# Perpetuity

Perpetuity is an infinite series of periodic payments of equal face value. In easy words, perpetuity is a situation where a constant payment is to be made periodically for an infinite amount of time. It’s as an annuity having no end and that is why the perpetuity is sometimes called as perpetual annuity.

**Perpetuity Formula**

The following formula is used to calculate the present value of perpetuity:

## Perpetuity Examples

Perpetuity Examples: Calculate the present value on Jan 1, 200 of a perpetuity paying $1,000 at the end of each month starting from January 2050. The monthly discount rate is 0.8%.

### Perpetuity Solution

Periodic Payment **A** = $1,000

Discount Rate **i** = 0.8%

Present Value **PV** = $1,000 ÷ 0.8%

= $125,000

**We Explain ‘Perpetuity’**

This is not as abstract a concept as you may think; the British issued bonds, which called consoles, which are a best example of a perpetuity. By purchasing this console from the British government, a bondholder is entitled to receive annual interest payments forever. Although it may seem to be a bit illogical, a series of infinite cash flows can have a finite present value. As a result of the time value of money, each payment is only a fraction of the last payment.

This concept of the perpetuity is used often in financial theory, like as the dividend discount model (DDM).

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