Understanding the Mathematics of Personal Finance


Another type of term life insurance is decreasing term life insurance. A decreasing term life insurance policy pays a little less each year for the term of the insurance. As an example, consider a $100,000, 20-year decreasing term policy. In year 1, the policy pays $100,000. In year 2, it pays $95,000 and so on, up to year 20, when it would pay $5,000.

At first blush, this seems like an odd sort of life insurance. Why would you want a beneficiary to receive less if you die later? This type of insurance is the equivalent of the loan insurance described in the last section, but it is more appropriate when it’s insuring a loan that is being paid off over time. If you are paying a loan back with regular payments, then each month you owe less. Consequently, you can save on your insurance premium if you buy insurance that pays less as time goes buy.

Decreasing term life insurance is often sold under the name of mortgage insur­ance. This is a policy that pays off your mortgage if you die so that your family doesn’t lose your house. Auto loan providers often offer similar loans. In both of these cases, the loans might be a combination of life insurance and some sort of health and/or disability insurance. That is, in addition to paying off your loan if you die, the policy will make payments on the loan if you’re sick and possibly pay off the loan if you’re disabled and can no longer earn a living. Since there are so many possible variations of this combination of insurance policies, it is very important that this type of policy be scrutinized carefully so that you know what you’re buying. Typically, these policies are fully paid for up front, but I guess that anything is possible.

Table 10.4 shows the year-by-year calculations, for the same person as above, for a 20-year, $100,000 decreasing term policy that decreases by $5,000 per year. This table could have been built from scratch using the same process that I used for Table 10.3, but I took a shortcut; I started with Table 10.3 . Then, I simply scaled the costs each year. That is, the costs for the second year (a $95,000 policy) are just 19/20 (= 0.95) of the original costs for that year. I referred to this multiplication, or scaling, factor as scale in the table. The cost for the third year (a $90,000 policy) is just 18/20 (= 0.90) of the original costs for that year and so on. In the table, I showed the numbers for the $100,000, 20-year term policy as well as the numbers for the decreasing term policy. This should make it a bit easier to follow where the decreas­ing term policy numbers came from.

The premium for the policy, again, is the sum of all the present value costs of the right-hand column, which is $4,278. This is considerably less expensive than the 20-year term life insurance policy for $9,340, as you can see in the table.

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