Present Value of a Perpetuity Calculator
Definition – What is a Present Value (PV) of a Perpetuity?
The present value (PV) of a perpetuity is the value in today’s dollars of a series of payments that has no end. It uses a payment amount and rate of return to calculate the value of the payments in today’s dollars.
Compared with the present value of an annuity (which has the payment occur for a set number of periods), a perpetuity has payments continue forever (theoretically).
Formula – How the PV of a Perpetuity is calculated
Present Value = Payment Amount ÷ Interest Rate
- “Payment” is the payment each period.
- “Rate of Return” is a decimal rate of return per period (the calculator above uses a percentage). A return of 2.2% per period would be calculated in the formula as “0.022”.
We will receive a perpetuity of $100 each year. The interest rate is 2.2% compounded annually. What is the present value of this perpetuity?
Present Value = 100 / 0.022
Present Value = 4545.45
Present Value of a Perpetuity Table
What is the difference between the present value of an annuity and a perpetuity?
The present value of an annuity is for a set number of payments. A perpetuity is for an unlimited number of payments.
What is the difference between a perpetuity and a growing perpetuity?
A perpetuity keeps the same payment through its entire existence. A growing perpetuity increases by a set amount each payment period.
Sources and External Resources
- Wikipedia – Time Value of Money, Present Value, & Perpetuity – An overview of time value of money and the concept of present value and a perpetuity.
- The Street – What is Perpetuity and Why Does It Matter in 2019? – A discussion on why a perpetuity matters in 2019.
- Columbia Business School – PreMBA Finance – Evaluating Cash Flows: Perpetuities – Derivation of the present value of a perpetuity formula.