Talk:Annual percentage rate/Archive 1

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This is an ARCHIVE talk-page for: Annual percentage rate.

Notes: Don't edit the entries here. To resume a topic, move that entry back to the main talk-page. Archive other older entries by moving them to this page. Goal: Have ONE ARCHIVE page, searching it finds all older topics.

Main talk-page: Talk:Annual percentage rate.

Topics from 2004

From VfD:

Dictionary definition that looks like it was written by someone who doesn't understand what he's defining. - Kenwarren 02:10, Jul 26, 2004 (UTC)

• I'd like to withdraw my nomination for deletion, considering how much cleanup it's undergone. The article perhaps isn't my brand of encyclopedic, as it goes off on several tangents from the title of the article, but it's certainly nowhere near useless. - Kenwarren 03:28, Jul 27, 2004 (UTC)

---

• Delete: Seems to be trying to do a car loan discussion, misnamed. Geogre 03:12, 26 Jul 2004 (UTC)
  • Keep rewrite. Geogre 16:03, 28 Jul 2004 (UTC)
• Delete. Spectatrix 06:20, 2004 Jul 26 (UTC)
• Delete and lower my APR while you're at it. - UtherSRG I still want my APR lowered... keep. - UtherSRG 15:16, 27 Jul 2004 (UTC)
• Keep. Send to Clean-Up. Concept is real and could be expanded upon. Article is salvagable. Rossami 23:39, 26 Jul 2004 (UTC)
• Keep, good clean up in progress by Rossami. --Sideshow 02:47, 27 Jul 2004 (UTC)
• Agree with Rossami and like the improved version. Keep. Ianb 05:58, 27 Jul 2004 (UTC)
• Keep. Looks pretty good. - Eisnel 06:42, 27 Jul 2004 (UTC)
• Keep. It is a widely used term. Jayanta Sen 04:12, 1 November 2006 (UTC)

end moved discussion

Topics from 2005

Loan retention assumption

user:GraemeL and user:Chuck1962 (who is presumably the same as the anon editor user:136.2.1.103) have been repeatedly inserting and deleting the text below. Rather than continuing the revert war, let's discuss the proposed addition here for a while and see if we can work out the objections and concerns. Rossami (talk) 17:43, 8 September 2005 (UTC)

Loan retention assumed to equal loan pay-back period
Another problem with the APR calculation is the assumption that an individual will keep a particular mortgage loan until it is completely paid off resulting in the up-front fixed closing costs being amortized over the full term. The usual pay-back periods are 30 and 15 years but how many people keep the same mortgage that long? Not many, because the odds someone will either refinance or move before the loan is paid off are very high. Computing the APR over the full loan term deflates the apparent cost of the loan, making it harder to decide if it truly makes sense to refinance an existing mortgage. An APR calculator should allow the user to enter a loan retention period or time-in-loan period to more fully gauge the cost of the up-front fixed closing costs.

• A mortgage APR calculator that solves Loan Retention Problem mentioned above.

• The reason I was reverting the edits was that I considered them linkspam. The anon user was linking to an individual realtors site and the page was very broken on anything but Internet Explorer. There also seem to be links to working APR calculators already and I don't think the article benefits from having more of the same. I think I remember adding a spam1 to the talk page of the user/anon IP and also commented on the page being broken. Putting this on watch to follow the discussion. --GraemeL ^(talk) 17:56, 8 September 2005 (UTC)

Chuck1962 Responds

I would like to thank GraemeL and Rossami for the warm welcome they have given me on my first attempt to contribute content to wikipedia.org! Yes, you were right, I am a spammer of the most monstrous proportions (a realestate agent's website from Ann Arbor, Michigan might make spam fodder out of about 0.045% of your user base!) Hell, I don't even own a bank so where did I get off thinking I could educate others in the arcane world of Annual Percentage Rate calculations! My proposed changes just don't add up to the high standards of the commercial links already on the page that are being given a free pass(http://www.mortgages-loans-calculators.com/calculator-mortgage-apr.asp)! I especially liked the trudging through the instructions from the OCC to download and try their APR calculator. Hell, after about 15 minutes I was actually able to run their bloated, over-engineered product and conclude that it didn't address the issues you so generously censored from my edits!

The comments from GraemeL were particularly fun and just filled me with warm fuzzies. For example, GraemeL claims that my lame website doesn't support non-windows browsers but fails to mention that the APR calculator at www.mortgages-loans-calculators.com assumes a java plug-in that is geared toward Windows IE and may not be readily avaliable on non-Windows browsers (It wouldn't run on my version of Mozilla.) He also claims the good folks at wikipedia.org don't need another APR calculator (GraemeL's non-myopic, penetrating, well researched views are o-so appreciated---I'm sure he's had to spend plenty of time trying to compare different rate and closing cost combinations from different lenders on his mortgages!)

