Talk:Interest

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Contents 1 POV for neoclassical economics 2 Simple and compound interest for the layman 3 Um 4 "interest" in economics is the return to capital 5 Proposed Move 6 Day counts conventions 6.1 actual days/365 convention for Government bonds 6.2 actual days/360 convention for money market 6.3 30/360 convention for Corportate & Municipal bonds

[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

[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:

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:

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 , 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 . In the last case we need to modify the limit equation in the main article getting

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.

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

Again

After n periods or payments we have

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:

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:

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:

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 = Pe^rt"

So if i have $1000 at 10% interest,

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)

[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

Always assume one year is 360 days, and half year is 180 days.

[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)