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# numpy.pmt

`numpy.``pmt`(rate, nper, pv, fv=0, when='end')

  Compute the payment against loan principal plus interest.

  Parameters: | rate : array_like Rate of interest (per period) nper : array_like Number of compounding periods pv : array_like Present value fv : array_like Future value 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.

  Notes

  The payment `pmt` 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

  Examples

  What would the monthly payment need to be 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 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.

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