The word “perpetuity” means forever. The concept of a perpetual annuity — an infinite stream of identical cash flows — has been used since the Middle Ages to determine how much to charge for leasing farmland.

Definition

A perpetuity is a financial term that refers to an income stream that continues indefinitely and never ends. Perpetuities are useful in financial calculations because they’re easy to predict: if you have enough money invested in an account today, your income will increase by a small percentage each year (perhaps 2%).

Perpetuities are also important because they can be used as the basis of valuation for preferred stocks and perpetuity bonds. Using a perpetuity formula, investors can determine the value of these securities based on their current interest rates and dividend payments.

The name “perpetuity” comes from Latin and means “forever.”

Uses

When calculating the future value of an ordinary annuity, you are trying to find out how much money will be available at a specific time in the future. Annuities can be used as financial planning tools or they can be applied to other areas of finance and accounting.

In accounting, perpetuities are used as an assumption to calculate the future value of ordinary annuities.

History

The concept of a perpetual annuity — an infinite stream of identical cash flows — has been used since the Middle Ages to determine how much to charge for leasing farmland. It is also commonly used in present value and valuation analyses. In finance, it’s commonly used to calculate the present value of a stream of cash flows.

Formula

The perpetuity calculation formula used in present value and valuation analyses can be derived from the standard formula for calculating an annuity. The perpetuity formula is:

PV = \frac {C}{r-g}

The future value (FV) is simply a sum at some time in the future with all payments known; this time period can be 1 year or 100 years, so long as all payments are known upfront. The interest rate (r) can change over time if you’re doing an analysis on a project with an adjustable interest rate (adjustable mortgages), but it must be constant throughout each period of your analysis.

FAQ

What is a good example of perpetuity?

For example, a rental property will give you a fixed amount every month.

What is the difference between perpetuity and annuity?

An annuity uses a compounding interest rate to calculate its present value or future value, while perpetuity uses only the stated interest rate or discount rate.

Do perpetuities actually exist?

There are few actual perpetuities in existence.