EXAMPLE 14 How Much Do You Need to Retire?

Suppose that your father is ready to retire at 65 and wants to purchase an annuity that pays $5000 per month for 25 years. The insurance company offering the annuity is willing to assume that the long-range steady interest rate will be 3% per year compounded monthly (and that rate also takes into account its costs and profit). What should be the cost of the annuity—that is, how much should your father expect to pay for such a stream of income?

We apply the amortization formula “in reverse.” We know the amount of the monthly payment and we need to find the principal .

We apply the amortization formula with , , , and , to find the amount :

So such an annuity would cost about a million dollars in retirement savings.