This may be a dumb question, but I am getting frustrated trying to figure it out on my own. When interest is calculated on an auto loan, how do they do it? I know it is not simply amount financed multiplied by loan rate. I have used all the calculators on different websites for this but I want to know the calculations behind all of those, the actual formulas they are using. I know, I am a nerd for wanting to know this, but it comes with the territory (I am an engineer). Thanks for the help!

 

Look at the "remaining balance method."

 

Every auto loan I've ever had uses a variation on the remaining balance method, which is a simple interest calculation, added up on a daily basis, for the number of days since the last payment. Here's how it works:

1) The annual percentage rate is divided by 365.25 to get a daily periodic rate. Let's say the APR for your loan is 5%. Then your daily rate would be 0.01369%.

2) Whenever you make a payment, the bank calculates the total interest that has accrued since your last payment by taking the principal balance during that period, multiplied by the daily rate. Note: with simple interest accrual (not compounded), this calculation is always done with the principal balance (that is to say, accrued interest is not added to the principal balance). Here's an example: let's say there were 25 days since the last payment was made, and the principal balance was $10,000.00 during that time. The total interest accrued for that period would be 0.01369% * 10,000 * 25 = $34.22. This works because the principal balance will only change when you make a payment. If you make more than one payment in a single statement cycle, the calculation will be done separately for each payment.

3) After the period interest accrual is calculated, that amount is taken off your payment. The principal balance will be reduced by the remainder of your payment. In the above example, let's say your payment was $300. The accrued interest was $34.22, which means your principal would be reduced by $265.78 as of the date the payment posted to your account.

I think the main reason banks use this method is that the amount or frequency of payments doesn't make any difference (as long as you make the minimum payment required for your loan). There's no compounding, and the interest is calculated according to your daily principal balance. This is actually a better deal for the customer, because there are no prepayment penalties, and you only pay for the interest you truly accrued on a daily basis.

-Tom

 

Thanks, guys, that helps alot! I thought I might have to break out the old math books!

 

FWIW, I believe all the auto loan calculators use the same formula, which doesn't take into account the actual interest computation I mentioned above. The loan payment formula is a simple installment loan (non-compounding, non-amortized) fixed payment scheme. Basically, it calculates interest monthly instead of daily. If you pay the exact amount of your required payment exactly on the due date every month, I believe it will come out pretty close in the end. But if you pay more than the minimum, or if you make your payments on different days in your statement cycle, then of course the numbers will be a little off.