1 2 Calculate the value of each of the following functions, using the given basis: 65:201...

 

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1 2 Calculate the value of each of the following functions, using the given basis: ä65:201 AM92 mortality and 4% pa interest A68:2 4 (1) (iv) (v) (vi) a A[60]+1 4401:201 Calculate the values of: (12) 50:15 (i) 62:5 (iii) [55]+1:4 (a) (b) using AM92 mortality and 4% pa interest. 3 Calculate the expected present value of a payment of £2,000 made 6 months after the death of a life now aged exactly 60, assuming AM92 Select mortality and 6% pa interest. (12) 50:15 0 AM92 mortality and 6% pa interest PFA92C20 mortality and 4% pa interest g(K)=10 AM92 mortality and 4% pa interest Calculate A30.25 and 30:25 independently, assuming AM92 mortality and 6% pa interest. Hence verify that the usual premium conversion relationship holds approximately between these two functions. 10 AM92 mortality and 4% pa interest 5 Let K be a random variable representing the curtate future lifetime of a life aged 40, and let g(K) be the function defined as: ä25 AM92 mortality and 6% pa interest if 0≤K <10 if 10 ≤K <35 if 35 ≤K In a mortality table with a one-year select period qx]=a.qx for all x 20 and for a certain constant 0<a<1. (i) Let: K[x]+t =curtate future lifetime of a person aged x+t who became select t years ago Explain whether the expected value of K[x]+1 is less than, greater than, or equal to the expected value of Kx+1 [1] . Kx = curtate future lifetime of a person aged x whose mortality is reflected by the ultimate part of the mortality table. Calculate A451:20 based on the following assumptions: . a=0.9 Interest: 4% pa Ultimate mortality: ELT15 (Males) Financial functions using ELT15 (Males) mortality are given on page 136 of the Tables. [6] [Total 7] 1 2 Calculate the value of each of the following functions, using the given basis: ä65:201 AM92 mortality and 4% pa interest A68:2 4 (1) (iv) (v) (vi) a A[60]+1 4401:201 Calculate the values of: (12) 50:15 (i) 62:5 (iii) [55]+1:4 (a) (b) using AM92 mortality and 4% pa interest. 3 Calculate the expected present value of a payment of £2,000 made 6 months after the death of a life now aged exactly 60, assuming AM92 Select mortality and 6% pa interest. (12) 50:15 0 AM92 mortality and 6% pa interest PFA92C20 mortality and 4% pa interest g(K)=10 AM92 mortality and 4% pa interest Calculate A30.25 and 30:25 independently, assuming AM92 mortality and 6% pa interest. Hence verify that the usual premium conversion relationship holds approximately between these two functions. 10 AM92 mortality and 4% pa interest 5 Let K be a random variable representing the curtate future lifetime of a life aged 40, and let g(K) be the function defined as: ä25 AM92 mortality and 6% pa interest if 0≤K <10 if 10 ≤K <35 if 35 ≤K In a mortality table with a one-year select period qx]=a.qx for all x 20 and for a certain constant 0<a<1. (i) Let: K[x]+t =curtate future lifetime of a person aged x+t who became select t years ago Explain whether the expected value of K[x]+1 is less than, greater than, or equal to the expected value of Kx+1 [1] . Kx = curtate future lifetime of a person aged x whose mortality is reflected by the ultimate part of the mortality table. Calculate A451:20 based on the following assumptions: . a=0.9 Interest: 4% pa Ultimate mortality: ELT15 (Males) Financial functions using ELT15 (Males) mortality are given on page 136 of the Tables. [6] [Total 7]

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1 Calculating the values of the given functions i 6520 AM92 mortality and 4 pa interest ... View the full answer