Assume you are 25 years old. The IAW insurance company is offering you the following retirement contract (called an annuity): Contribute $2,000 per year for the next 40 years. When you reach 65 years of age, you will receive $30,000 per year for as long as you live. Assume that you believe that the chance that you will die is 10% per year after you will have reached 65 years of age. In other words, you will receive the first payment with probability 90%, the second payment with probability 81%, and so on.
If the prevailing interest rate is 5% per year, all payments occur at year-end, and it is now January 1, is this annuity a good deal?