TERM INSURANCE

The simplest kind of life insurance policy you can buy is term insurance. As the name implies, a term insurance policy insures you for a specific term. You pay a premium up front for the policy. If you don’t die during the term, you and the insur­ance company no longer have any contractual relationship. Whatever happens, the insurance company keeps the premium. Actually, term insurance is the only kind of life insurance there is. All the other life insurance products that you can buy are built on term insurance policies, sometimes combined with savings/investment accounts.

Term insurance policies themselves can get very complicated. They might be written for many years, and payments made might be spread out over these years rather than up front. There are so many possible variations that it’s impossible to cover them all. But let’s look at a few simple cases. I will be losing accuracy by considering only average values and by not considering the business costs, the return on investment of all the money that the insurance company is holding, the need for the insurance company to make a profit for its owners (investors), and so on. Also, life insurance companies have many sets of life tables that get far more specific than the few sets I’m using for my examples. In other words, I will show you what goes on in putting together a life insurance policy. I can’t actually price your policy.

Suppose that a 50-year-old woman wants a 1-year, $100,000 term life insurance policy for the following year. Table 10.2 shows the 2004 Life Table for all women. This table just shows the age (x) and the probability of dying at that age (q) because that ’s all that ’s needed.

Table 10.3 shows a part of Table 10.2 from age 50 to age 100. In addition, I have added column l and column d, with column l starting at 100,000 people. The numbers for column l and column d were generated following the procedure shown above.

Looking at the top line (age 50), the table shows that if 100,000 people sign up for this policy, on the average, 320 will die during the year. The insurance company will have to pay out 320($100,000). Since 100,000 people bought these policies, the cost per person is just 320($100,000)/100,000 = $320.

Подпись: $320 (1.04)05 Подпись: $313.80.

Let’s make this a little more complicated. If the insurance company sold a lot of these policies, it would expect to see a few women die every day of the year, since some women die early in the year, and some die very late in the year. The average date of death is the middle of the year. This means that the insurance company gets to hold everybody’s money for an average time of half a year. If an average woman has to pay an amount today that will be worth $320 half a year from now, then she should only pay the present value of that amount. At 4% interest, therefore, she should only have to pay (assuming annual compounding)

What if this same woman, who’s just turning 50 years old, wants to buy a 2- or more year term policy? At first blush, you might ask why she would do this. If she

Table 10.2 The 2004 U. S. Life Table for All Women (Age and q Columns Only)

