Asking Python

Imagine that you get paid on the 1st and 15^th of the month. After looking at your budget, you feel you could spend $200 a paycheck and you are thinking of buying a car. You know the interest rate will be 4.74%. You figure the car loan will be spread over 4 years, paying 2 payments per month (24 a year). The care you are looking at is $20,000. Can you afford it?

There is a financial formula out there you could use.

With this formula, you would need to understand what the variables are.

• PMT = Payment per period
• PV = Present Value you are borrowing
• FV = Future Value you want (which is likely 0!)
• N = Number of Payments a year (24 twice a month)
• ip = interest rate (4.74%) per period
• k = 1 if payment is made at the end of the period (Trust me its a financial thing)

Lets use Pythons shell to see if we can afford the car? Here I am using the interpreter and commands.

Python 3.9.1 (tags/v3.9.1:1e5d33e, Dec 7 2020, 17:08:21) [MSC v.1927 64 bit (AMD64)] on win32

Type "help", "copyright", "credits" or "license()" for more information.

>>> PV= 20000

>>> i = 4.74

>>> NumYrs = 4

>>> PmtPerYear = 24 #2 payments per month

>>> FV = 0 # Future Value of loan is $0. (You want this paid off, right?)

>>> k = 1 # (payment is at end of period ... it's a finance thing!)

>>>

>>> ## Now ... off to calculate payment. This will look messy.

>>>

>>> numerator = PV + FV

>>> ip = i/100/PmtPerYear

>>> NumPmts = NumYrs * PmtPerYear

>>> denominator = (1 + ip)**NumPmts - 1

>>> fraction = numerator/denominator

>>> other_fraction = (-1 * ip/k)

>>> Payment = PV + fraction

>>> Payment = Payment * other_fraction

>>>

>>> Payment

-228.91210686170604

>>>

So, the payments would be $-228.91, twice a month! Why negative? Because you are paying DOWN a loan. If you were INVESTING, it would be positive.

But, to take the guess work out, why dont we just put the payment into a FUNCTION that gives us the Absolute Value (always positive) and then print it out, using a format function!

>>> abs(Payment)

228.91210686170604

>>> print(f"Your payment would be ${abs(Payment):,.2f} a period")

Your payment would be $228.91 a period

So, how much did you totally spend on your car? (The number of payments multiplied by the payments)

>>> totalCost = abs(Payment) * NumPmts

>>> print(f"Your Total Cost of the car would be ${totalCost:,.2f}")

Your Total Cost of the car would be $21,975.56

How much interest? (What is the cost of borrowing??)

>>> costOfBorrowing = totalCost - PV

>>> print(f"The cost of borrowing would be ${costOfBorrowing:,.2f}")

The cost of borrowing would be $1,975.56