Present Value of an Annuity Calculator
Definition – What is the Present Value (PV) of an annuity?
The present value (PV) of an annuity is the value today of a series of payments in the future. It uses a payment amount, number of payments, and rate of return to calculate the value of the payments in today’s dollars.
Formula – how the Present Value of an Annuity is calculated
Present Value = (Payment ÷ Rate of Return) x (1 – (1 ÷ (1 + Rate of Return)Number of Periods))
- “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”.
- “Number of Periods” is the number of periods (any payments).
We will receive $100 each year for the next 10 years. The interest rate at the moment is 2.2% compounded annually. What is the present value of this annuity?
Present Value = (100 / 0.022) x (1 – (1 ÷ (1 + 0.022)10))
Present Value = 4545.4545 x (1 – (1 ÷ 1.02210))
Present Value = 4545.4545 x (1 – (1 ÷ 1.243108))
Present Value = 4545.4545 x (1 – 0.80444)
Present Value = 4545.4545 x 0.19556
Present Value = 888.91
Present Value of an Annuity Table
What is the difference between an annuity and an annuity due?
The two are very similar. With an annuity, the payment occurs at the end of the period. With an annuity due, the payment occurs at the beginning of the period.
What is the difference between an annuity and a perpetuity?
An annuity stops after a specific amount of time, a perpetuity goes on forever (in theory).
What is the difference between the present value and future value of an annuity?
The present value of an annuity is the value of the annuity in today’s dollars. The future value of the annuity is the value of the annuity on the date it is finished.
Sources and External Resources
- Wikipedia – Time Value of Money & Present Value – An overview of present value and the time value of money.
- Accounting Coach – Present Value of an Ordinary Annuity – A full introduction to present value as it relates to an annuity.
- Math is Fun – Annuities – Explaining present value and future values of annuities.
- The Balance SMB – Calculate the Present and Future Value of an Ordinary Annuity – Another explanation of present value calculations. Includes how to calculate the present value of an annuity with a financial calculator.
- Khan Academy – Introduction to Present Value & Present Value 2 – A video introduction to present value from Khan Academy, a provider of free learning and tutorial videos.
- The Theory of Interest by Irving Fisher – 1930s book in public domain detailing the concept of interest. One of the first books detailing the concept of interest and how it is calculated.
- Concise Encyclopedia of Economics – Present Value by David R. Henderson – An explanation of present value from David R. Henderson of Stanford University’s Hoover Institution.
- StudyFinance.com by Dr. Sharon Garrison – Time Value of Money, Present Value, and Annuities – A simple explanation of time value of money and present value from the University of Arizona’s Dr. Sharon Garrison.