Growing Annuity

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

E.g., Income streams, savings strategies, project revenue/expense streams

The PV of a growing annuity is computed as follows:

PV of Growing Annuity = $\frac{CF}{R-g}*(1-(\frac{1+R}{1+g})^{-T})$

Again, this formula assumes that the first cash flow occurs at t=1. If it occurs at t=0, add it to the above formula.

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 for the next 19 years, if you earn 5% per annum?

The timeline is as follows:CF=100, g=0.025, T=20, R=0.05

So, PV = $\frac{100}{0.05-0.025}*(1-(\frac{1+0.05}{1+0.025})^{-20})$ = $1529.69