Question

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?

Answer 1

IAW insurance company is offering the retirement contract.

$2,000 is deposited every year for 40 years.

The prevailing interest rate is 5% per year, all payments occur at year-end.

We deposit $2,000 for 40 years at 5% interest rate.

Future Value of the investment when we reach 65 years of age = $241,600

We receive $30,000 per year as long as we live.

We will receive the first payment with probability 90%,

the second payment with probability 81%, and so on.

We reach 65 years of age and calculate the present value of the payments

we receive from the insurance company as long as we live.

The present value of payments received is $171,750.

(we have calculated for 20 years).

We compare it with our investment of $241,600.

As a customer of the insurance company, this annuity is not a good deal.

Present Value of outflow is more than the present value of inflow.