The fact of the matter is that my APR calculator was written with the needs of mortgage borrowers in mind because I personally have run into the problems my calculator seeks to solve. Check it out for yourself, most of the APR calculators on the web are offered by Lenders or Mortgage Brokers; that is, people who are trying to sell you a loan. Furthermore, I have yet to find another APR calculator that lets one select a loan retention period shorter than the loan term. This feature allows one to find out what the pay-back period for the closing costs is or if it makes sense to re-finance an existing mortgage.

I will end by pointing out that the over-all jist of the APR calculation article is to not simply define its most prominent feature, but to place heavy emphasis on the real and serious shortcomings of it from a consumer point of view. The over-all direction of the article is pro-consumer information anyone involved in securing a mortgage will inevitably become caught-up in. My additions most certainly strengthen that direction and would certainly be appreciated by someone looking to either re-finance or purchase a home.

All of the testing I did was under Windows. Your page renders correctly under IE, but the images are all broken on the three other browsers I tried. This is probably something to do with the HTML as your server appears to be sending the correct MIME type for them. I would normally do enough digging to present you with a fix for your problem, but the use of frames has been depreciated for several years and I would have to re-learn the markup.

You have a fair point in that Java is no longer installed by default on Windows machines and that particular link may present problems with people having to go through the install of Java to get it to work. However, Java is available for pretty much every platform that I have worked with, so people not using Windows shouldn't have problems accessing it.

Would suggesting that you supply a link directly to the calculator (framed or unframed) rather than the home page help to bring this dispute to a conclusion? --GraemeL ^(talk) 12:36, 9 September 2005 (UTC)

Copied from User talk:Chuck1962

Good evening. I'm sorry that you took my comments as hostile. I actually don't have strong feelings one way or the other about the addition you proposed. I merely would prefer that the dispute be resolved through discussion. On Wikipedia, that generally happens better and more completely when we discuss concerns on the article's Talk page than when we make competing edits to an article. When two editors acting in good faith start repeatedly undoing each others' edits without explanation, we call that a revert war.

I certainly understand your comment about the weaknesses of some of the existing links in the APR article. I may have even been the one who added that link in an early draft of the article. Corrections or improvements are always welcome. We do tend to defer to "impartial" sources because we've had problems in the past with wikispam. The OCC's APR calculator may have lots of shortcomings but no one can accuse them of having an ulterior motive. If you know of a source for a better traditional APR calculator, I for one would encourage you to replace the OCC link.

I also think I understand your comment about the shortcomings of the traditional APR calculation. It's an interesting correction. Can you provide an independent source for your analysis. The difficulty that we run into is that Wikipedia has a strong policy against original research. We've found that to be an essential control in our quest to stay true to our goal - the creation of an encyclopedia. (Note that the proscription against original research is not what many people assume from the name. I encourage you to read the full article.) If this is your personal analysis and original thought, our policy says we can't keep it in the article. On the other hand, if you can provide an independent citation for your analysis, then it is probably appropriate to keep in.

Lastly, I would encourage you to be patient with folks like GraemeL. Wikipedia really does have problems with serious spammers and we depend on folks like him to volunteer to patrol and keep them out. They see so much abuse that sometimes it's hard to remember to assume good faith. When mistakes happen, though, we can generally work them out through discussion. Thanks for your patience. I hope you stay and continue to contribute. Rossami (talk) 04:26, 9 September 2005 (UTC)

I'll cite as my sources the text book "Principles of Engineering Economy", 8th Edition by Grant/Ireson/Leavenworth, ISBN 0471-63526-X; copyright 1990 by John Wiley & Sons, Inc. Also, the existing link on the APR page for efunda (ie, http://www.efunda.com/formulae/finance/apr_calculator.cfm). The method is pretty standard for calculating an effective interest rate from a series of debits and credits (the cash flow diagram.) I learned this method in a graduate level course on engineering economics. Believe it or not, it takes one or two semesters of college calculus to understand the solution to the interest rate problem because no closed form solution is avaliable and numerical methods must be used.

While the method for calculating the effective rate of the loan is standard, the fact that I am offering a calculator that lets the user effectively select the payback period for the closing costs is unique. I say this because I have trolled the net looking for something like this and have been unable to find another site. I would hope that this fact does not exclude this contribution since it is a mathamaticly verifiable fact that paying off a mortgage sooner than the original loan period will increase the effective APR if closing costs were paid at the loan origination (precisely the thing I was taught to do in my class.)

Here is a real-world example of how my mortgage calculator could help both an honest loan officer or broker and a consumer. Say a young professional is living in a condo with a 30-year, $150,000 mortgage at 6%. Now say the loan agent at the bank where the loan was originated two years earlier wants to sell a new loan at 5.75% with $2000 in closing costs. The question is, does it make sense for the borrower to agree to the new loan? The answer hinges on how long the borrower plans on staying with the current mortgage. The full-term APR is 5.8721% but the four year APR is 6.1314%. The borrower in this case would have to keep the new mortgage for at least 81 months or six years and nine months to realize a savings which is not very likely given the fact that condo owners tend to not stay in the same location for more than five years. An honest lender would realize this and wait for interest rates to fall further before making the sales pitch but a dishonest lender would hype the full-term APR to try and close the deal.

