pmt¶

numpy_financial.
pmt
(rate, nper, pv, fv=0, when='end')¶ Compute the payment against loan principal plus interest.
 Given:
a present value, pv (e.g., an amount borrowed)
a future value, fv (e.g., 0)
an interest rate compounded once per period, of which there are
nper total
and (optional) specification of whether payment is made at the beginning (when = {‘begin’, 1}) or the end (when = {‘end’, 0}) of each period
 Return:
the (fixed) periodic payment.
 Parameters
 ratearray_like
Rate of interest (per period)
 nperarray_like
Number of compounding periods
 pvarray_like
Present value
 fvarray_like, optional
Future value (default = 0)
 when{{‘begin’, 1}, {‘end’, 0}}, {string, int}
When payments are due (‘begin’ (1) or ‘end’ (0))
 Returns
 outndarray
Payment against loan plus interest. If all input is scalar, returns a scalar float. If any input is array_like, returns payment for each input element. If multiple inputs are array_like, they all must have the same shape.
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
>>> import numpy_financial as npf
What is the monthly payment needed to pay off a $200,000 loan in 15 years at an annual interest rate of 7.5%?
>>> npf.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.