An Annuity is a regular payment made at fixed intervals over a set period of time on a cash investment. A Perpetual Annuity is an annuity with no assigned end, a stream of cash payments that will continue indefinitely regardless of the recipients of their beneficiaries life-spans. A Perpetual Annuity can also be referred to as a Perpetuity.

## Function

The value of a perpetual annuity or perpetuity is calculated using a simple mathematical formula. PV stands for Perpetual Value of the annuity, A is the amount of the periodic payment and R is the yield or discount rate. Therefore the formula is PV = A/r. Although the payments on a perpetual annuity are assumed to continue indefinitely, there is a finite value on the perpetuity. This is because anticipated returns in the distant future have a low present day value.

## Types

Examples of perpetuities include consols (see History). Other more recent examples include the use of a cap rate to value real estate and the dividend stream on shares. A cap rate in real estate effectively assumes that the current income from the property will continue indefinitely while a dividend stream model assumes that the discounted future dividends on the shares will be perpetual.

## History

One example of a perpetual annuity are the British government bonds that were issued during the 18th Century. These bonds are called "Consols" and this is short for either consolidated annuities or consolidated stock. They came into existence in 1752 when all existing government stock was converted into one stock: Consolidated 3.5% Annuities. This was part of a bid to reduce the coupon rate on government debt. (coupon rate is the amount of interest paid annually on a bond and in this example, the coupon rate is 3.5% of its value yearly.) The 3.5% coupon rate on these bonds dropped to 3% and then to 2.25 % before settling on its current rate of 2.5% in 1903.

## Considerations

True perpetual annuities are very rare. Consols, as mentioned above, are among the few perpetual annuities that are still in existence. However, some investments, such as real estate, can be considered to be effectively perpetuities and the value of the investment can be established by using the same equations applied to a perpetuity.

## Significance

Despite their relative scarcity perpetual annuities, particularly consols, have appeared in various works of literature, such as David Copperfield by Charles Dickens, Vanity Fair by Wiliam Thackery and The Forsyte Saga by John Galsworthy.