If you look at my last edits, you will see that the link goes directly to the mortgage calculator and not the home page for my wife's site. I hope this helps!

Chuck1962

Thanks for keeping on top of this Rossami, I do try to assume good faith and often pass over removing links where I'm in doubt over the intentions. This one ,originally going to the home page, just struck me as an attempt at linkspam. That said, Chuck1962's last edit (the one that you reverted) seems like a link that I would have no problems with. The link was direct to the calculator (http://www.aysel.com/mortgage.php).

To chuck; If you have the time and inclination, you may want to re-write the pages on the site to remove the frames and include the navigation on each page. This would allow you to link straight to the calculator, but still leave the site navigation links visible. --GraemeL ^(talk) 14:17, 12 September 2005 (UTC)

Topics from 2006

A Small Point concerning RESPA

a small point: it is a violation of RESPA for a lender to require a borower to use a specific closing agent (attorney or title agent or otherwise) It is a small distinction but technically it is against the law to REQUIRE it. Lenders will usually assume that you are willing to work with their preferred closing agent it is true. Thanks - Ryan -[70.176.77.27 00:14, 7 July 2006]

More please

I'd like to see some more formulas and examples on the main page for this subject. I'd always assumed that APR was what would end up outstanding on a borrowed/lent sum at the end of a year but it seems that what I was thinking of was the "effective annual rate". It appears that if you borrow money at 10% APR, you pay differently if the interest is calculated annually, monthly, or weekly. I am pretty strong mathematically but this all seems a bit odd to me. I think this is something that Wikipedia could really make a strong contribution to clarifying for people. Pictures would be nice :)

You're thinking of compounding of interest which is generally not applicable (at least in the US). Interest is rarely, if ever, capitalized on consumer loans and so an interest only loan that pays DAILY will pay the same in a year as an interest only loan that pays annually (just to illustrate the extremes). APR is an attempt to provide an illustration of the impact of fees versus rate on the amount paid by the borrower. --Laxrulz777 22:01, 28 August 2006 (UTC)

(edit conflict) The point of APR is to standardize the answer regardless of the interest timing. That's what the article is trying to describe in the "Rate format" section. 10% compounded annually (at the end of the year) is the same as 9.091% compounded annually (at the beginning of the year) is the same as 9.569% compounded monthly (end of month). All three of those will create the same amount due at the end of the year. APR is an attempt to cut through the advertising jargon and to create a single, intuitive measure. (Thinking about it, "Rate format" is not necessarily the best header for that section.) In this regard, APR attempts to achieve the same end as the effective interest rate. APR attempts to go further by also including the effects of one-time costs and fees associated with the loan.

Unfortunately, we can not provide an equation for this measure because no universally-accepted formula exists. The EU and the UK have attempted to standardize this equation but so far have been unsuccessful. Both of those algorithms still allow discretion in the calculation. As of Oct 2005, the EU had (another) proposal on the table for harmonizing the calculation but I never heard whether it was implemented. Rossami (talk) 22:51, 28 August 2006 (UTC)

I think it's important to note that the concept of compounding interest charges on the loan side is a concept that is completely foreign to the US market (I do not know if this is true in the UK). Even in the credit card industry, where interest & fees are capitalized monthly, the minimum payment requirements create an environment in which APR is equivalent to note rate. The only thing that makes APR <> Note Rate is origination fees (included as rate adjustments) and origination costs (included as principal adjustments that inflate interest slightly). --Laxrulz777 12:59, 29 August 2006 (UTC)

USPOV

I'm putting in a USPOV note. The definition at the beginning of the article, which I do not understand, appears to be using a "monthly interest rate". The example calculation doesn't even give a precise number.

The EU actually gets this one right: the EU definition is what an annualised percentage rate is. It's very simple: if you give $100,000 to a bank that compounds interest continuously at a rate of x% p.a., and you take out a loan of $100,000 with an APR of x at another bank, the (included) payments will cancel out exactly.

That's the gist of it; that the US gets the definition wrong (apparently?) should be a note relegated to a slightly later point.

Details about how APR is criticised because it wasn't made clear enough which payments to include or not to include in its calculation are a relatively minor issue, to be honest. I don't think the article should be giving them quite as much weight.

RandomP 15:00, 26 September 2006 (UTC)

I'm sorry that you don't understand the definition. We should fix it. The example is not using a "monthly interest rate" but I can see the confusion. Rossami (talk) 18:47, 26 September 2006 (UTC)

I've actually gone and found the legal texts, and they are no less confusing :-) There is no way what is described in the US documents, for example here, matches either the definition in the article or the EU definition. The EU definition is, by the usual economic assumptions, the right one. I can thus conclude the US definition is wrong. RandomP 19:28, 26 September 2006 (UTC)

