Talk:Interest

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[edit] POV for neoclassical economics

I have to debate the definition of interest given in this topic. Interest is not necessitated by inflation, but inflation instead necessitated by interest. Inflation is caused by allowing the central banks to print currency for the government to use to pay off its debt _to the central banks_. (A surplus of currency makes your money worth less). Since the interest on this debt is exponentially larger than the principal of the debt all payments go directly fighting off the evil curse of interest.

I agree completely. The article in its present form is propaganda for neoclassical economics. Your explanation is basically valid, as far as I know from reading John Kenneith Galbraith and others who know the process of money supply and central banking. Islamic economics and green economics have plenty of alternatives to interest as solutions to inflation. There is no excuse for this bias in the current article. EofT

Well, printing money is one cause of inflation, but there are others, no? Martin

I have edited this page for accuracy and taken the NPOV alert off. I agree there are alternative financial systems other than capitalism and they should be written about, but as an introduction to the role of interest in capitalism, this article, as it presently stands, is a good start. mydogategodshat 22:39, 27 Sep 2003 (UTC)

"Interest is not necessitated by inflation"? This is nonsense; an economy which had inflation but a zero interest rate is simply inconceivable/impossible. "..but inflation instead necessitated by interest"? Again this is simply untrue; there have been deflationary economies with positive interest rates. As for calling the article propagands, that's bull; the article simply reflects orthodox (not just neoclassical) economic thinking. Islamic economics and green economics may have plenty of alternatives but few or none are taken all that seriously in the field of economics. User:jimg

Ultimately, the problem here is that economics is, unfortunately, easily politicized. We must remember that it is a science, and that we are obligated to accept the model that best describes reality. A lot of the problems with politicizing economics can be fixed by simply remembering that economics is not in the least bit normative. As an Objectivist, I oppose government restrictions on collusion. I recognize that collusion tends to result in gross economic inefficiencies; however, since economics is positive rather than normative that does not in the least bit mean that "economics supports the conclusion that government should prohibit--or at least severely regulate--collusion." Whether or not the gross economic inefficiencies that collusion results in are desirable or not, or whether or not the benefits outweigh the cost of prohibiting them, are purely normative value judgments and thus are the concern not of economics but of ethical philosophy.

Now, how is this relevant to the above discussion? Quite simply, it appears that the above individuals have simply found an economic model that they claim supports their pre-existing political philosophies. This is the source of their contention. If they would remember that economics is non-normative, they would realize that economic models properly have absolutely nothing to do with political philosophy, and so their approach would be less combative and more collegial--they would be interested in describing all the legitimate theories of the nature of interest (there are several, including one which I find best describes observed reality, but they are all legitimate and worthy of exposition here) dispassionately, without making shrill claims of "POV!". Kurt Weber (Go Colts!) 04:18, 31 March 2008 (UTC)

[edit] Simple and compound interest for the layman

It would be nice to have the formulas for simple and compound interest included and explained nicely. - Omegatron 15:56, Apr 9, 2004 (UTC)

Sure!

See Future value

First the nomenclature.

I - The stated interest rate, for example, 5%/year. This is not the APR (annualized percentage rate).

m - The number of periods in the time frame of I. I is usually based on a year but it could be based on any amount of time.

i - The interest rate for the compounding period which is needed for the calculation. For example, a real property mortgage is usually based on a monthly period. In this case i=I*1/12 where I is based on the normal yearly period. In general i=I/m. Also I needs to be a decimal not a percent thus it also needs to be divided by 100.

n - The total number of periods or payments. Things like mortgages usually cover multiple years.

B - The balance, for example, the balance remaining on a mortgage or an interest baring check book or savings (pass) book balance.

Simple Interest: $B_0 (1 + in) \,$

Inside the parentheses the first term, namely 1, gives back the original investment and the second term, namely in , generates the period interest and multiplies it by the number of periods.

Compound Interest: $B_0 (1 + i)^n \,$

In the compound case we have a binomial expansion where the first two terms are the same as the simple interest and the remaining terms calculate the interest on interest. Actually all interest calculations can be carried out using simple interest. Compound interest is simply a special case when the calculations can be simplified by the use of the binominal expansion.

