Formula and Use
This annuity due payment formula FV calculates the annuity payment required to provide a given future value (FV). The formula assumes payments are made at the start of each period for n periods, and a discount rate i is applied.
An annuity due is different from a regular annuity in that payments are made at the beginning of each period, rather than at the end of each period.
In the formula the terms have the following meanings.
Future Value (FV). Future value is the amount of money that an investment or loan is expected to grow to in the future. The future value of an annuity due represents the total value of a series of equal payments made at the beginning of each period.
Discount Rate (i).The discount rate represents the interest rate used to calculate the future value of an investment or loan. In the context of an annuity due payment formula, it is the rate at which payments are discounted.
Number of Periods (n). The number of periods refers to the number of payment periods in the annuity due. It is typically expressed in years but can be in any unit of time.
Payment Amount (PMT).The payment amount is the fixed amount of money paid at the beginning of each period.
Excel Function
Additionally the Excel PMT function can be used instead of the formula, 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
The annuity due payment formula FV can be used 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).
To illustrate suppose an investor wants to save an amount of 8,000 by depositing regular annuity payments at the start of each period for 15 periods. Additionally the interest rate is 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
Additionally 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
This formula is one of many annuity formulas used in time value of money calculations. Discover another at the links below.
In summary an annuity due is a financial instrument that consists of a series of payments made at the beginning of each period for a fixed period of time. The annuity due payment formula for future value (FV) calculates the payment amount required to achieve this future value.