numpy.pmt(rate, nper, pv, fv=0, when='end')[source]

Compute the payment against loan principal plus interest.

  • 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
the (fixed) periodic payment.
Parameters :

rate : array_like

Rate of interest (per period)

nper : array_like

Number of compounding periods

pv : array_like

Present value

fv : array_like (optional)

Future value (default = 0)

when : {{‘begin’, 1}, {‘end’, 0}}, {string, int}

When payments are due (‘begin’ (1) or ‘end’ (0))

Returns :

out : ndarray

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.


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.


[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 Information Standards (OASIS). Billerica, MA, USA. [ODT Document]. Available: ?wg_abbrev=office-formulaOpenDocument-formula-20090508.odt


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)

In order to pay-off (i.e., have a future-value 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.

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