## 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.