numpy.fv

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

Compute the future value.

Parameters:

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, )

Payment

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}.

Returns:

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.

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

Examples

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