Present Value of Annuity Formula

Formula

PV = Pmt x (1 - 1 / (1 + i)n) / i
Variables used in the annuity formula
PV = Present Value
Pmt = Periodic payment
i = Discount rate
n = Number of periods

Use

The present value of annuity formula shows the value today of series of regular payments. The payments are made at the end of each period for n periods, and a discount rate i is applied.

The annuity calculation formula discounts the value of each payment back to its value at the start of period 1 (present value).

Excel Function

The Excel PV function can be used instead of the present value of annuity formula, and has the syntax shown below.

PV(i, n, pmt, FV, type)

*The FV and type arguments are not used when using the Excel present value of an annuity function.

Present Value of Annuity Formula Example

If a payment of 5,000 is received at the end of each period for 10 periods, and the discount rate is 4%, then the value of the payments today is given by the present value of annuity formula as follows:

PV = Pmt x (1 - 1 / (1 + i)n) / i
PV = 5,000 x (1 - 1 / (1 + 4%)10) / 4%
PV = 40,554.48

The same answer can be obtained using the Excel PV function as follows:

PV = PV(i, n, pmt)
PV = PV(4%,10,-5000)
PV = 40,554.48

The present value of annuity formula is one of many annuity formulas used in time value of money calculations, discover another at the link below.

Last modified July 16th, 2019 by Michael Brown

About the Author

Chartered accountant Michael Brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years in all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a BSc from Loughborough University.

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