Compute the present value.
Parameters:  rate : array_like
nper : array_like
pmt : array_like
fv : array_like, optional
when : {{‘begin’, 1}, {‘end’, 0}}, {string, int}, optional


Returns:  out : ndarray, float

Notes
The present 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
for pv, which is then returned.
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, PreDraft 12. Organization for the Advancement of Structured Information Standards (OASIS). Billerica, MA, USA. [ODT Document]. Available: http://www.oasisopen.org/committees/documents.php?wg_abbrev=officeformula OpenDocumentformula20090508.odt 
Examples
What is the present value (e.g., the initial investment) of an investment that needs to total $15692.93 after 10 years of saving $100 every month? Assume the interest rate is 5% (annually) compounded monthly.
>>> np.pv(0.05/12, 10*12, 100, 15692.93)
100.00067131625819
By convention, the negative sign represents cash flow out (i.e., money not available today). Thus, to end up with $15,692.93 in 10 years saving $100 a month at 5% annual interest, one’s initial deposit should also be $100.
If any input is array_like, pv returns an array of equal shape. Let’s compare different interest rates in the example above:
>>> a = np.array((0.05, 0.04, 0.03))/12
>>> np.pv(a, 10*12, 100, 15692.93)
array([ 100.00067132, 649.26771385, 1273.78633713])
So, to end up with the same $15692.93 under the same $100 per month “savings plan,” for annual interest rates of 4% and 3%, one would need initial investments of $649.27 and $1273.79, respectively.