Lets take $B_0 = 1\,$ , I = .06 and n = m and consider the case where m = 1, 12, 365 and infinity, compounding namely, yearly, monthly, daily and instantaneously. For the first three cases we can use the binomial expansion $(1 + I/m)^m \,$ . In the last case we need to modify the limit equation in the main article getting

$\lim_{m\to\infty} \left(1+\frac{I}{m}\right)^m = e^I,$

Running the calculations gives:

for yearly (m = 1) 1.06

for monthly (m = 12) 1.061677812

for daily (m = 365) 1.061831287

for instantaneously (m = infinity) 1.061836547

Subtracting one and multiplying by 100 to get the percentage interest rate gives: 6, 6.1677812, 6.1831287 and 6.1836547.

The first number is simple interest since there is only a single period. The remaining numbers give the simple interest required to provide the same value as that given compounding at .06. Thus they are the APR the annual percentage rate. In the 1960s banks were attempting to lure customers by compounding instantaneously rather than daily. As one can see there is not a lot of difference, less than a hundredth of a percent.

Mortgage Calculations:

Let B₀ be the original mortgage or opening bank balance.

Let B₁, B₂, B₃ etc. be the balance after the first, second, third period respectively.

Obviously, one can think of B₀ as the balance after the zeroth period namely the beginning balance.

P - The payment in the case of a mortgage or a deposit or withdrawal (a negative deposit) in the case of a bank account.

Now lets write down the balances. First the initial balance, the amount of the mortgage.

B₀

Now lets calculate the balance after one period or payment.

$B_1 = B_0 (1 + i) - P \,$

During the first period the initial balance has grown by the period interest and has been decreased by the first payment. Similarly

$B_2 = B_1 (1 + i) - P = B_0 (1 + i)^2 - P (1 + i) - P\,$

Again

$B_3 = B_2 (1 + i) - P = B_0 (1 + i)^3 - P (1 + i)^2 - P (1 + i) - P\,$

After n periods or payments we have

$B_n = B_0 (1 + i)^n - P (1 + i)^{n-1} ..... - P (1 + i)^2 - P (1 + i) - P\,$

B_n is set equal to zero. When the mortgage is paid off the balance is zero. Now one can solve for P the payment. Rearranging gives:

$B_0 (1 + i)^n = P [1 + (1 + i) + (1 + i)^2 + .... + (1 + i)^{n-1}]\,$

The righthand side is a geometric series where each term is equal to the preceding term multiplied by (1 + i) which is known as the ratio.

Multiplying the righthand side by [1 - (i + 1)]/(-i) gives:

$B_0 (1 + i)^n = P [1 - (1 + i)^n]/(-i) = P [(1 + i)^n - 1]/i\,$

Note: What one is doing is multiplying and dividing by -i and in the numerator adding and subtracting 1. The reason for this is that multiplying a geometric series by one minus the ratio leaves simply the first term minus the last term with the exponent incremented by one since all the other terms cancel in pairs.

Solving for P gives:

$P = B_0 [i(1 + i)^n]/[(1 + i)^n - 1]\,$

The payment can be readily calculated to the penny with a scientific calculator. Does a spread sheet have enough accuracy?

Note: B₀ is just a simple multiplier. Therefore one can do the calculation for a unit of currency such as a dollar and then multiply the result by the amount of the loan. In essence B₀ is just a scale factor. For example think of the loan amount as my dollar where my dollar is just a currency whose exchange rate is just the loan amount difference.

Now lets do some calculations. Mortgages are usually for 15, 20 or 30 years. Interest rates use to be around 9%/year and today around 6%/year. For all calculations B₀ = 1

years, n, (1 + i)^n, P, nP for i = .09/12 = .0075

 15  180  3.838043267  .010142665     1.8256797

 20  240  6.009151524  .008997259559  2.15934216

 30  360  14.73057612  .00804622617   2.89664136

years, n, (1 + i)^n, P, nP for i = .06/12 = .005

 15  180  2.454093562  .008438568281  1.51894224

 20  240  3.310204476  .007164310585  1.7194344

 30  360  6.022575212  .005995505252  2.158381891

First calculate (1 + i)^n since it occurs in both the numerator and the denominator. Then complete the calculation for the payment P. In the first case, for each dollar of loan the payment is a little over a penny per month. Multiplying the amount of the payment P by the number of payments n gives the total amount paid. In the first case, for each dollar of loan the repayment is a little over a dollar and 82 cents. The 1.82 is also the ratio of the repayment amount to the amount of the loan.

Again this is the best I can do with the tables, etc. Also someone may want to work this into the main article. Next chance I get I will go into bank accounts, US Treasury Bills and whatever else I can think of. Also I will bring out the where, what, when, why of simple and compound interest.

