# numpy.nper¶

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

Compute the number of periodic payments.

Parameters: rate : array_like Rate of interest (per period) pmt : array_like Payment pv : array_like Present value fv : array_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
```

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 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]]])
```

numpy.mirr

numpy.rate