Understanding the Mathematics of Personal Finance

INSURANCE FOR THE REST OF YOUR LIFE

What if you want a life insurance not for a specific period such as 20 years but simply for the rest of your life? This type of policy would be different from that which I’ ve already presented. In the previous examples, the insurance company never knew if it would have to pay. The insured person could still be alive at the

Table 10.4 A 20-Year Decreasing Term $100,000 Life Insurance Policy

Age

q

l

d

Term PV ($)

Scale

Decreasing term PV ($)

50

0.003204

100,000

320

314.23

1.00

314.23

51

0.003432

99,680

342

322.59

0.95

306.46

52

0.003695

99,337

367

332.78

0.90

299.51

53

0.004000

98,970

396

345.14

0.85

293.37

54

0.004346

98,574

428

359.11

0.80

287.29

55

0.004725

98,146

464

373.76

0.75

280.32

56

0.005137

97,682

502

388.84

0.70

272.19

57

0.005594

97,181

544

405.06

0.65

263.29

58

0.006110

96,637

590

423.05

0.60

253.83

59

0.006697

96,046

643

443.17

0.55

243.74

60

0.007389

95,403

705

466.97

0.50

233.49

61

0.008167

94,698

773

492.62

0.45

221.68

62

0.008977

93,925

843

516.42

0.40

206.57

63

0.009776

93,082

910

535.87

0.35

187.56

64

0.010581

92,172

975

552.24

0.30

165.67

65

0.011466

91,197

1,046

569.35

0.25

142.34

66

0.012498

90,151

1,127

589.87

0.20

117.97

67

0.013661

89,024

1,216

612.21

0.15

91.83

68

0.014966

87,808

1,314

636.09

0.10

63.61

69

0.016407

86,494

1,419

660.50

0.05

33.03

Total:

9,340

4,278

end of the term. With what you’re asking for now, the insurance company, sooner or later, must pay.

Working this problem out is not difficult—we do the same thing we did in the previous examples, but we extend the upper age to 100. Since q100 = 1, the fact that the insurance company sooner or later has to pay is automatically included in the calculation. Without showing the details here, the policy for a 50-year-old woman comes to approximately $31,000. This is considerably more than the $9,340 it took to insure her from age 50 to age 69, but remember that we’ve not only more than doubled the policy term, but we’re adding the older years where death is more prob­able, up to age 100 where, at least according to our tables, death is inevitable.

Figure 10.5 shows the premium for this kind of policy, for a man and for a woman, based on the age that he or she buys the policy. As you would expect, the women’s policy is less expensive. Near age 100, either policy costs about $100,000. This is to be expected; if you buy a $100,000 policy close to age 100 and (according to the tables) you’re not going to live past 100, you should be prepared to pay about what you’re going to get back.

Some term policies are sold by the year. That is, at the beginning of each year the premium cost is based on the q value in the Life Table. For a man of age 20, for

image089

Figure 10.5 Cost of a $100,000 lifetime policy versus age at purchase.

example, q = 0.001266, and therefore, before looking at costs and profits, the insurance company must charge $100,000 x 0.001266 = $127. This doesn’t seem like a lot. However, at age 70, that same $100,000 policy would cost $100,000 x 0.02765 = $2,707. This adds up for a several hundred thousand dollar policy.

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