Sorry be back as soon as I figure out how to make the math show up right. Well a little bit more. I'll keep working on it. Thanks for the help.

Go here: meta:MediaWiki_User's_Guide:_Editing_mathematical_formulae - Omegatron 20:31, Jun 29, 2004 (UTC)

look here for more material: http://mathforum.org/dr.math/faq/faq.interest.html

[edit] Um

"This formula is usually written:

I = P e r t

So if i have $1000 at 10% interest,

$I = \$1000 \cdot e^{0.1 \cdot 1} = $1105.17$

I is not the interest. It is the principal plus interest after 1 year. - Omegatron 03:04, Aug 6, 2004 (UTC)

I fixed it sort of. Not too happy with the nomenclature. Guess, I should get around to improving

things.

Problem is, I've heard of P=ert as "PERT" before, so it is usually called P. But it needs to be explained concisely - Omegatron 01:03, Aug 12, 2004 (UTC)

Sorry for the edit i did awhile ago, i didn't read this before hand. The notations are inconsistant throughout the different fields that use TVM. I took the notations of my notes from "interest theory" because it actually defines "accumulation" a(t) and "amount" A(t) in function format. (feels more mathematical) --Voidvector 19:37, Nov 8, 2004 (UTC)

You did a nice job improving this article. Nomenclature is always a problem. I believe being consistant is the top priority. Also, reducing interest and compounding periods to single variables makes for improved clarity.

Suggestions: Perhaps there should be a note providing additional details on interest and compounding periods. For example see Mortgage 5 Fixed rate mortgage calculations under Contents. Everyone reads the encyclopedia, so I feel that we should be careful not to assume that the reader is familiar with the subject. Also, concerning the sentence, "Since the principle k is simply a coefficient, it is often dropped for simplicity.", I feel there is something deeper than just simplicity involved. I would try something like: Without loss of generality, the principle k can be taken as unity since it is simply a coefficient or scale factor. For example see Geometric progression.

I just noticed that in Continuous Compounding the meaning of t has changed.

[edit] "interest" in economics is the return to capital

Only in neoclassical economics and in finance is money considered to be capital. In classical economics and political economy there is no claim that fiat money is anything akin to capital though commodity money such as gold might be considered as such in some circumstances. In real economics interest is the return to capital. And capital is tractors, roads, structures, tools, and hydroelectric plants.

An example if "interest (economics)":

A farmer with access to 400 acres has only a mule and a 1 shear plow. He can only manage to work 40 acres so he borrows the dough to buy a tractor and a multisheared plow and now he can plant and harvest 400 acres. The income he gets from the additional produce minus the depreciation (payment in step with depreciation) is economic "interest". The payment that he makes to the bank over the term of the depreciation is called principle and "interest". But the "interest" is actually a combination of a "finance charge" (depreciation on the lenders actual "capital" i.e. a safe, a fixed structure like a bank building, and furniture and office supplies, wages for the staff of the bank, a socialized repossession and remarketing charge necessitated by folks that borrow money for tractors and then do not pay it back) and the rest is actually economic rent. Within the bank, money is created from thin air to keep track of who owes who and how much. As such it has no cost to the banker/lender. And all payment for loans in excess of the actual costs associated with acting as a financial intermediary between the tractor builders and the farmers that are not actual costs (costs include a very healthy wage for the bankers) is simply economic rent.

The Trucker 22:50, 11 July 2006 (UTC)

It may be argued that a central bank (i.e., the Federal Reserve in the US) can "create money from thin air", but the Fed does not lend directly to business or consumers. A commercial bank's ability to lend is primarily constrained by its deposit base (yes, it is possible for a bank to lend over 100% of deposits, but such action will bring the regulators a'calling). Therefore the statement that loaned funds have no cost to the bank is erroneous. When considering the price of a loan (that is, the interest rate), a bank calculates the cost of funds (the average cost of its deposits and other sources of funds), administartive costs (salaries, rent, utilities, paper, etc.), expense associated with credit risk, and interest rate risk (i.e., the impact of loaning fixed-rate funds over time vs the rising cost of short-term funding needed to replace those funds). When all is said and done, the typical commercial bank in the US is earning 150 to 200 basis points over its cost of funds. This is not readily apparent to the average consumer, especially when your Visa statement arrives with a 18% annual interest rate. However, the vast majority of a bank's portfolio is loans made to businesses, and at much lower interest rates as compared to consumer lending. 206.169.172.212 20:38, 28 June 2007 (UTC)

[edit] Proposed Move

There are a ton and a half [1] of articles with the word interest in the name, but no good article on the generic concept. Interests and Interesting both redirect to "Attention", but that's not necessarily an appropriate solution.

