### What Is Perpetuity?

A perpetuity is a security that pays for an infinite amount of time. In finance, perpetuity is a constant stream of identical cash flows with no end. The formula to calculate the present value of a perpetuity, or security with perpetual cash flows, is:

$begin{aligned} &text{PV} = frac { C }{ ( 1 + r ) ^ 1 } + frac { C }{ ( 1 + r ) ^ 2 } + frac { C }{ ( 1 + r ) ^ 3 } cdots = frac { C }{ r } \ &textbf{where:} \ &text{PV} = text{present value} \ &C = text{cash flow} \ &r = text{discount rate} \ end{aligned}$PV=(1+r)1C+(1+r)2C+(1+r)3C⋯=rCwhere:PV=present valueC=cash flowr=discount rate

The concept of a perpetuity is also used in a number of financial theories, such as in the dividend discount model (DDM).

### Key Takeaways

- A perpetuity, in finance, refers to a security that pays a never-ending cash stream.
- The present value of a perpetuity is determined using a formula that divides cash flows by some discount rate.
- The British consol is an example of a perpetuity.