Pmt = FV x i / ( (1 + i)n - 1 )
FV = Future Value
Pmt = Periodic payment
i = Discount rate
n = Number of periods
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).
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.