numpy.ipmt¶
- numpy.ipmt(rate, per, nper, pv, fv=0.0, when='end')[source]¶
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.
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