Understanding the Mathematics of Personal Finance


A viatical settlement is a payment of a life insurance policy while the policyholder is still alive. These settlements are not available to the general public; they’re restricted to people fitting specific requirements of having a terminal disease and/or short anticipated life span. The intent of the settlement is to help the policyholder handle the unexpected high costs of a very serious illness.

From a financial point of view, the insurance company has an expected date of death based upon medical prognoses and can easily come up with a present value of the policy at the time of writing the check to the policyholder. Unlike with a reverse mortgage, the insurance company has no ongoing relationship with the policyholder. When the check is received by the policyholder, the relationship between the policyholder and the insurance company ends because the policy has been paid off.


Reverse mortgages are complicated products with factors such as housing market values, interest rates, and so on, varying drastically by location and over time. Also, the laws govern­ing them are still evolving. This problem is intended to show how a reverse mortgage works as a product for an insurance company and how the risks are really kept under control.

1. Suppose that there never had been such a thing as a reverse mortgage and that you, an insurance company business planner, just thought of the idea. Your task now is to explain your idea by means of a worked through hypothetical example, showing how the insurance company makes money and really isn’t taking on much risk.

Assume that your customer is a 77-year-old single man. He owns a home in a good neighborhood that appraises at $450,000. Your company can borrow money today at 5.00%, but there is some concern about rates changing, so you want to be able to write a contract with an adjustable interest rate. Your company’s business model assumes a 2% spread between borrowing and lending to fund profits. Estimate your company’s costs for preparing the package and servicing it as a $25,000 up-front fee. Looking at the Life Table for men (Table 10.1), a 77-year-old man is most likely going to live about another 10 years. Start by keeping interest rates constant at 5.00% so you’ll have to charge your client 7%.

2. Using the calculator at the website http://www. reversemortgage. org/, run some estimates of your own. Vary the location, the value of the home, and the age of the borrower.

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