## Formula

FV = Pmt 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 annuity formula shows the value at the end of period n of a series of regular payments. The payments are made at the end 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 annuity formula, and has the syntax shown below.

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

*The PV and type arguments are not used when using the Excel future value of an annuity function.

## Future Value Annuity Formula Example

If a payment of 5,000 is received at the end of each period for 10 periods, and the discount rate is 4%, then the value of the payments at the end of period 10 is given by the future value annuity formula as follows:

FV = Pmt x ( (1 + i)^{n}- 1 ) / i FV = 5,000 x ( (1 + 4%)^{10}- 1 ) / 4% FV = 60,030.54

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

FV = FV(i, n, Pmt) FV = FV(4%,10,-5000) FV = 60,030.54

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