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MATH20962 Tutorial 1 Life expectancy 1. Find values for the following using your table books (and write down the correct actuarial notation): (a) The expected future lifetime of a newborn (also known as the complete future lifetime) assuming ELT15(Female) mortality. (b) The expected complete future lifetime of a person aged exactly 55 assuming ELT15(Female) mortality. (c) The expected age at death (including fractional years) of a person aged exactly 55 assuming ELT15(Female) mortality. Bonus question: explain why this is higher than the expected age at death of a newborn. (d) The expected curtate future lifetime of a person aged exactly 55 assuming AM92 mortality. 2. Is a person aged 60 assumed to live longer if he follows PMA92C20 or she follows 0 PFA92C20? Lookup e x for both tables and state a common conclusion for male versus female pensioner life expectancy. Looking up 3. Lookup: (a) The expected present value of a 25 year endowment assurance of a life aged exactly 40, using an interest rate of 6% and AM92 ultimate mortality. Write down the correct actuarial notation. (b) The expected present value of a whole life assurance payable at the end of year of death of a life aged exactly 40, using an interest rate of 6% and AM92 mortality. (c) The expected present value of a whole life assurance payable at the end of year of death of a life aged exactly 40, using an interest rate of 12.36% and AM92 select mortality. [Hint: 1:06^2 = 1:1236] Tx, Kx 4. A person dies aged 82 yrs and 142 days. What are the values of T25 and K25? Expected value and variance 5. April 2011 (subject CT5) Institute exam Q10: Calculate the expected present value and variance of the present value of an endowment assurance of 1 payable at the end of the year of death for a life aged 40 exact, with a term of 15 years. Basis: Mortality AM92 Select Rate of interest 4% per annum l55 9557.8179 [You may use: 15 p[ 40] 0.969913 ] l[ 40] 9854.3036 General relationships between expected present value 6. State with reason whether the following statements are true or false. Where necessary assume 5%pa interest. (i) A25:3| A35:3| (ii) A35:10| 0.6 (iii) A1 0.6 35:10| 7. Evaluate A70:2| using AM92 ultimate mortality and 4%pa interest. (You may assume 2 p 70 = l 72 / l 70 7637 .6208 / 8054 .0544 0.94830 ) 8. Correct the following formulas n| Ax v Ax n n (i) (ii) Ax:n| Ax:t| v t t p x . Axt:nt| 9. State which has the highest value: 2 A[55 ] A55 A25:5| A55 2 The suffix indicates a modified interest rate of i’ where 1+i’ = (1+i)2 Derivation of key formula 10. April 2005 (subject CT5) Institute exam Q12: (i) By considering a term assurance policy as a series of one year deferred term assurance policies, show that: i A1 A1 x:n| x:n| (ii) Calculate the expected present value and variance of the present value of a term assurance of 1 payable immediately on death for a life aged 40 exact, if death occurs within 30 years. Basis: Interest 4% per annum Mortality AM92 Select l70 8054.0544 You may assume 30 p[ 40] 0.8173134 l[ 40] 9854.3036 Derivation of formula for the variance of the present value of a deferred assurance 11. April 2007 (subject CT5) Institute exam Q10: Let X be a random variable representing the present value of the benefits of a whole of life assurance, and Y be a random variable representing the present value of the benefits of a temporary assurance with a term of n years. Both assurances have a sum assured of 1 payable at the end of the year of death and were issued to the same life aged x. (i) Describe the benefits provided by the contract which has a present value represented by the random variable X - Y. [1 mark] (ii) Show that cov( X , Y ) 2 A1 Ax . A1 x:n| x:n| and hence or otherwise that var (X – Y) = 2 Ax ( n| Ax ) 2 2 A1 x:n| where the functions A are determined using an interest rate of i, and functions 2 A are determined using an interest rate of i 2 2i . January 2012

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posted: | 8/29/2012 |

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