def ppmt(rate, per, nper, pv, fv=0.0, when='end'):
"""
Compute the payment against loan principal.
Parameters
----------
rate : array_like
Rate of interest (per period)
per : array_like, int
Amount paid against the loan changes. The `per` is the period of
interest.
nper : array_like
Number of compounding periods
pv : array_like
Present value
fv : array_like, optional
Future value
when : {{'begin', 1}, {'end', 0}}, {string, int}
When payments are due ('begin' (1) or 'end' (0))
See Also
--------
pmt, pv, ipmt
"""
total = pmt(rate, nper, pv, fv, when)
return total - ipmt(rate, per, nper, pv, fv, when)
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