Tutorial 2 - FIN 3220A Actuarial Models I Tutorial 2 28...

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Unformatted text preview: FIN 3220A Actuarial Models I Tutorial 2 28 Swimmer 2005 1. Mortality follows de Moivre’s Law and E“, = 42. Calculate Var[T(16)]. 2. YOU are given the following extract from a 2-year select-and-ultimate mortality table: [x] lix] l[x}.1 lx+2 x+2 92 6300 94 93 5040 95 94 3024 96 The following relationships hold for all x: (i) 2 0 Q[x]+1= 3 0 q[x+1] (ll) 3 " am 3 4 ' (“”1144 Calculate IE94] 3. You are given: (l) Q70 3 0.040 (ll) ([71 = 0.044 (iii) Deaths are uniformly distributed over each year of age. Calculate Emma 4. A whole life insurance of 50 is issued to (x). The benefit is payable at the moment of death. The p.d.f. of the future lifetime, T, for (x) is l/\ f(t) = t/5000, 0 g t _ 100 The force of interest is 0.1. Calculate the net single premium. 5. There are 100 club members age x who each contribute an amount N to a fund. The fund earns interest at 10%. The probability is 0.95 that sufficient funds will be on hand to pay a 100 death benefit to each member. You are given the following values calculated_at i = 10%: (i) the: 0.06 (with: 0.01 Calculate N. (Assume the future lifetimes are independent so that normal distribution may be used. P(Z < 1.645) = 0.95) FIN 3220A Actuarial Models I Tutorial 2 28 September 2005 6. Let Z be the present value variable for $1 of whole life insurance with benefits payable at death and issued on (40). If lx : 110 - x for 0§x§110 and 5 = 0.05, find fz(0.8). 7. You are given the following extract from a select-and—ultimate mortality table with a 2-year select period: “— 80625 79954 79137 78402 Assume that deaths are uniformly distributed between integral ages. Calculate 0.9q[60]+0.6 ...
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