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.
An annuity is a financial product that pays out a fixed stream of payments to an individual. These financial products are primarily used as an income stream for retirees. Annuities are created and sold by financial institutions, which accept and invest funds from individuals. Upon annuitization, the holding institution will issue a stream of payments at a later point in time