# given principal and interest rate
# + periods = minimum payment amount and total cost
# + extra payment = periods, total cost, and savings over minimum

import math

def calculate(principal,rate_yearly,periods,extra=0):

	# variables
	rate_monthly = rate_yearly / 12 / 100

	# calculate minimum payment
	if rate_monthly > 0:
		payment = rate_monthly * principal / (1 - (1 + rate_monthly)**(-periods))
	else:
		payment = principal / periods
	payment = round(payment,2)

	# calculate costs at minimum payment
	total = payment * periods
	interest = total - principal
	interest = round(interest,2)

	# calculate payment with extra
	if extra:
		payment_extra = payment + extra
		payment_extra = round(payment_extra,2)

	# calculate period with extra
	if extra:
		periods_extra = -(math.log(-(rate_monthly * principal / payment_extra) + 1) / math.log(1 + rate_monthly)) # yes, this uses log, so thank your high school math teacher
		periods_extra = round(periods_extra,1)
		months_extra = periods - periods_extra
		months_extra = round(months_extra,1)

	# calculate costs with extra
	if extra:
		total_extra = payment_extra * periods_extra
		interest_extra = total_extra - principal
		interest_extra = round(interest_extra,2)
		savings_extra = interest - interest_extra
		savings_extra = round(savings_extra,2)

	# output
	print("\n"*3)
	print(f"For a loan of ${principal} at a {rate_yearly}% interest rate, your minimum payment will be ${payment} per month for {periods} months, and you'll pay a total ${interest} in interest.")
	if extra:
		print(f"\nIf you pay ${extra} extra per month, your payments will be ${payment_extra} per month for {periods_extra} months, and you'll pay a total ${interest_extra} in interest. That's ${savings_extra} less and {months_extra} months faster than if you only pay the minimum!")
	print("\n"*3)

# run the calculator
calculate(
	principal = 100000 - 10000, # the amount of the loan, you can put the total cost minus down payment as well as shown here
	rate_yearly = 5, # yearly interest rate out as a percent
	periods = 30 * 12, # number of months for repayment, or as shown here, years for repayment times twelve
	extra = 1000 # any extra you can pay each month above and beyond the minimum payment
)