Understanding the Mathematics of Personal Finance


If you want to buy a 20-year policy using the data shown in Table 10.3, the premium is $9,340. What if you don’t have this money available? The reasonable answer is to take a loan. You’ll be insured for 20 years; why not “pay as you go?”

A 20-year loan for $9,340, at 6% compounded monthly, requires payments of about $67 each month. This doesn’t seem like a lot but keep in mind that this is just an example.

If you take the loan, it looks like everything is taken care of. The insurance company has its premium, you have your 20-year insurance policy, and you have monthly payments on the loan you took that you can handle. There is, however, one more item to consider here—what happens if you do die during the 20-year period? The insurance company pays $10,000 to your beneficiary, as was promised. However, your estate still owes the balance on your loan.

If you die exactly 10 years after you took the policy out, on your sixtieth birth­day, then there is a loan balance of $6,030. One way to balance the books is for the beneficiary of the insurance policy to pay off the loan. This means that, in effect, the insurance policy only paid the beneficiary $100,000 - $6,030 = $93,970.

If, for whatever reason, you wanted your beneficiary to receive the full intended amount, then you could purchased a $110,000 policy. The premium for this policy and the monthly payments on your loan would both go up to 10%.

Another way to handle the time payment situation is for the insurance company to be the banker. That is, the insurance company, acting internally like a bank, arranges to pay your premium up front and collect monthly premiums from you. This has the advantage that the insurance company can look at the Life Tables and come up with an average balance left on the loan after many people in your situation arrange this package deal and then calculate how much insurance it must sell you (internally, on its books) so that, on the average, there is enough money to pay the beneficiary exactly $100,000 while repaying the balance of the loan. This arrangement also has the advantage of simplicity. When you die, your estate might be split between heirs who are not necessarily identically the beneficiary(ies) of your life insurance.

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