# numpy.ppmt() in Python

`numpy.ppmt(rate, nper, pv, fv, when = ‘end’) `: This financial function helps user to compute payment value as per the principal value only.

Parameters :
rate : [scalar or (M, )array] Rate of interest as decimal (not per cent) per period
nper : [scalar or (M, )array] total compounding periods
fv : [scalar or (M, )array] Future value
pv : [scalar or (M, )array] present value
when : at the beginning (when = {‘begin’, 1}) or the end (when = {‘end’, 0}) of each period.Default is {‘end’, 0}

Return : Payment value as per the principal value only.

Equation being solved :

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

or when rate == 0
fv + pv + pmt * nper == 0

Code:

 `# Python program explaining  ` `# ppmt() function  ` ` `  `import` `numpy as np  ` ` `  `'''  ` `Question :  ` ` `  `monthly payment needed to pay off a \$10, 000 loan ` `in 12 years at an annual interest rate of 10 % ` `'''` ` `  `# rate     np         pv  ` `Solution ``=` `np.ppmt(``0.10` `/` `12``, ``12` `*` `12``,  ``10``, ``000``)  ` ` `  `# Here fv = 0 ; Also Default value of fv = 0  ` `print``(``"Solution : "``, Solution)  `

Output:

```Solution :  -0.1195078262827336
```
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