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# numpy.ipmt

`numpy.``ipmt`(rate, per, nper, pv, fv=0.0, when='end')

  Compute the interest portion of a payment.

  Parameters : | rate : scalar or array_like of shape(M, ) Rate of interest as decimal (not per cent) per period per : scalar or array_like of shape(M, ) Interest paid against the loan changes during the life or the loan. The per is the payment period to calculate the interest amount. nper : scalar or array_like of shape(M, ) Number of compounding periods pv : scalar or array_like of shape(M, ) Present value fv : scalar or array_like of shape(M, ), optional Future value when : {{‘begin’, 1}, {‘end’, 0}}, {string, int}, optional When payments are due (‘begin’ (1) or ‘end’ (0)). Defaults to {‘end’, 0}.
  Returns : | out : ndarray Interest portion of payment. If all input is scalar, returns a scalar float. If any input is array_like, returns interest payment for each input element. If multiple inputs are array_like, they all must have the same shape.

  See also

  `ppmt`, `pmt`, `pv`

  Notes

  The total payment is made up of payment against principal plus interest.

  `pmt = ppmt + ipmt`

  Examples

  What is the amortization schedule for a 1 year loan of $2500 at 8.24% interest per year compounded monthly?

      >>> principal = 2500.00

  The ‘per’ variable represents the periods of the loan. Remember that financial equations start the period count at 1!

      >>> per = np.arange(1*12) + 1
      >>> ipmt = np.ipmt(0.0824/12, per, 1*12, principal)
      >>> ppmt = np.ppmt(0.0824/12, per, 1*12, principal)

  Each element of the sum of the ‘ipmt’ and ‘ppmt’ arrays should equal ‘pmt’.

      >>> pmt = np.pmt(0.0824/12, 1*12, principal)
      >>> np.allclose(ipmt + ppmt, pmt)
      True

      >>> fmt = '{0:2d} {1:8.2f} {2:8.2f} {3:8.2f}'
      >>> for payment in per:
      ...     index = payment - 1
      ...     principal = principal + ppmt[index]
      ...     print fmt.format(payment, ppmt[index], ipmt[index], principal)
       1  -200.58   -17.17  2299.42
       2  -201.96   -15.79  2097.46
       3  -203.35   -14.40  1894.11
       4  -204.74   -13.01  1689.37
       5  -206.15   -11.60  1483.22
       6  -207.56   -10.18  1275.66
       7  -208.99    -8.76  1066.67
       8  -210.42    -7.32   856.25
       9  -211.87    -5.88   644.38
      10  -213.32    -4.42   431.05
      11  -214.79    -2.96   216.26
      12  -216.26    -1.49    -0.00

      >>> interestpd = np.sum(ipmt)
      >>> np.round(interestpd, 2)
      -112.98

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