numpy.nper

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

Compute the number of periodic payments.

Deprecated since version 1.18: nper is deprecated; for details, see NEP 32 [1]. Use the corresponding function in the numpy-financial library, https://pypi.org/project/numpy-financial.

decimal.Decimal type is not supported.

Parameters

ratearray_like

Rate of interest (per period)

pmtarray_like

Payment

pvarray_like

Present value

fvarray_like, optional

Future value

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

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

Notes

The number of periods nper is computed by solving the equation:

fv + pv*(1+rate)**nper + pmt*(1+rate*when)/rate*((1+rate)**nper-1) = 0

but if rate = 0 then:

fv + pv + pmt*nper = 0

References

1

NumPy Enhancement Proposal (NEP) 32, https://numpy.org/neps/nep-0032-remove-financial-functions.html

Examples

If you only had $150/month to pay towards the loan, how long would it take to pay-off a loan of $8,000 at 7% annual interest?

>>> print(np.round(np.nper(0.07/12, -150, 8000), 5))
64.07335

So, over 64 months would be required to pay off the loan.

The same analysis could be done with several different interest rates and/or payments and/or total amounts to produce an entire table.

>>> np.nper(*(np.ogrid[0.07/12: 0.08/12: 0.01/12,
...                    -150   : -99     : 50    ,
...                    8000   : 9001    : 1000]))
array([[[ 64.07334877,  74.06368256],
        [108.07548412, 127.99022654]],
       [[ 66.12443902,  76.87897353],
        [114.70165583, 137.90124779]]])