Compute the payment against loan principal plus interest.
Parameters:  rate : array_like
nper : array_like
pv : array_like
fv : array_like (optional)
when : {{‘begin’, 1}, {‘end’, 0}}, {string, int}


Returns:  out : ndarray

Notes
The payment 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 pmt.
Note that computing a monthly mortgage payment is only one use for this function. For example, pmt returns the periodic deposit one must make to achieve a specified future balance given an initial deposit, a fixed, periodically compounded interest rate, and the total number of periods.
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=officeformulaOpenDocumentformula20090508.odt 
Examples
What is the monthly payment needed to pay off a $200,000 loan in 15 years at an annual interest rate of 7.5%?
>>> np.pmt(0.075/12, 12*15, 200000)
1854.0247200054619
In order to payoff (i.e., have a futurevalue of 0) the $200,000 obtained today, a monthly payment of $1,854.02 would be required. Note that this example illustrates usage of fv having a default value of 0.