Consider two people age 40.

a. What is the expected number of years that both are alive?

b. What is the expected number of years that at least one is alive?

c. 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.]

DATA PROVIDED:

A B

Number of

Age Survivors

0 100000

1 99249

2 99193

3 99155

4 99126

5 99102

6 99083

7 99066

8 99051

9 99035

10 99019

11 99001

12 98983

13 98963

14 98938

15 98906

16 98860

17 98791

18 98700

19 98580

20 98444

21 98311

22 98163

23 98023

24 97888

25 97752

26 97624

27 97489

28 97359

29 97224

30 97092

31 96954

32 96818

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

52 90707

53 90127

54 89527

55 88839

56 88161

57 87382

58 86542

59 85600

60 84654

61 83582

62 82458

63 81231

64 79920

65 78506

66 76988

67 75391

68 73665

69 71830

70 69875

71 67824

72 65652

73 63335

74 60880

75 58335

76 55655

77 52874

78 50001

79 47012

80 43928

81 40856

82 37568

83 34457

84 31192

85 27975

86 24820

87 21766

88 18852

89 16113

90 13580

91 11277

92 9218

93 7412

94 5857

95 4546

96 3462

97 2586

98 1893

99 1357

100 953

101 600

102 400

103 200

104 100

105 50

106 30

107 15

108 7

109 3

110 1

111 0