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^{edit · history · watch · purge} 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)

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[edit] Statutory EU formula - minor point

Would it not be better to use a different letter to represent the powers on the two side of this equation? For example, if the first advance occurs on a different date from the first repayment, then t₁ takes on a different meaning on the lhs than on the rhs. Should one or other be changed to T or t', or something? —62.77.181.1 (talk) 12:41, 7 May 2008 (UTC)

Also, I suggest removing the assertion at the end of the list of terms below the formula that t1=0, which is often not the case. —62.77.181.1 (talk) 12:44, 7 May 2008 (UTC)

No, it should not have a different letter. t_n must be identical on both sides for any instances where t_k and t_l represent the same date. If the dates of advance and repayment are different, you are merely saying that at that point, k ≠ l.
t₁ always equals zero by definition. Interest does not start until some cash flow occurs. Rossami (talk) 14:58, 7 May 2008 (UTC)

But your assertion does not make sense in the normal meaning of subscripted terms in mathematics. t₂ on the left hand side refers to the date of the second advance; t₂ on the right hand side refers to the date of the second repayment. Therefore it is clearly possible for t₂ to be representing two different numbers in the same equation. Take the example of a regular loan consisting of a single advance being repayed with three equal annual instalments, the first repayment being made one year after the advance. In this case, you have t₁ = 0 on the left hand side, and on the right hand side you have t₁=1, t₂=2 and t₃=3. You're clearly then using t₁ to represent two different things. On my second point, the EU directive defines the zero date for calculations as the date of the first advance. And, since this is not necessarily the same date as the date of the first repayment, t₁ as used on the left hand side is always 0 by definition, but t₁ as used on the right hand side is not. If one were to use, say, T_k instead of t_k on the right hand side, then the ambiguities would disappear, and one could then legitimately retain the assertion that t_l=0. —62.77.181.1 (talk) 14:22, 8 May 2008 (UTC)

That's the point. k=2 and l=2 may represent different dates but they're both on the same timeline, t. The normal mathematical convention is to use the same variable with the two different subscripts.
On your second point, you are missing the fact that this calculation can be run in either direction. The APR calculation works the same whether you are calculating a standard loan (where the first advance would be before the first payment) or calculating in annuity with balloon payments (where you might well make payments before receiving a payout). Rossami (talk) 14:55, 8 May 2008 (UTC)

I understand the calculations completely. I am unable to accept your assertion that a notation than leads to, for example, t₂ taking on two different values in the same equation is "The normal mathematical convention" and am unable to find examples of this in a reputable source in any other context than in this formula. I stand by my position on this matter. I also stand by my position that, if t₁ is allowed to represent the date of the first repayment, then it is incorrect to assert that t₁ always equals 0. I understand the different contexts in which the formula can be used, and perfectly comfortable with the possibity of negative values for t_k on the right-hand side. I merely pointed out that the EU directive defined time=0 to be the date of the first advance. Anyway, I leave the matter to rest and will not attempt to edit the main page. You are clearly knowledgable about this topic; if I have failed to convince you and the other major contributors to this article of the merits of the points I raised, then I'm happy to just let it go. (I believe this to be a technical inaccuracy in any case and don't believe that it will lead anyone who actually uses the formula astray, since they will know what was intended anyway.)

[edit] Tags

I've tagged this article with refimprove and confusing. The former tag is because the entire article is basically OR; there's only one reference given. All of the calculations, formulas, and so on are entirely unsourced. The confusing tag was added because I find the text of the page rather jumbled. To someone with little or no experience working with finance math, this article is obtuse. — HelloAnnyong ^{(say whaaat?!)} 23:12, 3 June 2008 (UTC)

I agree. I've tackled the second section. I haven't added new references yet; I just reorganized what was there. Mebden (talk) 11:36, 12 July 2009 (UTC)

[edit] Effective interest rate, APR and APY

What is the relationship between effective interest rate, annual percentage rate and annual percentage yield? Finnancier (talk) 11:48, 23 August 2008 (UTC)

http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Mathematics#Annual_Percentage_Rate Sentriclecub (talk) 17:12, 15 September 2008 (UTC)

APR = (Per-period rate) X (Periods per year)

EAR = $e^{APR}-1\,$

APR = $ln ( 1 + EPR ) \,$ ^[1]

I'm going to look more into all this for you, and will have a full report back in an hour--it looks as though neither the APR nor EAR are independent of the number of compounding periods. The best way to interpret interest rates is with calculus. It appears that the APR and EAR are dependent on the number of periods per year, which bothers me. I'll re-read everything, and will also consult my HP-10Bii user manual, 2 feet away from me at all times. While you are waiting, check out Khan academy on youtube, this guy is a bona fide expert. The finance videos he has produced are wonderful. Sentriclecub (talk) 13:35, 15 September 2008 (UTC)

[edit] Disputed section

The following paragraph was added at the top of the Does not represent the total cost of borrowing subsection back in July. I do not think that it is appropriate in the encyclopedia for two reasons.

