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December 16, 2010

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Wait, so I have a CD with Ally bank that is 2.46% compounded daily...this is good or bad?

We should all take individual responsibility for our own actions and decisions. Nobody is more responsible for your well being than you are. This applies to decisions with personal finance, as well.

Read the fine print, ask the right questions - heck, try to LEARN what the right questions are. Doing such things will guide each of us toward good decision-making and avoidance of those who try to exctract our money through shady means.

WARNING: THIS ARTICLE IS WRONG!

This highlights Squirrelers point that you have to take individual responsibility and not take what you read at face value.

The APR that banks quote is, by law in the US, supposed to be the nominal interest rate. The article states if you look at the nominal interest rate, you will be okay. I would argue that the opposite is true. The nominal interest rate doesn't take into effect the compounding period. Two banks can offer what appears to be the same APR but because they compound differently, you might end up paying different amounts in interest. The rule of thumb is that APR's cannot be compared unless the compounding periods are the same. This is in contrast to the advice the article gives that you want the unqualified APR. Repeat after me: the unqualified APR is meaningless!

Let's say that Bank A offers a loan that advertises a 12% APR. If the interest is compounded monthly, then the monthly interest rate is 1% on this loan, meaning that the bank charges you 1% interest on whatever the loan balance is at the end of every month.

Now let's say that Bank B offers a loan that advertises a 12% APR. If interest on this loan is compounded semi-annually, then the semi-annual interest rate is 6% on this loan, meaning that the bank charges you 6% interest on whatever the loan balance is at the end of every 6 months.

Which is a better deal for the borrow?

From a borrowers standpoint, you want the loan that compounds the least frequently. Everytime you are charged interest, you are accumulating interest on the original loan and interest on the interest which accumulated in the previous period.

To prove this mathematically, you need to convert this to an effective annual interest rate. This converts the interest rate into what the equivalent interest rate would be if you were compounding annually. The formula is e = (1-i/n)^n - 1, where e is the effective interest rate, i is the nominal rate, and n is the number of compounding periods per year (12 for monthly compounding, 2 for semi-annual compounding).

In the case of my examples, Bank A's effective annual interest rate is 12.68% and Bank B's is 12.36%. That means that Bank A's loan is equivalent to a loan that compounds annually at a rate of 12.68%, and Bank B's loan is the equivalent of a loan that compounds annually at a rate of 12.36%. Because the compounding rates are now equivalent, you can compare the two loans and obviously Bank B is the better deal. However, you would not know it just by looking at the APR.

It always amazes me that banks are required to quote the APR. If the goal is to allow consumers to compare interest rates, the government ought to require them to quote the effective interest rate, and not the APR. Very strange.

To answer Jeff's question, when you have a bank account or CD, you want the most frequent compounding, so daily is better than monthly or yearly. Again, with CD's, banks are required to quote the APR, but you will also see that some quote a higher number which is the "effective yield" or APY. This number is the equivalent of the effective interest rate and is a better gauge for comparison. This is the amount that you would end up with at the end of the year. If a bank has a APY or effective yield of 2.5%, then you will end up with 2.5 cents for every dollar. If they quote an APR of 2.5%, then you have no idea of what you will get back at the end of the year for every dollar invested, unless they also give you a compounding rate.

Sorry this is a long post but somebody had to refute the original article.

In case anyone is wondering, I am not going to be buying Mr. McFarlane's book anytime soon! :-)

I must admit MBTM – I wish you had rested your case with your first comment and not followed it with what was, in my opinion, a snarky and unnecessary bash at the author of this post and his book.

That being said, I found your analysis and supporting examples to be phenomenal. Probably the best thing I have read all day – I truly enjoyed it. I also checkout out your blog and your material is very good. Thank you for the insights!

MBTN is correct.

The author seems to be implying by his examples that the APR does take into account compounding. But in fact it's the APY that takes into account compounding. APR does not take into account compounding. In the example the author used, he said that a lender might advertise 5.94% when the real rate is 6.1%. However in his example 5.94% is the APR and 6.1% is the APY. Yet he advises going by APR. But in truth the APR is the lower rate while the APY is the rate you will end up paying after 1 year.

To further complicate things, in this country by law, mortgage APR must also include closing costs and loan fees amortized over the length of the loan. So in that way the APR is often shown as higher than the actual rate that you are paying because the mortgage APR must include the non interest rate things in it (does that make any sense, the Annual Percentage Rate includes non Rate elements, yes you can thank the government for that).

It makes it very hard to compare rates because there are so many different ways that things are reported and required to be reported.

The only way you really know what you are comparing is to take the raw rate and compound it for a year and then compare loan costs as well.

Interest rate comparisons are complicated, but the confusion between APR and APY in this article is disappointing from an author who has written a book on the subject.

Thanks for your comments.

@MBTN and Apex. First MBTN:

I wrote one passage that I could have worded better:
"If you look only at nominal APRs and nothing else from lender to lender, you won’t encounter this problem" (of fees varying between lenders)

I should have made it clear that the fees themselves are frequently large enough to negate the difference between one lender's ostensibly low APR and another's higher one. Yes, compounding frequency is as big a criterion as interest rate for determining how good a loan is. I was simply trying to warn readers of the absurdity of lenders trying to flout the law by using phrasing that includes disparate time periods (e.g. "annual rates compounded monthly.")

@Apex:

"the mortgage APR must include the non interest rate things in it"
Really? I've bought at least one property where I was forced to retain the services of a particular (expensive) title company and attorney. Using them was a condition of receiving the lender's attractive APR. I'd thus argue that until the law mandates that a lender include every single cost in the calculation of its interest rates (save late fees, which are incurred at the borrower's impetus), all a borrower can do is
a) get every possible cost disclosed upfront, and
b) understand my original point, which is that there are vast differences between competing lenders' loans, only one of which is the number in front of the percentage sign.

In my credit union, we offer both an home equity line of credit(which you can draw advances from) and fixed equity loans(which are a straight second mortgage.

Not a week goes by- I swear to G'd, not a week-in which at least one person doesn't call up confused about which type of loan they have.Despite having signed a deed of trust and a Note giving their home as collateral, they honestly have no idea what type of loan they have, let alone the interest rate or balance. We're not talking Countrywide-style sneakiness here, we're talking a small-to-middling local credit union that operates near the red ona yearly basis because it's forwarding all the profits back to the members.

Banking reform is a great idea. But as the saying goes, you can't fix stupid.

Nate:

Thank you for your kind words. They are much appreciated.

Mr. McFarlane:

Thank you for responding, sir. One thing which I did not address directly in my original comment which you brought up is this concept that if a lender uses the phrase "APR compounded monthly" that they are "deceptive" or "flouting the law". I am having a hard time grasping your logic here. Lenders are required by law to state the APR. As I have pointed out, APR tells you nothing about the compounding period. If a lender goes the extra mile and states the compounding period, then they are to be APPLAUDED. There is nothing deceptive about this. On the contrary, they are providing you with additional information. They are not flouting the law. They are going above and beyond. As you probably know, 99% of loans in the US are compounded monthly anyway, so I find it hard to fault a lender who states what a consumer would naturally assume.

If I were truly trying to be deceptive, I would compound interest on the loan daily, but I would only mention that in the fine print. I would state the unqualified APR as required by law, hoping that the borrower would assume that the compounding is monthly like a loan from most respectable institutions. If anything, by adding "compounded monthly" it would give me as the borrow extra assurance that there is no funny business happening in the fine print.

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