






from numpy import exp, pi, sqrt







def 					SCREAMING_SNAKE_CASE    (			snake_case_ :							List[Any]					,  snake_case_ :							float = 0.0					,  snake_case_ :							float = 1.0       ):
	return 1 / sqrt(2 * pi * sigma**2       ) * exp(-((x - mu) ** 2) / (2 * sigma**2)       )


if __name__ == "__main__":
	import doctest

	doctest.testmod()











from __future__ import annotations







def 					SCREAMING_SNAKE_CASE    (			snake_case_ :							float					,  snake_case_ :							float					,  snake_case_ :							float       ):
	if days_between_payments <= 0:
		raise ValueError("days_between_payments must be > 0"       )
	if daily_interest_rate < 0:
		raise ValueError("daily_interest_rate must be >= 0"       )
	if principal <= 0:
		raise ValueError("principal must be > 0"       )
	return principal * daily_interest_rate * days_between_payments







def 					SCREAMING_SNAKE_CASE    (			snake_case_ :							float					,  snake_case_ :							float					,  snake_case_ :							float					,  ):
	if number_of_compounding_periods <= 0:
		raise ValueError("number_of_compounding_periods must be > 0"       )
	if nominal_annual_interest_rate_percentage < 0:
		raise ValueError("nominal_annual_interest_rate_percentage must be >= 0"       )
	if principal <= 0:
		raise ValueError("principal must be > 0"       )

	return principal * (
	    (1 + nominal_annual_interest_rate_percentage) ** number_of_compounding_periods
	    - 1
	)







def 					SCREAMING_SNAKE_CASE    (			snake_case_ :							float					,  snake_case_ :							float					,  snake_case_ :							float					,  ):
	if number_of_years <= 0:
		raise ValueError("number_of_years must be > 0"       )
	if nominal_annual_percentage_rate < 0:
		raise ValueError("nominal_annual_percentage_rate must be >= 0"       )
	if principal <= 0:
		raise ValueError("principal must be > 0"       )

	return compound_interest(
	    snake_case_					,  nominal_annual_percentage_rate / 365					,  number_of_years * 365       )


if __name__ == "__main__":
	import doctest

	doctest.testmod()



