If you are buying an annuity, the net price you will pay will be the present value of the annuity. Your outflow will be the cost of the annuity, and your inflows will be the payments you receive. The interest rate i is the rate that makes the present values of the outflows and the inflows equal. In the previous chapter, we called this the internal rate of return. In the case of an annuity certain, the rate you use to evaluate the present value of the annuity is the internal rate of return. In finance, this is also called the yield.

In this chapter, we computed the present values of the future payments using the same interest rate for all the payments. We don t need to use the same rate. We could use a different rate for some payments and could even use a different rate for each payment. Later in the book, we will demonstrate a way to obtain these different rates and use them to compute the present value of a future flow of funds.

But if you use more than one rate to evaluate the present value of the payments, or if you have payments of differing sizes, then you cannot use the equation we developed earlier in this chapter. That equation requires that all the payments be the same size, that the present values all be evaluated at the same interest rate, and that the time periods between payments all be the...