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

 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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