## Present Value of an Annuity Due Calculator

## Definition – What is a Present Value (PV) of an annuity due?

The present value (PV) of an annuity due 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.

Compared with the present value of an annuity (which has the payment occur at the end of a period), an annuity due has the payment occur at the beginning of a period.

## Formula – how the Present Value of an Annuity Due is calculated

Present Value = (Annuity Payment ÷ Interest rate) x (1 – (1 ÷ (1 + Interest Rate)^{Number of Periods})) x (1 + Interest Rate)

Where:

- “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).

### Example

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})) x (1 + 0.022)

Present Value = 4545.4545 x (1 – (1 ÷ 1.022^{10})) x (1 + 0.022)

Present Value = 4545.4545 x (1 – (1 ÷ 1.243108)) x 1.022

Present Value = 4545.4545 x (1 – 0.804435) x 1.022

Present value = 4545.4545 x 0.195564 x 1.022

Present Value = 908.49

## Present Value of an Annuity Due Table

## FAQ

### What is the difference between an annuity due and an annuity?

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 due and a perpetuity?

An annuity due 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 due?

The present value of an annuity due is the value of the annuity due in today’s dollars. The future value of the annuity due is the value of the annuity due 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 – The formula for the present value of an annuity due – The formula for an annuity due.
- Math is Fun – Annuities – Explaining present value and future values of annuities.
- The Balance SMB – How Do You Calculate The Present Value of an Annuity Due? – 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, Annuities, and Annuities Due – A simple explanation of time value of money and present value from the University of Arizona’s Dr. Sharon Garrison.