Boy, I really hate it when people interweave comments. It makes the discussion far harder for future readers to follow or to join in. But now that we've started, I suppose we have to finish the thoughts.
I will certainly agree that the legal texts are confusing. That's why they are clearly linked in the respective sections of the article but why we don't try to simply regurgitate them. I believe the problem in this case is that you found the US definition for calculation of APR for open-end credit. The opening paragraph of our article is instead attempting to describe the calculation for closed-end credit (which can be found here. Despite what it looks like when you try to read the FDIC's page, closed-end is the simpler and more intuitive case.
Our example also uses the simplifying assumption that the loan for which you are calculating APR is fixed rate and has all the one-time costs paid at the front. Why? Because that's the kind of loan that most consumers are familar with. The EU and the US regulations allow for the more general case where payment streams can be almost completely variable but we should not be trying to explain that level of complexity in the opening paragraph. When you apply those simplifying assumptions to either the full US or EU algorithms, you will get the same answer. In fact, if you look at Section 8 (General Equation) of the US rule for closed-end instruments, the equation resolves to exactly the same calculation used in the EU regulations.
That said, if you're sure that you've found an error in our explanation, fix it. But please stop saying that the US definition is "wrong". The several hundred banking regulators and thousands of bankers who use it successfully would appear to disagree with you. Rossami (talk) 00:29, 27 September 2006 (UTC)

But I'm going to have to disagree with the rest of your comment. The US definition is not "wrong" and the EU definition is not "right". The goal in both jurisdictions is basically what you describe in your second paragraph - a single interest rate that can be consistently and fairly compared across vendors. So far, that goal has been unachievable in both jurisdictions. Rossami (talk) 18:47, 26 September 2006 (UTC)

Per what I said above, it seems, alas, the US act uses an incorrect (but easily calculable) approximation to the annualised percentage rate; the EU directive (which is considerably younger, and can safely assume everyone has a spreadsheet) uses the correct definition of annualised percentage rate.

Keep in mind there's a difference between the concept of APR and its legal definition - I think it's more important we get the concept across, while currently the article reads more like a "how do I choose my loan" guide. Wikipedia is not a "how to" guide, and we should not get bogged down into details.

The two legal definitions should not just be judged by how well they perform their "goal" of making prices comparable, but also by whether they do what their name says. The US one doesn't. The EU one does. RandomP 19:28, 26 September 2006 (UTC)

See above. I strongly agree that we should be teaching the concept first and the legal definitions second. That's why the article is organized the way it is. I don't see how you are interpreting it as a "how to" guide. The closest I can get is "how to interpret an APR" - and that's a pretty reasonable encyclopedia topic. Rossami (talk) 00:29, 27 September 2006 (UTC)

The EU regulators provide an apparently more precise algorithm for calculation while the US regulators provide slightly more specific guidance on which cost components should be included in the calculations. I say that the EU algorithm is only "apparently more precise" because 1) the EU equation is surprisingly difficult to solve for APR without resorting to heuristics, 2) the EU equation can only be applied to closed-end credit - applying it to open-ended credit instruments such as credit cards is problematic and 3) the EU regulations still allow some discretion in the time period component of the calculation. All three of those factors allow discretion into the equation and can result in slightly different answers even when you have identical cash streams. US regulators attempt to duck the problem by defining the output without specifying the calculation. But since US bankers are still faced with the same choices, you get the same variability of result. Rossami (talk) 18:47, 26 September 2006 (UTC)

As for your objections to the EU definition:

1) is irrelevant - virtually every office worker these days can operate a spreadsheet, and that's all that's needed.

2) there's no problem here, that I can see. you just have to specify the period for which you calculate the APR, and make a note that you assume interest rates remain constant,

3) can you provide examples of this?

Sounds interesting, and certainly a valid point. How much discretion there is in the calculation needs to be pointed out.

RandomP 19:28, 26 September 2006 (UTC)

1) is not irrelevant though it is perhaps overly subtle. For the equation to be solvable directly, you have to be able to mathematically reformulate the equation to APR = something. Except for the simplest of scenarios, that equation is extraordinarily complex. Spreadsheet users solve it through iteration instead. Set up the cash flows and then change the value of the APR cell until the result gets arbitrarily close to zero. Iteration is a very useful heuristic and will produce a valid approximation but it is still an approximation.
I'm afraid that you've brought out the mathematical purist in me. And to be fair, that criticism applies equally to the full calculations used for US closed-end credit.

The difference for calculations between open-end and closed-end credit is significant because of the way that finance changes are normally applied. On an auto loan, your origination fees are almost invariably paid up front. In a credit card loan, finance charges may be charged up front, each period or on the basis of specific actions. If you can fully define all your assumed transactions, the EU algorithm works. But the more I think about this, the more I'm convincing myself that the opening article doesn't I've written and rewritten my response to this section a dozen times already. I need to withdraw the comment and think about it some. When I finally figure out what I'm trying to say, I'll reply below. Thanks for your patience.

3) you can test for yourself. The EU allowable periods are a) 365 days (366 days for leap years), b) 52 weeks of 7 days (364 days regardless of whether it is a leap year or not) or c) 12 equal months of 30.41666 days (364.999 days again regardless leap year). For small or short loans, the distortion will be small - probably within the limits of rounding. But for longer loans, the distortion can become evident. Rossami (talk) 00:29, 27 September 2006 (UTC)

1) Uh .. agreed that it's an approximation, but so's taking a square root, in most cases. "Bringing out the mathematical purist", of course, is something I like to do, but I can't really follow your argument that the absence of a closed-form solution for the EU APR counts as an argument against it. (And it's not that complex, really. You've got to find a zero of a high-degree polynomial, sure, but that's hardly a terribly-behaved problem (in this case, you know a priori that there is a unique solution!).

