## Formula

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

**Variables used in the annuity formula**

FV = Future Value

Pmt = Periodic payment

i = Discount rate

n = Number of periods

## Use

The future value of an annuity due formula shows the value at the end of period n of a series of regular payments. The payments are made at the start of each period for n periods, and a discount rate i is applied.

The formula compounds the value of each payment forward to its value at the end of period n (future value).

## Excel Function

The Excel FV function can be used instead of the future value of an annuity due formula, and has the syntax shown below.

FV = FV(i, n, pmt, PV, type)

*The PV argument is not used when using the Excel future value of an annuity due function.

## Example Using the Future Value of an Annuity Due Formula

If a payment of 3,000 is received at the start of each period for 7 periods, and the discount rate is 8%, then the value of the payments at the end of period 7 is given by the future value annuity due formula as follows:

FV = Pmt x (1 + i) x ( (1 + i)^{n}- 1 ) / i FV = 3,000 x (1 + 8%) x ( (1 + 8%)^{7}- 1 ) / 8% FV = 28,909.88

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

FV = FV(i, n, Pmt,,1) FV = FV(8%,7,-3000,,1) FV = 28,909.88

The future value of an annuity due formula is one of many annuity formulas used in time value of money calculations, discover another at the link below.