Interest be moved to Interest (financial) or Interest (monetary) and be overridden with a more generic Britannica-based [2] definition of the term. MrZaius^talk 03:18, 5 February 2007 (UTC)

The only difference would be whether a user would have to click on the link at the top to go to the disambiguation page or have the disambiguation page brought up automatically. If the majority of people who search for just "Interest" want the financial kind, then the former (and current) way is better.

However, since we don't know (or, at least, I don't know) what the statistics are, I am against the move. "Interest" by itself seems pretty straight-forward. Self-interest, interests, etc. are completely different things and are much less likely, in my opinion, to have been searched for by just typing in "Interest." Ilikerps 02:10, 23 February 2007 (UTC)

I agree with the proposal to leave it without being more specific. The articles with interest in the name were mostly related to interest in the financial/economic sense, not the generic concepts.--Gregalton 11:29, 24 February 2007 (UTC)

[edit] Day counts conventions

In order to calculate the interest you earn between two dates. it should be easy.

assume T2-T1=T(in years)=t(in days). It is nature to assume T=t/365

annaul interest rate r

then the interest you earn on $1 is (1+r)^T-1, when T is small, it is approximate r*T.

However, in reality, it becomes complicated. There are 3 conventions:

[edit] actual days/365 convention for Government bonds

coupon is paid semiannually, so the compound period is not 1 year, but half year, although the coupon rate (r) is quote in annual rate. The "half year" (D) might be 184 days or 181 days. The actual days (d). interest you earn should be: (1+r/2)^(d/D)-1 approximate by r/2*d/D

[edit] actual days/360 convention for money market

[edit] 30/360 convention for Corportate & Municipal bonds

Always assume 360 days/year, and 30 days/month.

example 1:buy bond on February 28, and sell it on March 1st, d=3 days

example 2:buy on March 1, and sell on July 3, d=4*30+2=122

r quoted in semiannual rate, then interest is approximated r/2*d/180

Jackzhp 18:32, 26 March 2007 (UTC)

[edit] Compensation for other uses of funds?

"The lender receives a compensation for foregoing other uses of their funds, including (for example) deferring their own consumption."

Why should a lender expect to be compensated by a borrower for uses of their funds which they forwent by offering the loan in the first place?--TheNightFly 22:48, 28 April 2007 (UTC)

The lender can use the money for something else - see opportunity cost, for more detailed discussion. Those other uses play a role in determining the amount paid (the price) by means of supply and demand - if the lender will get paid more elsewhere, those other uses effectively set the price. Or, in your formulation, if I (the lender) am not paid for forgoing my other uses, I won't loan the money. Somebody else might, but presumably they are going through the same process of deciding whether or not to lend depending on their other uses for money.--Gregalton 05:19, 29 April 2007 (UTC)

You're saying that lenders make loans when they believe it promises a greater ROI compared to other investment opportunities. That makes sense, however, the statement from the article (above) tells me that lenders are not only expecting ROIs from loans but that they are also expect to get what they believe they would have earned from all other investments combined! If that's not the case, the statement should be replaced with something more accurate like: "The lender makes a loan because it promises him the highest return on investment (ROI). Compensation from a loan is received as interest paid on the principle over time."--TheNightFly 07:15 PM Monday, May 7, 2007

[edit] Irving Fisher?

The last section reads "Irving Fisher is largely responsible for shaping the modern concept of interest with his 1930 work, The Theory of Interest"

Irving Fisher couldn't tell interest from monkey balls if his life was depending on it. According to his theory, bananas now would cost more than bananas tomorrow. The guy who really explained that the source of interest is the human behaviour of liquidity-preference is John Maynard Keynes.

