1.000000 1.000000 1.000000 31 1 0.998690 0.952381 0.951133 32 2 0.997372 0.907029 0.904646 33 3 0.996045 0.863838 0.860421 34 4 0.994701 0.822702 0.818343 4.534543 1
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Thus the value we require is 4.534543. 3. Let P denote the premium to be solved for in each of the following sub-questions. (a) Using the equation (where & a 30 : 3 and A 1 30: 3 are calculated via the same procedure as before) P & a 30 : 3 = 100000 A 1 30: 3 + 20 + 0 : 02 P & a 30 : 3 we can solve to &nd P = 135 : 39 (b) Using the equation P & a 30 : 5 = 100000 A 1 30: 5 + 20 + 0 : 02 P & a 30 : 5 we can solve to &nd P = 134 : 37 (c) For a pure endowment we have P & a 30 : 5 = 100000 A 30 1 : 5 + 20 + 0 : 02 P & a 30 : 5 with A 30 1 : 5 = 5 p 30 v 5 , we &nd the the premium P = 17518 : 55 (d) For an endowment assurance we have P & a 30 : 5 = 100000 A 30: 5 + 20 + 0 : 02 P & a 30 : 5 where A 30: 5 = A 30 1 : 5 + A 1 30: 5 we &nd the the premium P = 17648 : 41 2
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Exercise 2 The company will not have su¢ cient funds to pay its total claims if premiums plus capital is less than total claims. Let C be the capital required
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This note was uploaded on 06/12/2011 for the course ASB 1001,2522, taught by Professor Nicole during the One '09 term at University of New South Wales.

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ct010s10 - UNSW ACTL1001 Actuarial Studies and Commerce...

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