


'''simple docstring'''







def 				lowerCAmelCase__	(    lowerCamelCase					:      List[str]  ,lowerCamelCase					:      str  ,lowerCamelCase					:      Dict       ):

       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(__UpperCAmelCase  ,__UpperCAmelCase       ):
              raise Exception('Years to repay must be an integer > 0'       )

       # Yearly rate is divided by 12 to get monthly rate
       _A					:     List[str]     = rate_per_annum / 12

       # Years to repay is multiplied by 12 to get number of payments as payment is monthly
       _A					:     str     = years_to_repay * 12

       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()










'''simple docstring'''







def 				lowerCAmelCase__	(    lowerCamelCase					:      int  ,lowerCamelCase					:      list[int]  ,lowerCamelCase					:      int       ):

       def count_of_possible_combinations(lowerCamelCase					:      int       ) -> int:
              if target < 0:
                     return 0
              if target == 0:
                     return 1
              return sum(count_of_possible_combinations(target - item       ) for item in array       )

       return count_of_possible_combinations(lowerCamelCase       )






def 				lowerCAmelCase__	(    lowerCamelCase					:      int  ,lowerCamelCase					:      list[int]  ,lowerCamelCase					:      int       ):

       def count_of_possible_combinations_with_dp_array(
           lowerCamelCase					:      int  ,lowerCamelCase					:      list[int]       ) -> int:
              if target < 0:
                     return 0
              if target == 0:
                     return 1
              if dp_array[target] != -1:
                     return dp_array[target]
              _A					:     Optional[Any]     = sum(
                  count_of_possible_combinations_with_dp_array(target - item  ,lowerCamelCase       )
                  for item in array       )
              _A					:     List[str]     = answer
              return answer

       _A					:     Optional[int]     = [-1] * (target + 1)
       return count_of_possible_combinations_with_dp_array(lowerCamelCase  ,lowerCamelCase       )






def 				lowerCAmelCase__	(    lowerCamelCase					:      int  ,lowerCamelCase					:      list[int]  ,lowerCamelCase					:      int       ):
       _A					:     Dict     = [0] * (target + 1)
       _A					:     List[str]     = 1

       for i in range(1  ,target + 1       ):
              for j in range(lowerCamelCase       ):
                     if i - array[j] >= 0:
                            dp_array[i] += dp_array[i - array[j]]

       return dp_array[target]


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   A				:					Dict    						=			3
   A				:					Union[str, Any]    						=			5
   A				:					Union[str, Any]    						=			[1, 2, 5]
   print(combination_sum_iv(n, array, target))