Just saying. 84.75.130.173 15:01, 29 April 2007 (UTC)

What are you waiting for? Go explain that over at the Fisher article, and delete that line from this one. While you're at it, you charming, civil gentleman, start the monkey balls article. 68.121.161.21 03:38, 30 June 2007 (UTC)

Well, irving fisher was the first to distinguish nominal from real interest... So he Is largely responsible... I MIGHT agree with the fact that he wasnt largely accurate. And he is, of course not Entirely responsible... In that sense i dont see the problem, nevertheless i will delete it. In the history of interest section ive added a more suitable reference to fisher. Dryfee 01:41, 24 August 2007 (UTC)

[edit] Merging

I am in favor of adding the interest expense stub here under something like interesi in accountin or its effects on books if anyone oposes please speak. I will merge the article if there are no negative replies On September the 1st. Dryfee 02:00, 24 August 2007 (UTC)

Strong agree vote from me. Terry Carroll 02:45, 24 August 2007 (UTC)

Oppose: weak link to this article, which is far too general. The other may be a stub, but very specific in context, and would not fit well here. Leave it as a stub. If it must be merged somewhere, an appropriate finance/accounting article that is narrower would be better.--Gregalton 05:20, 24 August 2007 (UTC)

Agree. I am including a section in the accounting and taxation treatment of interest in my draft replacement article. JJMcVey 11:40, 10 September 2007 (UTC)

Oppose. This article on interest is far too general. Interest expense is more business related, while this article is written for the consumer. —Preceding unsigned comment added by 99.131.156.238 (talk) 17:40, 6 June 2008 (UTC)

[edit] e is Euler's e

Euler discovered e, not Bernoulli. —Preceding unsigned comment added by 68.77.113.94 (talk) 01:23, 9 September 2007 (UTC)

[edit] Definition of interest is incorrect

The first sentence of the article is incorrect. Interest is the price of borrowed money, not borrowed assets. The price of loaned shares is called a premium. The price of loaned consumer goods is called rent. Being new to this article, I didn't want to make changes without first getting some feedback. Wikiant 13:07, 9 September 2007 (UTC)

Wrong, though certainly the present opening paragraphs are way too terse. Interest is the price of CREDIT, not money. The idea that interest is the price of money is a common mistake - one even made by financial professionals, sadly. What interest paid for is the ability to use what has been borrowed without having to produce those things, or their value's worth. It does not matter what particular form that the borrowing takes. What is borrowed need not even necessarily be money, even though by value and number of transactions it is by far the most common thing that is borrowed.

Ordinary rent, as opposed to economic rent, is a subset of interest applied under certain conditions. You will find that rental payments on consumer goods are calculated in EXACTLY the same way as interest on borrowed funds. For instance, this is how hire-purchase agreements are formulated, whose mathematics are the same as for an amortising loan.

I noted the header saying that the article needed attention, and realised that mere grammar was the least of its problems, so I have taken it upon myself to rewrite the entire article (I am keeping a few bits and pieces from the present article). This includes the relationship between rent and interest, as well as with profit. I'll post it when it is in a presentable condition, and others can discuss it and modify it from there.

JJMcVey 11:37, 10 September 2007 (UTC)

[edit] Merger proposal

Should the compound interest article be merged into this general interest article? Doing so makes sense to me as the concept is necessarily raised in this article, and most easily discussed here. There is already a discussion of it in the present article, and I am including the salient content of the compound interest article in my draft as part of the mathematics section. Simple interest already redirects here, and if the merger proposal is accepted then compound interest should redirect to here too.

JJMcVey 09:11, 13 September 2007 (UTC)

I see no compelling reason to combine the two. Aside from the fact that they overlap, do you have any specific reasons? As a general thing, in an encyclopedia I would expect to see a general article with references to more specific and detailed sub-topics. Which is more or less what the current set-up does.--Gregalton 16:42, 15 September 2007 (UTC)

See comments on Talk:Compound_interest#Merger_proposal RichyBoy 22:42, 15 September 2007 (UTC)

"Overlap" is something of an understatement. There is not that much extra in the compound article, and at the time I figured it was just redundant material wasting space.

Looking at my draft and how large it actually is, I too have been thinking along the same lines of there being one main entry article and a collection of sub-articles. Alternatively, therefore, could all of the mathematics of interest be a whole article in its own right? The article on the time value of money also has a considerable overlap with the material on compound interest, though I've not yet much thought about how this all might possibly be reorganised to minimise redundancy.

Further, why stop at just compound interest? If there's no compelling reason to merge compound interest in, then I ask why should that alone be in a separate article? For example, by that standard the explanation of how market rates are formed should be a separate article - as well as this topic being a major NPOV issue. As it stands I am inclined to put up the warning sign on it now (the present organisation is a mess, so I also strongly agree with the copyedit sign).