3) oh! er .. I'm doubting your statement. Whatever the distortion is, it will balance out after a year, at most. (Wouldn't it?) I'd guess there's a "good" historical reason for that: some EU countries still use a traditional system in which, to make things easier (in the pre-calculator days), the year is made to consist of 360 days, 12 months of 30 days each. You thus get interest days (most days), no-interest days (in months of 31 days) and double-interest days (in February). The latter would seem very unfair, but as wages are also usually paid by the month, February is actually a fairly good month ...

I expect the EU wanted to make it easier for those countries; I think it would be rare for this distortion to amount to more than rounding 16.46% APR to 16.4% APR rather than 16.5% APR, and that national law will in most cases limit lenders further. However, I haven't done the maths, and I'm not going to check any significant sample of the 27 legal codes one would now have to consider (there's no way I'd be done until January) RandomP 01:29, 27 September 2006 (UTC)

The issue of which cost components to include can not be considered minor. Normalizing for one-time costs is, after all, the primary purpose for which the APR was created by the various regulators. When vendor A decides that application fees will be included and vendor B decides that they will not, the results are no longer truly comparable. Depending on the relative magnitude of the discretionary components, that can introduce a large or a small bias to the result. Now, we might assume that regulators think that the bias is small enough that APR is still a useful metric for consumers (otherwise, why would they still require it to be calculated and advertised) but it introduces enough variablity into the equation that regulators on both sides of the ocean still tell consumers to read and evaluate all the cost components. They recognize they have been unable to fully define which cost components must be included and that therefore APR is an inherently incomplete metric. Rossami (talk) 18:47, 26 September 2006 (UTC)

Another valid point, but I'm a bit confused by the fact that a bank would a) choose to include certain costs that a competitor doesn't b) not sue that competitor over not including them. After all, it's fairly obvious that banks would exclude everything they possibly could, in order to achieve a lower legal APR ... RandomP 19:28, 26 September 2006 (UTC)

Absent very clear regulatory language (and we've established above that the regulations are anything but clear), the decision about what they can or can not exclude is, in part, a risk assessment. If I include factor A, I will have to advertise a higher APR and have an x% chance of losing $y of new business but if I exclude it, there is a c% chance that some regulator will disagree with that judgment call after the fact and may impose a $d fine. Banks may reach different conclusions on which factors to include based on their risk tolerance.
The evaluation is also complicated by competitive secrecy. Is Bank B's APR lower because they charge less interest, because they've negotiated lower on-time fees or because they've chosen to exclude some factor? Bankers at A do not necessarily know which factors Bank B includes. Unless you have your employees take out loans with the competition or practice some other form of industrial espionage, you won't know for sure.
Regulators periodically try to sort this out with "definitive" lists of factors but then the business changes a bit and their list is out-of-date. This is a perennial problem for regulators in all fields, not just banking. Rossami (talk) 00:29, 27 September 2006 (UTC)

By the way, even though I agree with your general statement of the goal of an APR in your second paragraph above, it is wrong on several subtle but critical points. Interest is not compounded "continuously at a rate of x% p.a.", it is compounded at the note's base period and then normalized to an annual rate. You would also have to narrow your example down to "a loan of $100,000 with an APR of x" and for the same duration. Rossami (talk) 18:47, 26 September 2006 (UTC)

Your criticism of my second paragraph is invalid; please consider rereading it (the paragraph, not the criticism). Note that "interest compounded continuously at a rate of 5% p.a." means that after a year, you will have accrued 5% interest; there's a difference here to "5%/year", which can mean something else. RandomP 19:28, 26 September 2006 (UTC)

We may be miscommunicating here because of a technical point. When you talk about "continuous compounding", to me that has only one meaning - that interest is being calculated on infinitely small periods. See Compound interest#Continuous compounding for the equations. 10% interest compounded annually = 9.569% annual interest rate compounded monthly = 9.531% annual interest rate compounded continuously. Continuous compounding is very rare these days. Had you not used the word "continuously", I wouldn't have said anything. But you seem to know more know more than average so I thought it was safe to be technically precise. Sorry if I created more confusion than I cleared up. Rossami (talk) 00:29, 27 September 2006 (UTC)

That's correct (though I disagree that continuous compounding is very rare these days - in fact, I'd imagine that the whole point of the APR legislation was to get lenders to move back to simple models), except for the interest rate comparisons (which is just different terminology, but still). 10% p.a. compounded continuously results in the same situation after a year as 10% p.a. compounded annually (feel free to prove me wrong; however, I'd be extremely surprised if majority usage weren't still the way I remember it. Not that it matters with interest rates as low as they are today :-) ).

