Consider two people age 40.  What is the expected number of years that both are alive? What is the expected number of years that at least one is alive? Show your work in excel to solve the following: What is the actuarial present value of a pension that pays $50,000 per year as long as at least one of the two 40-year-old people survive? Use a 5% discount rate. [Remember actuarial present value means that you must discount in the usual way to get present value, but you also must weight (i.e., multiply) every yearly payment by the probability that at least one of the two 40-year-old people is alive in order to receive the $50,000 payment.]

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.9: Dividing Real Numbers
Problem 8E
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Consider two people age 40. 

  1. What is the expected number of years that both are alive?
  2. What is the expected number of years that at least one is alive?
  3. Show your work in excel to solve the following: What is the actuarial present value of a pension that pays $50,000 per year as long as at least one of the two 40-year-old people survive? Use a 5% discount rate. [Remember actuarial present value means that you must discount in the usual way to get present value, but you also must weight (i.e., multiply) every yearly payment by the probability that at least one of the two 40-year-old people is alive in order to receive the $50,000 payment.]
A
1 A
23456
2 Age
0
1
2
3
7
4
8 5
9 6
10 7
11 8
12 9
13 10
14 11
15 12
16 13
17 14
18 15
19 16
20 17
21 18
22 19
23 20
24 21
25 22
26 23
27 24
28 25
29
B
B
# of Survivors
100000
99249
99193
99155
99126
99102
99083
99066
99051
99035
99019
99001
98983
98963
98938
98906
98860
98791
98700
98580
98444
98311
98163
98023
97888
97752
D
A B
Age # of Survivors
26
97624
27
97489
28
97359
29
97224
30
97092
31
96954
96818
32
33 96677
34
96522
35
96359
36
96180
37
95997
38 95791
39
95569
40
95337
41
95087
42
94825
43
94542
44
94229
45
93892
46
93529
47
93142
48
92713
49
92254
50
91768
51
91247
E
F
G
A
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
B #
74 75 76 77
В
Age # of Survivors
52
53
H
90707
90127
89527
88839
88161
87382
86542
85600
84654
83582
82458
81231
79920
78506
76988
75391
73665
71830
69875
67824
65652
63335
60880
58335
55655
52874
J
K
A
B
Age # of Survivors
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
50001
47012
43928
40856
37568
34457
31192
27975
24820
21766
18852
16113
13580
11277
9218
7412
5857
4546
3462
2586
1893
1357
953
600
400
200
L
M
A B
Age # of Survivors
104
105
106
107
108
109
110
111
N
B #
100
50
30
15
7
3
1
0
Transcribed Image Text:A 1 A 23456 2 Age 0 1 2 3 7 4 8 5 9 6 10 7 11 8 12 9 13 10 14 11 15 12 16 13 17 14 18 15 19 16 20 17 21 18 22 19 23 20 24 21 25 22 26 23 27 24 28 25 29 B B # of Survivors 100000 99249 99193 99155 99126 99102 99083 99066 99051 99035 99019 99001 98983 98963 98938 98906 98860 98791 98700 98580 98444 98311 98163 98023 97888 97752 D A B Age # of Survivors 26 97624 27 97489 28 97359 29 97224 30 97092 31 96954 96818 32 33 96677 34 96522 35 96359 36 96180 37 95997 38 95791 39 95569 40 95337 41 95087 42 94825 43 94542 44 94229 45 93892 46 93529 47 93142 48 92713 49 92254 50 91768 51 91247 E F G A 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 B # 74 75 76 77 В Age # of Survivors 52 53 H 90707 90127 89527 88839 88161 87382 86542 85600 84654 83582 82458 81231 79920 78506 76988 75391 73665 71830 69875 67824 65652 63335 60880 58335 55655 52874 J K A B Age # of Survivors 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 50001 47012 43928 40856 37568 34457 31192 27975 24820 21766 18852 16113 13580 11277 9218 7412 5857 4546 3462 2586 1893 1357 953 600 400 200 L M A B Age # of Survivors 104 105 106 107 108 109 110 111 N B # 100 50 30 15 7 3 1 0
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