Understanding the Mathematics of Personal Finance
WHOLE LIFE INSURANCE
A popular policy with a fixed monthly payment is the so-called whole life policy. There are so many variations on how this can be structured that I can’t possibly cover them all. I’ll look at a 20-year-old typically healthy man and present one possible scenario. You should get the idea of what’s going on pretty easily and be able to understand different variations when they’re put before you.
As was shown above, for a 20-year-old man, a year’s $100,000 1-year term insurance should only cost $127. Suppose, however, that this man pays $900 a year instead. I’ll treat things annually even though payments are usually made monthly, just to keep the table showing these calculations from becoming uncomfortably long.
At the inception of the policy (our young man’s twentieth birthday), he writes a check for $900. A total of $127 goes to buy him a $100,000 term life insurance policy for the year. The remaining $773 goes into a savings/investment account. If we assume that this account earns 4% a year, then on his twenty-first birthday, he has (1.04)($473) = $804. On this day, he makes another payment (of $900), and the insurance company takes the required payment for the year’s term insurance ($136) out of the account, leaving the account with a balance of $1,568. As we continue this procedure, year after year, the balance in the account grows—even though the annual 1-year term policy payment is also growing (Table 10.5). Note that I didn’t
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Table 10.5 Whole Life Insurance Policy Example
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Table 10.5 Continued
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have to do any present value corrections to the premiums because they are being taken from the savings account on the day they are due.
After the annual payment at age 43, the policy is declared “paid off,” and no further $900 payments are needed. The balance in the account still continues to grow because the annual interest outweighs the insurance policy payment, until age 68, when the term insurance premiums get large enough to outweigh the accruing interest. At age 100, if our young man lives that long, there is a balance in the account of approximately $7,300.
At the time of death, whenever that may be, the insurance company pays the beneficiaries the $100,000 face value of the policy and also the balance in the account.
This type of policy is attractive to many people for several reasons:
1. At age 47, the policy is “paid off’ and no further premium payments are required.
2. Upon death, the beneficiaries get both the value of the life insurance policy and the balance of the account, the latter possibly being quite substantial. For example, if our young man dies at age 65, there is almost $65,000 in the account.
3. This policy has a “cash value.” At any time, the young man can cancel his policy and walk away with the balance in the account.
4. Sometimes an insurance company will offer a low interest loan to the policy owner, secured by the cash value in the insurance account. This is worth taking a minute to think about because even though the interest rate is low, remember that you’re paying interest to get the use of your own money!
A real insurance company has operating expenses and needs profits. Also, the money being held is invested, and things can go from very well to very poorly. The insurance company is investing our young man’s money, and all he can do is hope that it is investing wisely while keeping a close watch on its costs. And again, there are Life Tables that are much more specific and closely tailored to the statistics that pertain exactly to you—sex, race, medical history, and so on. Someone with a particularly dangerous career or someone with a serious congenital heart defect probably can’t get life insurance, and a table that reflects these considerations will look considerably different from a table that includes “all comers.”