Age

q

Age

q

Age

q

0-1

0.006091

34-35

0.000825

68 – 69

0.014966

1-2

0.000457

35-36

0.000892

69-70

0.016407

2-3

0.000267

36-37

0.000971

70-71

0.017945

3-4

0.000197

37-38

0.001071

71-72

0.019617

4-5

0.000168

38-39

0.001190

72-73

0.021503

5-6

0.000151

39-40

0.001321

73-74

0.023635

6-7

0.000138

40-41

0.001453

74-75

0.025987

7-8

0.000129

41-42

0.001586

75-76

0.028358

8-9

0.000120

42-43

0.001727

76-77

0.030849

9-10

0.000112

43-44

0.001883

77-78

0.033818

10-11

0.000107

44-45

0.002055

78-79

0.037481

11-12

0.000113

45-46

0.002243

79-80

0.041792

12-13

0.000135

46-47

0.002439

80-81

0.046463

13 – 14

0.000178

47-48

0.002633

81-82

0.051306

14-15

0.000237

48-49

0.002819

82 – 83

0.056613

15 – 16

0.000306

49-50

0.003005

83 – 84

0.062608

16-17

0.000371

50-51

0.003204

84-85

0.069533

17-18

0.000421

51-52

0.003432

85 – 86

0.076645

18-19

0.000446

52-53

0.003695

86 – 87

0.084411

19-20

0.000453

53-54

0.004000

87 – 88

0.092876

20-21

0.000456

54-55

0.004346

88 – 89

0.102085

21-22

0.000464

55-56

0.004725

89-90

0.112081

22-23

0.000471

56-57

0.005137

90-91

0.122907

23-24

0.000481

57-58

0.005594

91-92

0.134602

24-25

0.000492

58-59

0.006110

92-93

0.147201

25-26

0.000506

59-60

0.006697

93-94

0.160735

26-27

0.000522

60-61

0.007389

94-95

0.175225

27-28

0.000541

61-62

0.008167

95-96

0.190689

28-29

0.000565

62-63

0.008977

96-97

0.207132

29-30

0.000593

63 – 64

0.009776

97-98

0.224550

30-31

0.000627

64-65

0.010581

98-99

0.242924

31-32

0.000667

65 – 66

0.011466

99-100

0.262224

32-33

0.000712

66-67

0.012498

100 or over

1.00000

33-34

0.000764

67-68

0.013661

just planned to buy term policies year by year and then died, say, during the first year, her premiums for the subsequent years would still be part of her estate rather than in the hands of the insurance company. The need to buy such a policy can arise, for example, if there is a business loan with the repayment due as a lump sum, say, 5 years from today. The creditor might want to guarantee his or her repayment in case the borrower dies before the repayment is due, without having to get involved

Table 10.3 Life Table for Women Aged 50 and Up

X

q

l

d

X

q

l

d

50-51

0.003204

100,000

320

76-77

0.030849

74,058

2,285

51-52

0.003432

99,680

342

77-78

0.033818

71,774

2,427

52-53

0.003695

99,337

367

78-79

0.037481

69,347

2,599

53-54

0.004000

98,970

396

79 – 80

0.041792

66,747

2,790

54-55

0.004346

98,574

428

80-81

0.046463

63,958

2,972

55-56

0.004725

98,146

464

81-82

0.051306

60,986

3,129

56-57

0.005137

97,682

502

82-83

0.056613

57,857

3,275

57-58

0.005594

97,181

544

83 – 84

0.062608

54,582

3,417

58-59

0.006110

96,637

590

84-85

0.069533

51,165

3,558

59- 60

0.006697

96,046

643

85 – 86

0.076645

47,607

3,649

60- 61

0.007389

95,403

705

86 – 87

0.084411

43,958

3,711

61-62

0.008167

94,698

773

87 – 88

0.092876

40,247

3,738

62- 63

0.008977

93,925

843

88-89

0.102085

36,509

3,727

63- 64

0.009776

93,082

910

89-90

0.112081

32,782

3,674

64- 65

0.010581

92,172

975

90-91

0.122907

29,108

3,578

65- 66

0.011466

91,197

1,046

91-92

0.134602

25,530

3,436

66- 67

0.012498

90,151

1,127

92-93

0.147201

22,094

3,252

67- 68

0.013661

89,024

1,216

93-94

0.160735

18,842

3,029

68- 69

0.014966

87,808

1,314

94-95

0.175225

15,813

2,771

69-70

0.016407

86,494

1,419

95-96

0.190689

13,042

2,487

70-71

0.017945

85,075

1,527

96-97

0.207132

10,555

2,186

71-72

0.019617

83,548

1,639

97-98

0.224550

8,369

1,879

72-73

0.021503

81,909

1,761

98-99

0.242924

6,490

1,577

73-74

0.023635

80,148

1,894

99-100

0.262224

4,913

1,288

74-75

0.025987

78,254

2,034

100 or over

1.00000

3,625

3,625

75-76

0.028358

76,220

2,161

in chasing her estate for his or her money. If there is a life insurance policy with the creditor as beneficiary, then he or she doesn’t have to worry about getting his or her money back if she dies before the loan is due. The creditor would demand a paid-up term life insurance policy at the start of the loan period (when the woman gets the money), and the lender would have to consider the premium for this policy as part of her cost of getting the loan (i. e., increasing the effective interest rate).

Returning to Table 10.3, look at the fifty-first year. There are 100,000 – 320 = 99,680 women starting their fifty-first year, so we should expect 0.003432(99,680) = 342 deaths during this year.

During the first year of the 2-year policy, the insurance company has to pay out 320 times for every 100,000 people that signed up, as discussed above. In the second year, it has to pay out 342 times for every 100,000 people that originally signed up.

I just showed how much the 1-year term policy would be for the 50-year-old woman. This is identical to the cost of the first year of a 2-year term policy.

For the second year, the cost to the insurance company for a $100,000 policy, following the same procedure, is $342 per person in the original (100,000-person) group.

Подпись: $342 (1.04 )15 Подпись: $332.46.

This cost is incurred by the insurance company, on the average, 1.5 years after it collected the premiums on the policies, and the present value of this cost at the date of collecting the premiums is

The premium for the 2-year policy is the sum of the two individual premiums, $313.80 + $332.46 = $646.26.

This procedure may be continued for as many years as you want the policy.

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