I would then leave the main interest article as containing its basic meaning & related terms, intro on competing theories on what interest is and how rates are set, intro on economic substance & relationships with other factor incomes, intro on mathematics and conventions, intro on government intervention, the history of interest, and discussion on modern arguments about interest. The sub-articles would then be expansions on those intros.

JJMcVey 11:47, 17 September 2007 (UTC)

hutchesc 14:47 03 October 2007 (UTC)

Interest and compound interest are two related, yet wholey different, concepts. To merge these 'concepts' would be analogous to merging verb & adverb: one is derived from the other, but they are entirely different in function. As a better example, think of it like this: The interest accumulating on a Credit Card account is also calculated into the total; so a $100 credit card purchase, at 10% interest, after 4 months, would be calculated as [(100 x .10) x 4] = $140. (Note: .10 = 10% = $10). With compounding interest, however, the amount would be totaled as: 100 + [(1 x $10) + (1 x $11) + (1 x $12.1) + (1 x $13.31)] = $ 146.41. The difference, after only four months, is an increase of 6.41% of the principle, so the concepts cannot be said to be the same.

hutchesc 14:47 03 October 2007 (UTC)

No consensus, no move forward on merging, I am removing the proposal from the compound interest page.--Gregalton 20:36, 4 October 2007 (UTC)

On the same note, I am removing the merge tag from the interest page as well. -FrankTobia (talk) 18:35, 17 December 2007 (UTC)

[edit] Replacement draft

I've nearly completed my first hyper-rough draft of a replacement article. It incorporates (I think) all the salient detail from the old one, unresolved issued you guys have mentioned above, and other matters I believe are essential to it. I presently have it in my sandbox. Feel free to look and drop a comment in the discussion page. JJMcVey 13:22, 15 September 2007 (UTC)

[edit] Article enhancements

I've read through this article recently and it fails to explicitly mention the term Repo rate and Repo rate isn't even linked in the 'see also' section, which is surprising because 'interest' is the function of a Repo.

Probably a 'see also' to the Monetary Policy Committee would be useful as well at that page documents how the repo rate is set for the Bank of England in the UK. RichyBoy 00:02, 16 September 2007 (UTC)

[edit] Interest as Price of Credit vs. Money

The current definition, "interest is the price of credit" is incorrect. "Credit" is money *available* for borrowing. Interest is not charged on the money available, but on the money actually borrowed. Some evidence

• "credit -- money available for a client to borrow" (from www.thefreedictionary.com/credit)

• "credit -- an amount or sum placed at a person's disposal by a bank" (from www.britannica.com/dictionary?book=Dictionary&va=credit&query=credit)

• "credit -- any deposit or sum of money against which a person may draw" (from dictionary.reference.com/browse/credit)

Wikiant 21:29, 16 September 2007 (UTC)

The definition I provided is correct. What you have provided is the meaning of credit limit. I'll provide proper citations as per verifiability rather than truth in my draft, as required. Speaking of which, I thank you for your comments as it is good material for inclusion. JJMcVey 09:36, 17 September 2007 (UTC)

Happy to help. However, the above definitions are for the word "credit," not "credit limit." Wikiant 11:34, 17 September 2007 (UTC)

[edit] External Links

The first two links are useful tools to calculate interest. Since these tools can not be provided in the article, they are provided as external links. The Margill paper: "White paper: More than Math, The Lost Art of Interest Calculation" should be used as a source and cited in the article, not an external link per WP:EL; however, verify the source to determine its reliability. At first glance it looks like a self-published source, which requires the author to be an expert in the field to be reliable. --EGeek (talk) 19:49, 17 January 2008 (UTC)

[edit] Loan final balance for leasing

The reference to a fixed amount for a final balance for leasing was removed since deposits are handled separately and any interest accrued would most likely be factored into the rent payment. Any fees associated with the loan may affect the final balance. --Jbergquist (talk) 10:24, 28 January 2008 (UTC)

[edit] Conversion of an annual rate to a period rate

For convienence the annual rate, i, is often expressed as a multiple of the period rate, r, i.e., i = n r for n periods in a year. But with compound interest,

$r=\big(1+i\big)^\frac{1}{n}-1=\frac{i}{n}\bigg(1-\frac{n-1}{2n}i+\ldots\bigg)$

So the relative error in r is approximately i/2 and use of the simple interest formula works best for small i. Some discussion of conversion could be included in the article and as well as mention of customary usage. --Jbergquist (talk) 12:45, 30 January 2008 (UTC)

