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numpy.fv(rate, nper, pmt, pv, when='end')[source]

Compute the future value.

  • 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
the value at the end of the nper periods

rate : scalar or array_like of shape(M, )

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

nper : scalar or array_like of shape(M, )

Number of compounding periods

pmt : scalar or array_like of shape(M, )


pv : scalar 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}.


out : ndarray

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.


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


[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: OpenDocument-formula-20090508.odt


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?

>>> np.fv(0.05/12, 10*12, -100, -100)

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
>>> np.fv(a, 10*12, -100, -100)
array([ 15692.92889434,  16569.87435405,  17509.44688102])