## Formula

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

**Variables used in the annuity formula**

FV = Present Value

Pmt = Periodic payment

i = Discount rate

n = Number of periods

## Use

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

The annuity due payment formula FV can be used for example, to calculate the periodic deposits needed at the start for each period 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 due payment formula FV, and has the syntax shown below.

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

*In this instance, the PV argument is not used when using the Excel Annuity due payment function.

## Example Using Annuity Due Payment Formula FV

An investor wants to save an amount of 8,000 by depositing regular annuity payments at the start of each period for 15 periods at an interest rate of 4% per period. The amount of the annuity payment is given by the annuity due payment formula FV as follows:

Annuity payment = Pmt = FV x i / ((1 + i)( (1 + i)^{n}- 1 )) Annuity payment = Pmt = 8000 x 4% / ((1 + 4%)( (1 + 4%)^{15}- 1 )) Annuity payment = Pmt = 384.16

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

Annuity payment = PMT(Rate, Nper, PV, FV, Type) Annuity payment = PMT(4%,15,,-8000,1) Annuity payment = 384.16

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

- Doubling Time Formula Continuous Compounding
- Real Interest Rate Formula
- Simple Interest Doubling Time Formula