Tutorial 1 Flashcards
Question 1
Evaluate the following
Basis – Mortality AM92 Ultimate
p35
p35 = 1-q35 = 1-0.000689 = 0.999311
Question 1
Evaluate the following
Basis – Mortality AM92 Ultimate
q40
q40 = 0.000937
Question 1
Evaluate the following
Basis – Mortality AM92 Ultimate
20p30
20p30 = l50/l30 = 9712.0728/9925.2094 = 0.97853
Question 1
Evaluate the following
Basis – Mortality AM92 Ultimate
15q45
15q45 = (l45 – l60)/l45 = (9801.3123-9287.2164)/9801.3123 = 0.05245
Question 1
Evaluate the following
Basis – Mortality AM92 Ultimate
10|5q50
10|5q50 = 10p50 5q60
= l60/l50 x(l60 – l65)/l60 = (l60 – l65)/l50
= (9287.2164-8821.2612)/9712.0728 = 0.04798
Question 1
Evaluate the following
Basis – Mortality AM92 Ultimate
A population is subject to a constant force of mortality
of 0.015, calculate the probability that a life currently
aged 40 dies within the next 10 years
10q40 = 1 - 10p40 = 1 - e^(-10x0.015) = 1 - 0.86071 = 0.13929
Question 2
Which of the following is not correct for the
probability that a life currently aged 50 survives for 25
years?
a) 25p50
b) 20p50 x 5p70
c) 15p50 x 10p60
d) 10p50 x 15p60
c) 15p50 x 10p60
Question 3
Calculate 3p62.5 based on AM92 Ult using
i. Constant Force of Mortality
ii. Uniform Distribution of Death
i. Constant Force of Mortality
3p62.5 = 0.5p62.5 x 2p63 x 0.5p65
2p63 = l65/l63 = 8821.2612/9037.3973 = 0.976084
0.5p65 =(p65)^0.5 =(1-q65)^0.5 = (1-0.014243)^0.5 =0.992853
0.5p62.5 = (p62)^0.5 =(1-q62)^0.5 = (1-0.010112)^0.5 = 0.994931
3p62.5 = 0.994931 x 0.976084 x 0.992853 = 0.964196
ii. Uniform Distribution of Death
3p62.5 = 0.5p62.5 x 2p63 x 0.5p65
2p63 = l65/l63 = 8821.2612/9037.3973 = 0.976084
0.5p65 = 1 - 0.5q65 = 1 - 0.5q65 = 1 - 0.5(0.014243) = 0.992879
0.5p62.5 = 1 - 0.5q62.5= 1 - [(0.5)q62/(1 - 0.5.q62) ]
=1 - [0.5(0.010112)/(1 - 0.5x0.010112)] = 0.994918
3p62.5 = 0.994918 x 0.976084 x 0.992879 = 0.96420
Question 4
A. Calculate the EPV and SD of a whole life assurance with a sum assured of £75,000 for a life currently aged 50. Payable at the End of the Year of death.
B. What is the corresponding EPV if the benefit is paid
immediately on death?
Basis AM92 Ultimate @ 4% pa
A.
Basis AM92 Ultimate @ 4% pa
EPV = 75000A50
EPV = 75000x0.32907 = £24,680
SD = [75000^2(2A50 – (A50)^2]^0.5
SD = [75000^2(0.13065 – 0.32907^2)]^0.5
SD = £11,216
B.
EPV = 75000 x i/δ x A50
EPV = 75000 x 0.32907 x 0.04/ln1.04
= £25,171
Question 5
Calculate the EPV of a 25 year term assurance with a
sum assured of £150,000 for a life currently aged 35.
Payable at the End of the Year of death.
Basis AM92 Ultimate @ 6% pa
EA = TA + PE
150,000𝐴35:25 =150,000(𝐴^1,35:25 + 𝐴35:25^1)
150,000𝐴^1,35:25 =150,000(𝐴35:25 - v^(25)25p35)
= 150,000(0.24208 – 9287.2164/9894.4299x1.06^-25)
= 150000x0.02338 = £3,507
Question 6
Calculate the EPV of a 15 year endowment assurance
with a sum assured of £90,000 for a life currently aged 40. Payable at the End of the Year of death.
Basis AM92 Ultimate @ 4% pa
n|Ax = Ax -𝐴^1,𝑥:𝑛= v^(n)npxA,x+n
TA=𝐴^1,40:15 = (A40 – v^(15)15p40A55)
= 0.23056 - 0.3895 x 9557.8179/9856.2863 x 1.04^-15 =0.02083
PE = 𝐴,40:15^1=v^(15)15p40
= 9557.8179/9856.2863 x 1.04^-15 =0.53845
EPV EA = 90000(0.02083+0.53845) = £50,335
Question 7
Calculate the EPV of a 10 year endowment assurance
with a sum assured of £50,000 for a life currently aged 55. Death benefits are payable immediately on death.
Basis AM92 Ultimate @ 6% pa
50000Ā55:10 =50,000(Ā^1,55:10 + 𝐴55:10^1)
50,000𝐴55:10 =50,000(𝐴^1,55:10 + v^(10)10p55)
Ā^1,55:10= i/δ𝐴^1,55:10= i/δ(𝐴55:10 - v^(10)10p55)
= 0.06/ln1.06(0.56922 – 8821.2612/9557.8179 x 1.06^-10)
= 0.06/ln1.06(0.56922 – 0.51536) = 0.05546
50000Ā55:10 = 50000(0.05546 + 0.51536) = £28,541
