Is your car loan more expensive than you think? The difference between APR and the total interest you have to pay

Question from a reader (slightly edited):

I have 60-month loan for an $18500 car with a 5.69 percent APR. When I do the calculation using simple interest it comes to $1052.65. On my contract from the dealer it says $2726.20.

Why is their number closer to 15 percent? Am I missing something?

My answer:

This is a great question about interest rates. Their numbers, though correct, are confusing for a simple reason: car dealers want to be confusing. The main thing you are missing is an honest explanation of the numbers. I emphasize that I’m not a professional, but let me give my friendly thoughts on the math.

It would seem the interest should be 5.69 percent, corresponding to the APR. After all, APR stands for the annual percentage rate and measures the annual cost of the loan. And yet the total interest in the contract is much higher, a whopping 15 percent. Why is that?

The discrepancy is due to the structure of the loan. Your car loan isn’t calculated on simple interest. The method they use is add-on interest. That’s a method where they figure out all the interest at the start, add it on, and then average it into monthly (or installment) payments. This is also called an installment loan.

Why is APR different from add-on interest percentage? It is different for two reasons. First, the APR measures an annual cost, but most car loans span over several years. Second, the APR is dependent on the timing of the loan repayment.

And here’s what that means: the APR in your 5-year loan ends up lower than the add-on interest percentage. It will not indicate exactly how much you need to pay.

What most of us care about is the add-on interest percentage. Fortunately, it is possible to quickly estimate the add-on interest percentage from the APR. As a rule of thumb: multiply the APR by the years of the loan and then divide by 2 to get the add-on interest percentage:

Why does the formula work? The APR is an annual rate. This is why we need to multiply it by the number of years to capture the add-on interest percentage for the entire loan. But then there is a matter of timing. The APR depends on the timing of repayments. Since you pay off the loan every month, “on average” you are holding one-half of the money across the entire loan. We divide by 2 to account for timing.

In the above example, a 5.69 percent APR over 5 years (60 months) would result in an estimated add-on interest percentage of 14.2 percent. This is pretty close to the actual add-on interest of 14.7 percent.

To compute the exact answer, you’d have to use a time-weighted formula. Practically you can get away with using an online calculator that uses APR, loan amount, and term length to determine the add-on interest paid on a loan. You can try the following:

http://www.freeonlinecalculator.net/calculators/loan/auto-simple.php

(after you put in the numbers, look at the row labeled “interest as a percentage of principal” for the add-on interest percentage)

When I put in the numbers (an auto loan amount of $18,500, an APR of 5.69 percent, and the loan term of 60 months), the output confirms the terms of your loan with an add-on interest of about 15 percent.

So your car contract is right, even though it does not look right.

Key lessons:

1. Make sure you understand your car loan contract
2. The APR will be different from the add-on interest percentage you’ll pay in car loans
3. You can estimate the add-on interest percentage as (APR x years) / 2, or use an online calculator
4. Be cautious of car dealers, and run your own numbers
5. Ask for help if needed

(Also, the APR is closely related but slightly different from the APY…see the math here)

Do you have a question?

If you’d like to hear my thoughts on a money or game theory question, please feel free to email me at presh@mindyourdecisions.com. I will publish the best questions on this website. I may edit the question to make it more general. Please understand I cannot answer all emails due to time constraints.