I'll try replying more later, probably tomorrow. Thanks for taking out the uspov template (and the rest of the edit!) - while I think there are still issues here, the warning message it generates is way too stark. I shall stop using it.

RandomP 01:07, 27 September 2006 (UTC)

Topics from 2006

Questions

Okay, now let's end this interweaving of comments and try to fix the article. During this discussion, I have convinced myself that our opening example is at best only a very rough approximation under any of the allowed jurisdictions. So:

1. How do we explain the general concept without dragging readers too quickly into very complex spreadsheet-based algorithms?
2. Since the US general equation for closed-end instruments is the same as the EU general equation for their covered instruments, should we open with that as our general case?
3. When and how should we discuss the intricacies of those calculations for open-end instruments?
4. The "Failings" section already tries to talk about the problem of discretion in making APRs difficult to compare. How do we make that point clearer? Rossami (talk) 00:29, 27 September 2006 (UTC)

---

Short answers:

1. By explaining the concept, not giving an algorithm for calculation.
2. Yes; the EU definition is (I'll try to put this another way) the one most amenable both to economics and to price comparisons. I also think that "this is the interest rate you would have to earn on the money you borrowed to make it worth taking out this loan" is fairly easy to understand even for non-specialists.
3. I don't understand what those intricacies are; I'll try to read up on it. As far as I know now, the most important issue is that with the vast majority of open-end credit deals, such as my credit cards, the APR does not depend on how I pay back my debt, assuming the interest rate remains constant.
4. Counter-question: how can we trim down the Failings section to one or two paragraph, for everything but regional (US) details?

My suggestion:

• start with the EU/economics formula
• move all region-specific details (what is and what is not included in the APR for US mortgages, for example) to the very back of the article
• provide several clear examples, using the "purified" EU definition (i.e. actual time rather than 365 days/year or 52 weeks/year time).
• remove without replacement statements such as "The calculations can be quite complex and are poorly understood even by most financial professionals"
• merge with Annual percentage yield, which is the same thing with a flipped sign (and, again, a weird formula that gets things slightly wrong).
• redirect "effective annual rate" here
• merge with "effective interest rate"
• refactor things between compound interest and here.

The whole subject area on WP is, to be honest, a bit of a mess.

RandomP 19:52, 27 September 2006 (UTC)

I agree with the "My suggestions" of RandomP above. To my opinion everybody should decide for himselve how they compare loans, and savings accounts. People are free to choose the EU formula or the US formula. As a mathematician I recommend the EU formula, by the way.

The problem is that the APR is difficult to compute, especially with the EU formula. We should explain something about how the EU formula is solved. For instance that for equal payment periods the formula is simplified with the geometric sequence formula. There are calculators that solve the EU formula for a number of special cases. For instance equal periods/equal payments, equal periods/equal debt reduction, transaction costs in the beginning, transaction costs in the end, etc.

We have links to calculators that compute the US APR. We should also have some links to calculators that compute the EU APR. I recommend the following two links: Saving money with transaction costs and Compare repayment schemes of a loan

Ruerd 17:59, 18 November 2006 (UTC)

Comments on America-centric above, and on proposed merger

Part of the problem is that this specific terminology ("annual percentage rate") is either a U.S.-specific terminology, or one used with a specific meaning in the U.S. and if used outside the U.S. not necessarily the same specific meaning (it might be a more general meaning, or it might in some cases be a specific but different meaning). Similarly, IIRC the Canadian terminology is "effective annual yield", again with a specific--but different--method of calculation. Looks like annual percentage yield might be another of those terms sometimes used to identify a particular method of calculation. Don't remember the Canadian details, but think it somehow it gets to be twice a half-year rate under a certain method of calculation, something I haven't seen in the articles here.

It probably wouldn't be a bad idea to combine them, but somebody needs to make an effort to both explain this specific-meaning-within-specific-geographical-locations phenomenon and separate out both the location-specific names the various details of the calculations. Gene Nygaard 20:14, 27 September 2006 (UTC)

My personal opinion is that Wikipedia is not a dictionary, not even a legal dictionary, and mere legal definitions are thus of little relevance to us, per se. I'd thus suggest de-emphasising the legal definitions. Note that the meaning of the word does not change based on geographical location - it's merely the legal definition that changes based on jurisdiction, and there are quite a number of those to consider, not just English-language jurisdictions.

(My personal opinion still, but when you're finding it hard to write about non-anglophone countries, stop. you're writing a dictionary entry, not an encyclopedia article, and have probably chosen the wrong title).

So, apart from my personal opinions, I think it would make sense to go into legal details in a "legal details" section, or incorporate criticism specific to one jurisdiction and call the section "by jurisdiction", or something like that.

More important though might be to collect the legal definitions, and their sources, in a readable format; at least the US acts just aren't, as far as I'm concerned.

I'm going to get back to this, probably tomorrow.

RandomP 00:08, 28 September 2006 (UTC)

It's the mathematical details that are the most important, and they can best be sorted out by paying close attention to to the linguistics details. The linguistics are in large part determined by the specific language used by the laws of various jurisdictions, but that doesn't mean that they aren't important. And that's what keeps any of these from being what you denigrate as a dictionary definition.

