## Formula

Pmt = FV x i / ( (1 + i)^{n}- 1 )

**Variables used in the annuity formula**

FV = Future Value

Pmt = Periodic payment

i = Discount rate

n = Number of periods

## Use

This annuity payment formula FV calculates the annuity payment required to provide a given value in the future FV (future 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 payment formula FV can be used for example, to calculate the periodic deposits needed to provide a required savings account balance (FV), given the number of deposits (n), and the account interest rate (i).

## Excel Function

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

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

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

## Example Using Annuity Payment Formula FV

An investor wants to save an amount of 7,000 by depositing regular annuity payments for 14 periods at an interest rate of 3% per period. The amount of the annuity payment is given by the annuity payment formula FV as follows:

Annuity payment = Pmt = FV x i / ( (1 + i)^{n}- 1 ) Annuity payment = Pmt = 7000 x 3% / ( (1 + 3%)^{14}- 1 ) Annuity payment = Pmt = 409.68

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

Annuity payment = PMT(Rate, Nper, PV, FV, Type) Annuity payment = PMT(3%,14,,-7000) Annuity payment = 409.68

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