Perpetuitas

Perpetuitas, from Latin perpetuitas meaning “perpetuity,” is a term used in finance to describe a stream of payments that continues indefinitely. In its simplest form, a perpetuity provides a constant cash flow forever and is used as a modelling device for financial instruments and for teaching present-value concepts. It is often equated with the concept of a perpetuity in actuarial and economic literature.

Valuation and variants

The value of a perpetuity with annual payment C and discount rate r (payments start one period from now) is PV = C / r. If payments occur at the beginning of each period (a perpetuity due), the present value is PV = (C / r) × (1 + r). If payments grow at a constant rate g (with r > g), the value is PV = C / (r − g). In continuous time, a perpetuity paying rate c per year has present value PV = c / δ, where δ is the force of interest.

Example

A perpetuity pays 50 per year forever and is discounted at 5%. Its value is 50 / 0.05 = 1000. If the payments start immediately (perpetuity due), the value would be 1000 × (1 + 0.05) = 1050.

Context and usage

The term is rooted in Latin and appears in various academic and legal-historical contexts. In modern finance, the perpetuity model serves as a simple, idealized benchmark for valuing ongoing, fixed payments and for illustrating core present-value concepts, distinct from finite annuities or growing cash flows.