What is the relationship among an annuity, a perpetuity, and a growing cash stream?

All three are patterns of future cash flows for which simplifying time value formulas have been derived. An annuity is a sequence of equal cash flows for a finite period of time that are equal in three dimensions: amount, direction, and spacing. A perpetuity is a “perpetual annuity,” an annuity that continues forever; it is still made up of equal (amount, direction, and spacing) cash flows. A growing cash stream is a perpetuity in which the cash flows are still equal in direction and spacing but no longer equal in amount; instead each cash flow differs from the previous cash flow by a constant ratio, the rate of growth.