Exercise 9.13 You are given the following three-decrement service table for modelling employment. X 60 61 62 ₂01 (a) Calculate 3p. 00 (b) Calculate 201 lx 10 000 9 475 8 945 d¹) 350 360 380 (2) dx 150 125 110 (3) d 25 45 70 (c) Calculate the EPV of a benefit of $10 000 payable at the end of the year of exit, if a life aged 60 leaves by decrement 3 before age 63. Use an effective rate of interest of 5% per year. (d) Calculate the EPV of an annuity of $1000 per year payable at the start of each of the next 3 years if a life currently aged 60 remains in service. Use an effective rate of interest of 5% per year. *(1) (e) Show that 962 = 0.04292, assuming a constant force of decrement for each decrement. *(1) (f) Calculate the revised service table for age 62 if 962 is increased to 0.1, with the other independent rates remaining unchanged. Use (i) the constant force assumption, and (ii) UDD in the single decrement models assumption.
Exercise 9.13 You are given the following three-decrement service table for modelling employment. X 60 61 62 ₂01 (a) Calculate 3p. 00 (b) Calculate 201 lx 10 000 9 475 8 945 d¹) 350 360 380 (2) dx 150 125 110 (3) d 25 45 70 (c) Calculate the EPV of a benefit of $10 000 payable at the end of the year of exit, if a life aged 60 leaves by decrement 3 before age 63. Use an effective rate of interest of 5% per year. (d) Calculate the EPV of an annuity of $1000 per year payable at the start of each of the next 3 years if a life currently aged 60 remains in service. Use an effective rate of interest of 5% per year. *(1) (e) Show that 962 = 0.04292, assuming a constant force of decrement for each decrement. *(1) (f) Calculate the revised service table for age 62 if 962 is increased to 0.1, with the other independent rates remaining unchanged. Use (i) the constant force assumption, and (ii) UDD in the single decrement models assumption.
Chapter12: Sequences, Series And Binomial Theorem
Section12.3: Geometric Sequences And Series
Problem 12.57TI: What is the total effect on the economy of a government tax rebate of $1,000 to each household in...
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Transcribed Image Text:Exercise 9.13 You are given the following three-decrement service table for
modelling employment.
X
60
61
62
₂01
(a) Calculate 3P60*
00
(b) Calculate 2p1.
lx
10 000
9 475
8 945
d(¹)
350
360
380
150
125
110
d(3)
25
45
70
(c) Calculate the EPV of a benefit of $10000 payable at the end of the year of
exit, if a life aged 60 leaves by decrement 3 before age 63. Use an effective
rate of interest of 5% per year.
(d) Calculate the EPV of an annuity of $1000 per year payable at the start of
each of the next 3 years if a life currently aged 60 remains in service. Use
an effective rate of interest of 5% per year.
*(1)
(e) Show that q2 = 0.04292, assuming a constant force of decrement for
each decrement.
_*(1)
(f) Calculate the revised service table for age 62 if 962 is increased to
0.1, with the other independent rates remaining unchanged. Use (i) the
constant force assumption, and (ii) UDD in the single decrement models
assumption.
Transcribed Image Text:9.13 (a) 0.109 (b) 0.8850 (c) $125.09 (d) $2713.72
(f)(i) 885.4, 106.7, 67.9 (ii) 885.3, 106.8, 68.0
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