Wednesday, October 31, 2007

How much do you understand your auto loan - Can you find the fault in this calculation?

A small discussion with my room mate brought up the subject of auto loan that I have on my car and why I should / should not pay it off. I have some savings in my savings account and I have an auto loan on my car. If I open a CD (Certificate of Deposit) with Indymac bank they will give me an APR of 5.5% and my car loan is financed by a Credit Union at 5.5%. The argument that my roomie was making was that I should pay off the car loan instead of opening a CD. His reasoning was that, though the car loan and the APR on the CD were the same, I am actually losing money, because on the interest that I earn on the CD, I have to pay a tax. And since I am single and fall in the higher tax bracket, I will end up paying 25%(+) on the interest earned. Which means that I will actually be making around 75% of the 5.5% which is around 4.13% which means that I am losing around 1.37% (5.5-4.13) on the whole amount that I am planning to open a CD with. In a way, it made sense for a brief moment.

But then, further investigation showed that it is not a valid argument to me. Here was my case that I presented. Let us say you have $10000 with you, and you have two choices, put it in a CD for two years at the rate of 5.5%, or pay off your loan which is 5.5% and ends in 2 years. If you don't pay off the loan now, you keep paying it in monthly amounts of $440.96 (Calculation from Bankrate calculator) with your salary. If you put it in CD for 2 years, you make a simple interest of $1130.25 (550+550). Let us say, you pay 28% tax on it. So your net interest earned from that amount after paying taxes off is 72% of 1130.25 which is $813.28 and the total interest you pay on the car loan for these 2 years is $582.96 (Calculation from Bankrate calculator). So I argued that I actually am making $230.32 (813.28-582.96) extra by not paying off the car loan.

Sounds logical right, but the above calculation is wrong because it was one-sided. The reason is, if I pay off the car loan with the $10000, then I don't need to pay them the $441 that I was paying every month, which means that I can put it in a savings account like ING Direct for an APY of 4.3% or an APR of 4.21%. This means that the total amount I make in two years with this monthly savings would be $11541 (Calculation from dinkytown). This means I make an interest of $1541 in two years. After cutting the tax at the rate of 28%, I will be left with around 72% of 1541 which is $1109.52. This means the total I save is this 1109.52 plus the interest I would have paid for the car loan which is 582.96. So the net total I would have saved is $1692.48 So by not paying off the loan today, I am actually losing is $879.20. So the conclusion of the whole calculations is it is better to pay off the car loan, if you have the cash instead of saving in your bank account and having the loan aside and paying monthly payments.

Agreed this calculation has some flaws because of some assumptions. It assumes that the rate from ING Direct will be 4.21%, but since it is variable it can go up or come down. Also, we are assuming that you will have continuous money from your salary, and that you will actually put aside the car loan amount payment in a Savings account instead of spending it on the next cool thing like the Iphone :) It also assumes that you would pay the money off instead of having it in your savings account, which you can withdraw in case of an emergency. You obviously can't get a car loan again on your car in case of an emergency right :) It also assumes you have 10k or the total amount of your car loan with you in your savings. But anyways, under the given set of assumptions, it makes sense to actually pay off the car loan rather than put the amount in the CD or Savings account. One more thing, you can consider is taking the amount from a special offer like 0% APR (be careful with the Balance Transfer fee in the fine print) on Balance Transfer from a credit card company like Citi and paying off the loan, provided you have a good credit history. That way, you don't pay the interest to the auto loan provider and you can pay off monthly amounts to the credit card company. And when the balance transfer offer ends after one year, take another card and transfer the balance to that. All this provided you actually have time to do some research on these and wish to save some dollars :)

Feel free to challenge the above calculations or present counter arguments :)

PS: There is a big fundamental mistake in the above calculation, and the net amount you actually save is $272.19 and not $879.20 as mentioned above. Can you prove this?


AnneK said...

or you can not pay off the car loan and invest it in stocks-which gives you a much higher rate. Which is why we are not paying off the PMI on the house.

Devin said...

I think the flaw is that you are calculating the interest you would earn on the saved payments as though all of those saved payments could be invested now. In reality, you would only be able to save one payment at a time, and so the interest earned would be something like:

441 * .055/12 * 24 +
441 * .055/12 * 23 +
441 * .055/12 * 1

Devin said...
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