In finance, a perpetuity is an annuity that has no end, or a stream of cash payments that continues forever.
For example, the United Kingdom (UK) government issued them in the past; these were known as consols and were all finally redeemed in 2015.
Fixed coupon payments on permanently invested (irredeemable) sums of money are prime examples of perpetuities.
Effectively, the use of a cap rate to value a piece of real estate assumes that the current income from the property continues in perpetuity.
The constant growth dividend discount model for the valuation of the common stock of a corporation is another example.