# Future Value Annuity Formula

## 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.

Future Value Annuity Formula November 6th, 2016

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