I'm starting to think that merger is a bad idea. Better to keep separate entries, and spell out in them where that terminology is used, so that links from other articles can link to the proper meaning, the proper mathematics. Connect up and summarize the individual articles in either a general interest rate article, or one for interest rates expressed on an annual basis. Gene Nygaard 05:37, 28 September 2006 (UTC)

Note that in many cases such as the particular terminology used here, the legal definitions often drive the usage, not the other way around. In many jurisdictions, lawmakers choose not only a specific method of calculation but also specific terminology (maybe with a little flexibility, but not much) required to be used by sellers/lenders and the like and require that specific wording to be used in advertising and legal documents. Then that precise usage also becomes more general, even in cases not specifically covered under the requirements of the law. But in a different jurisdiction, that specific usage may remain quite unfamiliar. Gene Nygaard 13:59, 30 September 2006 (UTC)

Legal term APR

I've been thinking about this (among other things), and I'm now thinking that the legal term APR (or annual percentage rate, though given the widespread use of the acronym, this might fall under the NATO exception) should have an article, like annual percentage rate (US law). If the legal term is what we're writing about, we should not pretend there is more to it than that.

It's true that legal terminology can, of course, become a form of linguistic prescription (and historically, it usually has been).

I'm not quite sure what you meant, by the way, when you said the mathematical details are most important; IMHO, the most important thing is the general concept, which is expressed most easily mathematically; details of approximating algorithms, such as the various US ones, appear largely irrelevant to me.

RandomP 00:22, 1 October 2006 (UTC)

There is no perfect method. They aren't, strictly speaking, approximations of anythig. All that is necessary that we chose a reasonable one, and different people have made different choices as to what is reasonable. One of the biggest problems, of course, and one which can quite legitimately be dealt with differently in different places, or for different purposes in one place, is the vagaries of our calendar, with not all years having the same number of days, months having from 28 to 31 days, etc. Gene Nygaard 00:47, 1 October 2006 (UTC)

I hope I have understood the discussion. The term annual percentage rate refers to a method for comparing financial products, such as savings accounts, mortgages and loans. This term refers to a mathematical concept. The problem with the APR is that it is difficult to compute values using the mathematical definition, at least for consumers. So consumers have to trust the values banks and mortgage companies provide for the products they offer. Lawmakers are trying to protect consumers from manipulations in these computed values. They have made rules for what exactly needs to be computed in order to standardize and facilitate easy comparison between the computations of banks and loan providers.

I think that the mathematical concept drives here the legal definitions, not the other way around. A consumer can take a calculator from the internet and make his own comparison between financial products of different providers.

I think we should have one page for Effective_interest_rate explaining the mathematical concept. This page then can then refer to a page with the legal definitions in different countries. This second page should explain the fact that the purpose of the legal definitions is just a way to protect consumers from making the wrong comparisons. The terms "annual percentage rate" (US) and "effective annual yield" (Canada) can be linked to this second page. Furthermore I agree with the remark above that the US definition is not very clear, so we could try to improve the explanation.

Right now "effective interest rate" is linked to Compound_interest, which is something different. So this link should go.

Ruerd 10:23, 19 November 2006 (UTC)

A few thoughts in response. First, lawmakers have not yet been able to define exactly what needs to be computed. While everyone agrees that the concept ought to include the full costs of borrowing (or lending), in every jurisdiction we've researched so far there is a degree of discretion about what components of cost should or should not be included in the calculation.

Second, I'm not sure that we can say that a mathematical definition exists independent of the legal definitions. This is not a term that is discussed or defined independently of the legal definitions. It did not, for example, exist in standard financial texts prior to the laws requiring the calculation of this rate.

Likewise, effective interest rate has no standard definition that I have been able to find independent of the legal definitions. We should be cautious about making changes on the strength of our own interpretations. I would much prefer to use the definition as expressed in some specific reliable source. I notice that you've changed the redirect's target from compound interest to this page. I'm not sure that's any more correct but have never been able to find a definitive source either way for that term. Rossami (talk) 22:56, 19 November 2006 (UTC)

Lawmakers have just tried to express the mathematical concept in their laws rather than the other way around.

If you have a loan (or a savings account) and you borrow (or save) money for a specific amount of time and you want to express costs of borrowing (or the income from the savings account) as an fictitious annual interest rate, i.e. the rate you effectively pay (or get), then the mathematical formula's for computing this rate start with exactly the EU formula. I think the term APR is more closely connected to this effective interest rate concept than the term "Compound interest", so that's why I changed the redirect. At least one other language than English use a term that literally means "effective interest rate".

I have also made some additions to the text to make the relation between the term APR and the concept of a effective (fictitious) interest rate, including the total cost of borrowing (or income from saving) clearer.

Ruerd 16:55, 20 November 2006 (UTC)

merger

Object to merging the pages based on how users are searching for the terms. Home buyers look for APR as this is what they find quoted by banks. Users would not think to look for the other terms —68.3.139.57 (talk • contribs).

