Growing Perpetuity

A growing perpetuity is an infinite stream of cash flows that grow at a constant rate and that are evenly spaced in time.

E.g., Dividend streams

PV of Growing Perpetuity = $\frac{CF}{R-g}$

Again, this formula assumes that the first cash flow occurs at t=1.

Also, g must be less than R.

Simple Example

How much do you have to save today to withdraw $100 at the end of this year, $102.5 after the next year,
$105.06 the year after, and so on forever, if you earn 5% per annum?

The timeline is as follows:

PV = $\frac{100}{0.05-0.025}$ = $4000