numpy.fv¶

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

Compute the future value.

Given:

• a present value,pv
• an interestrate compounded once per period, of whichthere 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 thenper periods

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. Ifany 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, whenrate==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 InformationStandards (OASIS). Billerica, MA, USA. [ODT Document].Available:http://www.oasis-open.org/committees/documents.php?wg_abbrev=office-formulaOpenDocument-formula-20090508.odt

Examples

What is the future value after 10 years of saving $100 now, withan additional monthly savings of $100. Assume the interest rate is5% (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 notavailable today). Thus, saving $100 a month at 5% annual interest leadsto $15,692.93 available to spend in 10 years.

If any input is array_like, returns an array of equal shape. Let’scompare 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])