The Cost of Financing a Car (Car Loans)

Learn about how monthly car payments (equated monthly installments) are calculated. Learn how interest rates/APR affect monthly payments, and how the length of a loan affects total interest paid.

This tutorial gets into more than how the length of a loan affects monthly payments.

This tutorial will include:

How a Monthly Payment (Equated Monthly Installment) is Calculated.

How Interest Rates/APR Affect Monthly Payments.

How the Length of a Loan Affects Total Interest Paid

As always, the code used in this tutorial is located on my GitHub. With that, let’s get started!

How a Monthly Payment (Equated Monthly Installment) is Calculated

Your monthly payment, also called your Equated Monthly Installment (EMI) is defined by Investopedia as a fixed payment amount made by a borrower to a lender at a specified date each calendar month. Equated monthly installments are used to pay off both interest and principal each month, so that over a specified number of years, the loan is paid off in full.

A monthly payment can be calculated using an EMI formula similar to the one below.

Example: Calculating a Monthly Payment (Simplified)

I want to upgrade my car from a 2002 Toyota Sienna to a 2019 Toyota Sienna.

Say I buy want to buy a 2019 Toyota Sienna for $31,115. I am curious how much it will cost me each month if I decide on taking out a loan to buy this new vehicle. A car dealer offers me a fixed interest rate of 7.02% over a 60 month term. How much would a monthly car payment be assuming the sales tax rate is 7.5%?

Note that I rounded up to the nearest cent.

While this is a simplified and relatively accurate calculation (except for the sales tax being an assumption), there is a more accurate calculation in the next example.

Example: Calculating a Monthly Payment (with some fees included)

Say I buy want to buy a 2019 Toyota Sienna for $31,115 from a car dealership in Los Angeles which has a total sales tax rate of 9.75% (source). The price was originally $32,615 before the dealership reduced the price through a 1500 dollar rebate. I am curious how much it will cost me each month if I decide on taking out a loan to buy this new vehicle. A car dealer offers me a fixed interest rate of 7.02% over a 60 month term. How much would a monthly car payment be?

This can be solved the same way as the previous example, except that calculating the principal of the loan is actually more complicated. In other words, taxes and fees need to be added on to the price of the purchase. Most states tax vehicle purchases before rebates or incentives are applied to the price of a car (source). While fees can vary from place to place, this example calculation has the following fees

Emissions testing fee: $50

Registration Fee: $200

Plate Transfer Fee: $65

California Documentation Fee: $80 (keep in mind some states charge a lot more for documentation fees)

This monthly payment is higher by $24.59 (687.23 — 662.64) than the one shown in the previous example.

How Interest Rates/APR Affect Monthly Payments

Before going into this section, it is important to know a little about the term Annual Percentage Rate (APR). For car loans, APR is the rate you pay that accounts for interest charges plus all other fees you have to pay to get your loan while interest rate accounts only for the interest charges. While you can learn about APR here, APR is higher (hopefully only slightly higher) than your interest rate. Note though that while APR is higher (usually not much higher assuming small fees) than an interest rate, mathematically they are the same in that they both give you the same payment. For the purpose of this tutorial, let’s make it mathematically easier and assume APR and interest rate are the same.

By looking at the table below, it is clear that your FICO score affects your APR which affects your monthly payments.

If you are curious how The Simple Dollar was able to calculate the Total Interest Paid, read the next section. It goes into detail on how much interest you pay each month.

How to Calculate Total Interest Paid

An important part of taking out a loan is knowing how much in interest you will pay over the course of your loan. This is a little complicated as the percent of a monthly payment (EMI) that go towards paying off the principal of a loan increases over time. Using the same principal ($34689.96) and interest rate (7.02%) from the Calculating a Monthly Payment (with some fees included) section, the graph belows shows that with every subsequent monthly payment, the principal paid keeps on rising while the interest paid keeps on lowering.

Dollars that go towards interest and principal each month from a monthly payment (EMI) of 687.23 with an interest rate of 7.02%

Now let’s calculate the total interest paid by producing a table similar to the one below and then sum the Interest Paid column.

Notice how much interest and principal are paid each month.

While I will do this in Python, feel free to do this in a spreadsheet or whatever you feel comfortable with.

1-) The first thing is to calculate how much money of the monthly payment will be paid towards interest in a month.

2-) Each month, some of the monthly payment is paid towards principal and some towards interest. As principal lowers, to work out the interest you pay in the following months, you need to first calculate your new principal. You can see how to calculate this below.

3. Repeat steps 1 and 2 until the principal reaches 0. You can see an example of this in the Python code below.

Python Code to Create Payment Table

Notice how much interest and principal are paid each month.

4. After getting the Interest Paid for each month, sum the Interest Paid column.

np.round(payment_table['Interest Paid'].sum(),2)

Refinancing to a lower interest rate

This example looks at how much less a person could pay in interest (Total Interest Paid) over the course of a loan with a lower interest rate. In particular, the difference between a 3.59% interest rate vs a 7.02% interest rate over a 60 month term.

Code to generate tables of total interest paid for different interest rates

By using the same calculation method as the previous section, the lower interest rate would save $3285.63 (6543.51 — 3257.88) in total interest paid. Also, the monthly payment would be $54.76 less (687.23 — 632.47) with the lower interest rate.

If you have the option to refinance to a lower interest rate, it is important to note that your current loan could have a prepayment penalty or your new loan can have an origination fee. In other words, do your best to know what you are signing up for if you decide to refinance. I should note that Credit Karma has a guide on refinancing your auto loan and NerdWallet has a few ways to avoid to overpaying for your car loan.

How the Length of a Loan Affects Total Interest Paid

In general, with the same interest rate, the longer the length of your loan, the more total interest. Compare the two loans below. Both have an interest rate of 7.02%, but one has a term of 60 months and another has a term of 72 months. While the 72 month loan has a monthly payment (EMI) lower than the 60 month loan (591.76 vs 687.23), the loan will cost more in total interest paid.

The graph above shows that the 72 month loan costs $7916.58 in total interest whereas the 60 month loan costs $6543.51 (72 month loan costs $1373.07 more). If you want to learn more about deciding on how long a car loan should be, Edmunds has a nice article on it.

Conclusion

I hope you enjoyed this tutorial and gained a better understanding of how car loans work. If you any questions or thoughts on the tutorial, feel free to reach out in the comments below or through Twitter. If you want to learn how to utilize the Pandas, Matplotlib, or Seaborn libraries, please consider taking my Python for Data Visualization LinkedIn Learning course.