# fv¶

`numpy_financial.``fv`(rate, nper, pmt, pv, when='end')

Compute the future value.

Given:
• a present value, pv

• an interest rate compounded once per period, of which there are

• nper total

• a (fixed) payment, pmt, paid either

• at the beginning (when = {‘begin’, 1}) or the end (when = {‘end’, 0}) of each period

Return:

the value at the end of the nper periods

Parameters
ratescalar or array_like of shape(M, )

Rate of interest as decimal (not per cent) per period

nperscalar or array_like of shape(M, )

Number of compounding periods

pmtscalar or array_like of shape(M, )

Payment

pvscalar or array_like of shape(M, )

Present value

when{{‘begin’, 1}, {‘end’, 0}}, {string, int}, optional

When payments are due (‘begin’ (1) or ‘end’ (0)). Defaults to {‘end’, 0}.

Returns
outndarray

Future values. If all input is scalar, returns a scalar float. If any input is array_like, returns future values for each input element. If multiple inputs are array_like, they all must have the same shape.

Notes

The future value is computed by solving the equation:

```fv +
pv*(1+rate)**nper +
pmt*(1 + rate*when)/rate*((1 + rate)**nper - 1) == 0
```

or, when `rate == 0`:

```fv + pv + pmt * nper == 0
```

References

WRW

Wheeler, D. A., E. Rathke, and R. Weir (Eds.) (2009, May). Open Document Format for Office Applications (OpenDocument)v1.2, Part 2: Recalculated Formula (OpenFormula) Format - Annotated Version, Pre-Draft 12. Organization for the Advancement of Structured Information Standards (OASIS). Billerica, MA, USA. [ODT Document]. Available: http://www.oasis-open.org/committees/documents.php?wg_abbrev=office-formula OpenDocument-formula-20090508.odt

Examples

```>>> import numpy as np
>>> import numpy_financial as npf
```

What is the future value after 10 years of saving \$100 now, with an additional monthly savings of \$100. Assume the interest rate is 5% (annually) compounded monthly?

```>>> npf.fv(0.05/12, 10*12, -100, -100)
15692.928894335748
```

By convention, the negative sign represents cash flow out (i.e. money not available today). Thus, saving \$100 a month at 5% annual interest leads to \$15,692.93 available to spend in 10 years.

If any input is array_like, returns an array of equal shape. Let’s compare different interest rates from the example above.

```>>> a = np.array((0.05, 0.06, 0.07))/12
>>> npf.fv(a, 10*12, -100, -100)
array([ 15692.92889434,  16569.87435405,  17509.44688102]) # may vary
```