The first sentence is factually incorrect. Mortgages do account for the length of the loan. And while an advertised APR can not account for an individual borrower's intent to prepay a loan, the basic calculations can be used by any borrower based on his/her own intent. That is not a failing of the concept of APR. Furthermore, lender rebates which are not passed on to the borrower have no bearing on the borrower's rates. Money out is money out. The rate they "qualify for" is irrelevant to the calculation of what they will pay.
The second sentence comes across more as a spam link than as proper encyclopedic content. The Lender Police article was properly speedy-deleted back in July for a failure to meet even the minimum standards of an assertion of notability. All sources about this organization that I can find are self-published (their own website or republication of press releases, for example). The algorithm described is also not independently sourcable that I can find. It certainly doesn't seem to have attracted any attention beyond the company itself.

I am removing the paragraph from the page pending discussion here. Rossami (talk) 23:31, 27 August 2008 (UTC)

APR used for mortgages lacks several factors such as length of time the borrower intends to have the loan and lender rebates that a lender may receive and not pass on to a borrower by selling a borrower a higher interest rate than they qualify for. Lender Police Effective Annual Rate accounts for these factors and gives the borrower a true account of the rate of interest the mortgage borrower will be paying during the time the borrower plans to have the loan.

I was planning on removing that section too. See below... Sentriclecub (talk) 15:44, 18 September 2008 (UTC)

[edit] Ok, speak now or your content will be deleted

[edit] Content Issues

I'm doing a clean-thru and over the next few weeks, will tackle a couple paragraphs at a time, and will delete unsourced stuff which is bad for the article (the stuff which I believe warrants the two tags at the top of the article that say this article may be confusing or unclear).

I have already tackled and finished everything above the Contents_Box. I plan to use a different formula than this one...

$p = \cfrac{P_0*r^{(n+1)}}{\sum_{l=1}^n r^l}$

because its not the best one for APR, as it is not 100% relevant. There is a better equation which I plan to substitute.

The "Failings" dominates the article and is 50% of the article on my screen resolution. I'll condense it to 3 well written, clear paragraphs (I too believe strongly in the content, i'm not defending APR, I actually have an issue that APR depends on the number of periods e.g. daily, monthly, biyearly). Also i'll keep that table, as it makes some very good points.

I plan on making a section purely devoted to UK style APR, instead of merging the two articles (as they are now) and trying to make them explained every other sentence. They are so core different, that it's easier to explain the US version one time, then make a section on the UK version. (may sound unglobal, but you'll see it's one of the reasons why the article is bad, its like talking about the Tampa Bay bucaneers and the Tampa Bay Devil rays, all in the same article, one section at a time, and trying to make it "flow" well in style, which is impossible. Just because the UK APR and US APR differ by only one letter, they are about as dissimilar as the two different sports teams.

I plan on cutting down all stuff about other types of rates. Let them be explained on their own page (main article... template).

[edit] Style issues

Seems like many different editors took turns submitting paragraphs. Look at the top two paragraphs, how I idealized the style, and texture of the should-be article.

Length I think ideally the article should be much smaller than its current size.

"In the U.S., the calculation and disclosure of APR is governed by the Truth in Lending Act (also known as Regulation Z). In general, APR in the United States is expressed as the periodic interest rate times the number of compounding periods in a year^[2] (also known as the nominal interest rate); since the APR must include certain non-interest charges and fees, however, it requires more detailed calculation."

This section of the article does not belong at the bottom of the article, but rather towards the top or maybe I'll incorporate it into the intro. These are just after a 10 minute brainstorming. Ideally, I'm going to print the article, and use red-ink like marking up a poorly written essay by a classmate who procrastinated an assignment to write a wikipedia article and did it all the night before. Ideally guys and gals, I'm going to simulate that I'm on the tv show The Apprentice and I dont want to get fired, and my assignment is to fix this article. Collaborators, please drop me a note on my talk page (I work very slow, if left to do this alone) Sentriclecub (talk) 16:05, 18 September 2008 (UTC)

[edit] Retrofit topic year headers/subpages

14-Nov-2008: I have added subheaders above as "Topics from 2004" (etc.) to emphasize the dates of topics in the talk-page. Older topics might still apply, but using the year headers helps to focus on more current issues as well. The topic-year boundaries were located by searching from bottom for the prior year#. Afterward, I dated/named unsigned comments & cut auto-signature comments.
Then I added "Talk-page subpages" beside the TOC. -Wikid77 (talk) 13:44, 14 November 2008 (UTC)

[edit] Archived 2004 to mid-2006

14-Nov-2008: I have archived 7 older topics (49%) into new archive page "Talk:Annual percentage rate/Archive_prior_talk" listed under "Talk-page subpages" at top (near TOC). -Wikid77 (talk) 15:49, 14 November 2008 (UTC)

[edit] Added nominal APR & effective APR

14-Nov-2008: I am adding the main legal terms "nominal APR" and "effective APR" (used over 20 years in USA) into the article. I was very confused reading the article, due to lack of those 2 terms, which clearly separate nominal (simple-interest rate) from effective (compound-interest+fees), according to laws in the U.S. Without those terms, the article can seem very confusing for readers using USA meanings. -Wikid77 (talk) 15:48, 14 Nov 2008

[edit] Money factor

Due to its AfD resulting in a not-delete, I've merged money factor into this article. It's a very rudimentary merge (essentially a cut-and-paste, and some minor changes) so any help on cleaning up this section would be amazing. flaming lawye r^c 01:51, 15 January 2009 (UTC)

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