# 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

![](https://1463082227-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M5-0RGr8Q9QLqT32rM-%2F-M5-0TBzyC8aF6M53_Dz%2F-M5-0Yxpi3HqC-8tRu1D%2FGrowing%20Annuity.JPG?generation=1586990843259334\&alt=media)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:![](https://1463082227-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M5-0RGr8Q9QLqT32rM-%2F-M5-0TBzyC8aF6M53_Dz%2F-M5-0YxrOh35sNFyjM2L%2FGrowing%20Annuity%20Timeline.JPG?generation=1586990842242702\&alt=media)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