Annuity Payment Formula PV

Formula

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

Use

This annuity payment formula PV calculates the annuity payment required to provide a given value today PV (present value). The annuity formula assumes payments are made at the end of each period for n periods, and a discount rate i is applied.

The annuity formula can be used for example to determine the regular periodic payments required to clear a loan balance (PV).

Excel Function

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

PMT(Rate, Nper, PV, FV, Type)

*In this instance, the FV and type arguments are not used when using the Excel annuity payment function.

Example Using Annuity Payment Formula PV

A loan balance (PV) of 6,000 is cleared with regular annuity payments for 10 periods at an interest rate of 5%. The amount of the annuity payment is given by the annuity payment formula PV as follows:

Annuity payment = Pmt = PV x i / (1 - 1 / (1 + i)n)
Annuity payment = Pmt = 6000 x 5% / (1 - 1 / (1 + 5%)10)
Annuity payment = Pmt = 777.03 

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

Annuity payment = PMT(Rate, Nper, PV, FV, Type)
Annuity payment = PMT(5%, 10, -6000)
Annuity payment = 777.03

The annuity payment formula PV is one of many used in time value of money calculations, discover another at the links 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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