# Perpetuity

A perpetuity is an **infinite** stream of cash flows of **identical magnitude** and **equal spacing in time**.

E.g., Perpetuities, consol bonds

![](https://1463082227-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M5-0RGr8Q9QLqT32rM-%2F-M5-0TBzyC8aF6M53_Dz%2F-M5-0YSId8Yh7B6Txy7b%2FPerpetuity.JPG?generation=1586990841328052\&alt=media)PV of Perpetuity = $$\frac{CF}{R}$$

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

## Simple Example

```
How much do you have to save now to be able to withdraw $100 at the end of each year, forever, 
if you earn 5% per annum?
```

PV = $$\frac{100}{0.05}$$ = $2000