Merger doesn't mean lack of access, in many cases it means more access, since the reader is exposed directly to the broader context. Redirects are the most common result of merger for the merged from articles. --Bejnar 19:32, 30 December 2006 (UTC)

• I agree that merger would be appropriate, especially with an appropriate overview distinguishing the terms. --Bejnar 19:32, 30 December 2006 (UTC)

Topics from 2007

Proposal: Undo redirect from effective annual interest rate

Effective interest rate currently redirects here, but doesn't (IMHO) disambiguate well. Effective (annual) interest rate is a pretty well defined term in mathematics of finance (it is any rate converted into the equivalent with annual compounding). APR is - from the discussion here - dependent on what costs are included and the regulatory regime. I would like to undo the redirect to here and have a shorter article there with clear disambiguation. Thoughts/reactions?--Gregalton 00:19, 8 February 2007 (UTC)

No response, so I'm being bold and assuming there is a massive surge of support for this proposal.--Gregalton 07:46, 15 March 2007 (UTC)

Add some detail

I've skimmed over the discussions below, and wanted to add this...

I came to this page as a first time home buyer (in the UK); I understood APR was a standardised measure for comparing loans/mortgages etc. What I wanted was to know how it was calculated, and to this degree Wikipedia has failed.

Not only is there no proper details on how to calculate the APR (a couple of poor examples that don't explain themselves are worse than having nothing, IMHO), but there are links only to simple calculators.

In the UK many mortgages have a 'low start period' where the repayment and interest rate for the first, say, 3 years is lower, and then increases afterwards. I wanted to know how the APR was calculated on this, and came away only more confused.

Why can a section not be added on UK/EU and another for US, to show how in most cases the APR is calculated? —Preceding unsigned comment added by 80.6.43.252 (talk) 21:26, August 29, 2007 (UTC)

You are not the first reader to come to this article with the mistaken impression that APR is a standardized measure or there is one simple calculation for APR. The article tries very hard to explain that's not the case. Regulators have tried to standardize the term but so far they have been unsuccessful. And it's not just a US vs EU problem, either. Even within one country, APR is not always calculated the same way. In your specific case, the EU standardized some APR calculations but allowed some discretion in the costs to include and excluded mortgages altogether. That means the individual lender has some discretion. In many cases, APR is still more of a marketing term than a hard finance term. The best we can try to do is explain the general concept and its major weaknesses.
Still, if you walk through the EU formula that is given in the article (something that I wouldn't recommend attempting without a good spreadsheet program), you'll get a close approximation of the APR across most scenarios - including yours. Rossami (talk) 23:29, 29 August 2007 (UTC)

The APR calculations look wrong

But I agree with some of the earlier commentary that this may be because whoever did the calculations didn't completely explain how he did them. I poked around and looked at calculators and did the math from scratch and all of these things lead to the same conclusion, which is that there needs to be a very clear step by step explanation of how one would get an APR calculation, with final results.

I am going to add what I believe is an accurate example and remove the old one. Obviously, feel free to correct me if you think I'm wrong.

Pygmy goat 23:51, 6 September 2007 (UTC)

1. Pygmy: I can't find your example. 2. On this talk page two people are asking how the APR examples in the Wikipedia article were created or how they can be verified. Well, about a year ago I added some of the examples on the Wikipedia APR page. I think I used the following calculator for these examples: Loans: compare different types of repayment schemes. This calculator solves the Netherlands mortgage formula for either S or APR or A_k. I wrote this calculator myself after improving the description and the formulation of the EU formula in the Wikipedia article and adding the Netherlands formula as well. As a mathematician I find the EU formula the best way to define the APR. Some other calculators based on the EU formula are listed on this page.

Ruerd (talk) 16:26, 13 January 2008 (UTC)

Improper calculation

The summation at the bottom of the PMT calculation is meaningless. $({\sum _{l=1}^{n}r^{n}})$

The variable of summation is clearly $l$, but it is never used in the expression. I believe the author meant to put ${\sum _{l=1}^{n}r^{l}}$ --Yoda of Borg 21:37, 17 September 2007 (UTC)

Percentage Rate

The article states

"For example, $100,000 mortgaged (without fees, since they add into the calculation in a different way) over 15 years costs a total of $193,429.80 (interest is 93.430% of principal), but over 30 years, costs a total of $315,925.20 (interest is 215.925% of principal)."

While this is a pretty good example, I do feel that the person who wrote this should have included the headline interest rate s/he used to calculate these amounts

Jonewer 20:40, 14 November 2007 (UTC)

I second that, Jonewer. I was just about to say the same thing.

--68.253.53.130 (talk) 21:58, 20 February 2008 (UTC)

Topics from 2008

Assessment comment

The comment(s) below were originally left at Talk:Annual percentage rate/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

I have rated this article as a C-class for WikiProject Finance because while it provides a decent amount of information, it still requires more external references and some general clean-up. --Aka042 (talk) 01:25, 25 January 2009 (UTC)

Last edited at 01:25, 25 January 2009 (UTC). Substituted at 14:14, 1 May 2016 (UTC)