


"""simple docstring"""





import math

from numpy import inf
from scipy.integrate import quad


def    _snake_case  (  _snake_case :	float	):
      if num <= 0:
            raise ValueError('''math domain error'''	)

      return quad(_snake_case       ,      0       ,      _snake_case       ,      args=(_snake_case)	)[0]


def    _snake_case  (  _snake_case :	float       ,      _snake_case :	float	):
      return math.pow(_snake_case       ,      z - 1	) * math.exp(-x	)


if __name__ == "__main__":
 from doctest import testmod

 testmod()






"""simple docstring"""







def 					a__			(				SCREAMING_SNAKE_CASE    :    float				,      SCREAMING_SNAKE_CASE    :    float				,      SCREAMING_SNAKE_CASE    :    int				):


  '''simple docstring'''







  if principal <= 0:
    raise Exception("Principal borrowed must be > 0"				)
  if rate_per_annum < 0:
    raise Exception("Rate of interest must be >= 0"				)
  if years_to_repay <= 0 or not isinstance(SCREAMING_SNAKE_CASE				,      SCREAMING_SNAKE_CASE				):
    raise Exception("Years to repay must be an integer > 0"				)

  # Yearly rate is divided by 12 to get monthly rate
  lowerCAmelCase     :     Tuple								=							rate_per_annum / 1_2

  # Years to repay is multiplied by 12 to get number of payments as payment is monthly
  lowerCAmelCase     :     List[Any]								=							years_to_repay * 1_2

  return (
      principal
      * rate_per_month
      * (1 + rate_per_month) ** number_of_payments
      / ((1 + rate_per_month) ** number_of_payments - 1)
  )


if __name__ == "__main__":
     import doctest

     doctest.testmod()





