Introduction Females have longer life expectancy than males in virtually all countries. Gender related differences in life expectancy make it more likely that females will out live their retirement resources than will males. This post considers how differences in the expected future life of a 75yearold male and a 75 yearold female might impact annuity payments.
Sources: The analysis presented here pertains to males and females in the United States. The source of information is the United States Life Tables, 2008 published on September 24, 2012 by the National Center for Health Statistics of the Centers for Disease Control and Prevention
Table Two of the report has life statistics for males and Table Three of the report has life statistics for females. Both tables can be downloaded directly into an EXCEL Spreadsheet.
Questions: A 75 yearold person wants to set up a monthly annuity so that he or she has only a 10% chance of living past the final payment. How long is the annuity in number of months if the person is a U.S. male or a U.S. female?
The person has $100,000 to spend on this annuity. What is the payment on the annuity for the male and the female at an interest rate of 0%, 3% and 6%?
A CAUTION: The annuity that I am experimenting with here is not a marketbased annuity, which would be based on expected future life rather than the 10% chance of outliving resources rule.
Answer: The data in Table One is from the CDC life tables. Based on this cohort of 100,000 females, 73,974 females have survived to page 75. Around 90% of these females are still alive until somewhere between age 95 and 96. (This seems really high but perhaps not because we are looking at the probability of survival given that the woman lived until age 75.)
In a cohort of 100,000 men 61,980 are still alive at age 75 and the 90% survival mark for these 75year olds is reached somewhere between age 94 and 95.
Age

Total number of females alive at age x

Proportion of 75yearold females who survive to age X

Total number of Males Alive at age X

Proportion of 75year Males surviving until age X

75

73,974

61,980
 
76

71,973

97.3%

59,531

96.0%

77

69,831

94.4%

56,962

91.9%

78

67,539

91.3%

54,268

87.6%

79

65,080

88.0%

51,437

83.0%

80

62,448

84.4%

48,469

78.2%

81

59,647

80.6%

45,390

73.2%

82

56,688

76.6%

42,227

68.1%

83

53,563

72.4%

38,994

62.9%

84

50,253

67.9%

35,694

57.6%

85

46,782

63.2%

32,360

52.2%

86

43,166

58.4%

28,996

46.8%

87

39,414

53.3%

25,650

41.4%

88

35,567

48.1%

22,372

36.1%

89

31,677

42.8%

19,213

31.0%

90

27,805

37.6%

16,223

26.2%

91

24,017

32.5%

13,448

21.7%

92

20,380

27.6%

10,928

17.6%

93

16,962

22.9%

8,691

14.0%

94

13,821

18.7%

6,754

10.9%

95

11,006

14.9%

5,122

8.3%

96

8,549

11.6%

3,783

6.1%

97

6,467

8.7%

2,719

4.4%

98

4,754

6.4%

1,898

3.1%

99

3,392

4.6%

1,286

2.1%

100

2,345

3.2%

844

1.4%

Let’s interpolate to get an exact number of months for our annuity formula.
For females we get 9675 (21) years plus (11.610)/(11.68.7) x 12 or (7) months. The 75year old female must buy an annuity of 259 months in order to reduce the probability that she will outlive the annuity to 10 percent.
For males we get 9475 (19) years plus (10.910)/(10.98.3) x 12 or 5 months (I am rounding up to fulfill the contract.) The 75year old male must buy an annuity of 233 months in order to reduce the probability that he will outlive the annuity to 10 percent.
So now we calculate the annuity payments for the female and the male with the PMT function. The only input that differs is the duration of the contract – 259 months for females and 233 months for males.
The annuity payment calculations were obtained from the PMT function in Excel.
Female

Male
 
Rate 0%

0

0
 
Rate 3%

0.03

0.03
 
Rate 6%

0.06

0.06
 
NPER

259

233
 
PV

$100,000

$100,000
 
Type

1

1

DIFFERENCE

% DIFFERENCE WITH FEMALE AS BASE

PMT rate=0

$386.10

$429.18

($43.08)

11.2%

PMT rate =3%

$524.96

$566.77

($41.81)

8.0%

PMT rate=6%

$689.45

$727.62

($38.17)

5.5%

In order to reduce their greater longevity risk females must buy a longerterm annuity and will therefore receive a lower payment. The potential reduction in annuity payments is greatest when interest rates are low.
This annuity calculator on the web confirms that females receive lower annuity payments. I am not familiar with the specific formulas used by this calculator or the product that it pertains to. My sole interest here is to provide some insight on how gender determines longevity risk.
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