[edit] Use realistic interest rates

I would greatly appreciate using realistic interest rates in Jim's examples. If I were Jim, even if I were a fifty year old man with picture-perfect credit, I would crap my pants if someone offered me an interest rate of 5.5% The lowest I've ever seen was 7%. —Preceding unsigned comment added by Dstebbins (talk • contribs) 23:47, 2 February 2008 (UTC)

The quote at a Bank of America branch for mortgage loans yesterday was

Type of loan	30yr fixed	15yr fixed
rate	5.375%	4.875%
APR	5.546%	5.143%
points	1.763	1.648
monthly pymt	$5.60/$1000	$7.84/$1000

--Jbergquist (talk) 17:02, 6 February 2008 (UTC)

[edit] Need to distinguish between conventional APR and effective APR

The interest rate usually stated is the conventional APR which is defined as the number of periods in a year times the period rate. This is less than the effective annual interest rate for the loan computed from the formulas. The effective annual rate is often abbreviated as AER. One also needs to be clear about what one means by a year which could be 360 days or 365 days depending on the Day count convention. A good reference for financial terminology might be useful. --Jbergquist (talk) 12:49, 4 February 2008 (UTC)

This is covered, I believe, in the articles on nominal interest rate and apr. If you want to make it more explicit, that's fine, and I would be happy to assist. "Conventional" APR is not a term I am aware of. (It also differs from place to place).

I have seen the following as the most logical:

Effective annual rate: expressed as proper annual rate. This should include fees etc but may not.
Nominal rate: what you call conventional rate, periodic rate times number of periods.
APR: nominal rate, recalculated including fees and cetera.

Does this fit what you have seen and use? As I remember, the articles (before the recent edits) were quite explicit about this.--Gregalton (talk) 14:55, 4 February 2008 (UTC)

The rate in the Bank of America mortgage quote above which gives the payment is the "rate". This is used for a conventional loan. FHA loans includes mortgage insurance in their payments so are higher. The APR listed doesn't appear to be (1+rate/12)¹²-1. --Jbergquist (talk) 17:21, 6 February 2008 (UTC)

Which quote above? Keep in mind that, as noted, APR/effective/'conventional' will vary by jurisdiction, so using a US context only may cause problems.--Gregalton (talk) 05:51, 7 February 2008 (UTC)

I was referring to the BofA mortgage quote posted in Talk:Interest#Use realistic interest rates. Mortgage companies also include required escrow payments such as taxes and home owners insurance which are not part of the loan payment. The BofA payment calculator appears to use the "rate" also. The FSA (UK) payment calculator gives the same payment as the formula and along with the interest-only payments appear to be rounded to the nearest cent. They don't round up as is found in mortgage payment tables here in the US. Rounding the payment contributes an error to the final balance of about nper*Δp where Δp is the payment rounding error and the rounding errors in the balances have a smaller effect since they tend to average out. So in rare instances there might be some discrepancies.

I still think that we need a better handle on APR. --Jbergquist (talk) 17:03, 7 February 2008 (UTC)

The ΔB_n = -λ_n Δp where -$0.005<Δp<$0.005 and it seems to be a problem for large n, the number of payments, since λ_n grows exponentially. --Jbergquist (talk) 00:01, 8 February 2008 (UTC)

$1002.70 @ 5% over 40 years with a payment of $4.83 has a final balance of $7.60 which is greater than the payment so there are exceptions to the rule but one has to use small principals over a large number of years to force an error. These loans are unrealistic and unlikely to be written. --Jbergquist (talk) 03:23, 8 February 2008 (UTC)

[edit] Recent addition removed from article

"You need to find the Effective interest rate which is not 12.99%/12. It is Ieff = (1 + r)^(1/n)-1 = (1 + .1299)^(1/12)-1 = 1.02293% To prove my point Using the method below you get a apr of $2500 (1 + .1299/12)^12 = $2844.80 which is 13.791% higher than $2500 meaning a 13.791% apr was used and not the 12.99%. If you use the right number $2500 (1 + .0102293)^12 = $2824.75 which is 12.99% higher than $2500 meaning a 12.99% apr

so the payment would be I= $2500 * ((1+.1299)^(3/12) - 1) = $77.51

The .1299/12 stuff is flat out wrong" Nurg (talk) 10:08, 15 April 2008 (UTC)