#35 Compound Interest

References:

Wikipedia Article on Compound Interest
Get Objects – Software Components 
Moneychimp
The Compound Interest Paradox

We have said before on this blog that compound interest was as “usury on steroids,” that it exponentially grows the eleventh marble, etc. Many have doubted that this is so. We have already based our rigorous definition of usury on E. C. Riegel's clear observation that it was impossible to pay back what was never created. We say that compounding dramatically increases the amount of uncreated money that must be paid back. We will provide some examples.

But the first thing I want everyone to understand is that, in the world we live in today, there is no fundamental agreement on how to calculate compound interest! We'd like to cut through all the explanations and apologies for why there are so many ways to represent compounding interest and state up front that these various mathematical formulae amount only to the range of deceptions used to sell people on either borrowing money with which to purchase something that the buyer cannot afford at the present time, or getting people with a lot of extra money relative to the crowd (the rich) to invest money with a promise of a return on the investment, or “yield.” They might just as well have advertised “yield” as “take,” because that's what it amounts to.

One person (or company) means something by reference to a particular interest rate and monthly payment schedule that would not apply to another situation. Thus, a confusing maze of baffling mathematics faces the average person who is usually forced to accept the expert's advice and opinion, rather than recognizing the inherent deceit expressed as clearly as not as, “how much can we (the financial community) get away with stealing from either buyers or investors?”

We shall illustrate with some concrete examples.

A = P (1 + r/n)^nt

This is a standard formula for compound interest, which we shall understand as it relates to the present economic system where:

A = the amount of money accumulated after n years, including interest
P = the principal (the initial amount borrowed (or deposited)
r = the annual rate of interest
t = the number of years the amount is borrowed (or deposited)
n = the number of times the interest is compounded per year.

This formula is routinely used to calculate the future value of A. But it is not used for computing a monthly payment on a mortgage because ... they use a different formula for that: 

A = [ Pr(1 + r)^m ] / [ (1 + r)^m - 1 ]

A = monthly payment

P = principal
m = number of months (30 years = 360)
r = interest rate divided by 12 (for monthly compounding)

Let's begin with something we're more or less familiar with, a home loan for $100,000 at 3% interest for 30 years, interest compounded monthly, so that's 360 months.

A = [ 100,000 x .0025 ( 1 + .0025)³⁶⁰ ] / [ (1 + .0025)³⁶⁰ - 1 ]
A = [ 100,000 x .0025 ( 2.4568422115) ] / 1.4568422115
A = 245684.22115 x .0025 / 1.4568422115
A = 614.210552875 / 1.4568422115
A = 421.60 rounded (421.60403372894717912283666692754)

Your monthly payment on this standard fixed rate mortgage is $421.60 and by the time you have made all payments, the total you have paid would be $421.60 x 360 = $151,776 so you have paid $51,776 in interest or 51.776% of interest on a loan of $100,000 principal in 30 years.

The standard formula would make the same loan look like this:

A = 100,000 ( 1 + .03/12 ) ^{12 x 30}

A = 100,000 ( 1.0025 ) ³⁶⁰A = 100,000 ( 2.4568422115 )
A = 245,684

Now A is the total of all the principle P and interest compounded monthly for 360 months. Note that the original loan was for $100,000 but the interest over the term of the loan expressed this way was $145,684. In absolute terms this represents 145.7% (146%) of the principal.

But as I said, for mortgages they use a different formula otherwise a 30 year fixed rate loan at 3% compounded monthly would actually be a loan with interest charges of 146% instead of 51.78% which is what you're really paying.

Whatever interest you pay is due to how long it takes you to pay it off. Those loaning the money to you demand that interest back as your rent of their money for thirty years. Your monthly payment using this standard formula is A / 360 or $682.46. But the $421.60 per month seen above is the industry correct number ... because they use a different formula.

Would people more likely go for a loan offered at 51.78% or 146% interest over 30 years or one that is billed as a 3% loan compounded over 30 years? In absolute terms, they are the same thing. Therefore we contend that the low interest rate loans as advertised for real estate, or anything else of comparable value, represents deliberately misleading advertising, as far fewer would be willing to take a higher interest loan than one they believe to be low.

Yet this: A = P (1 + r/n)^nt is exactly the same as A = P + I, where I equals all the interest, understanding that time is equal in both cases. You see how easy it is to mislead or LIE using figures? So when they say “figures don't lie,” they may in fact and usually are using figures to lie. You can use the discussion so far to determine, in absolute terms, what you are actually paying in interest on whatever real estate, etc. that you are buying under such credit terms.

Now, if the money for the real estate or whatever else, is created as the result of a typical commercial bank loan (this would be legitimate money for E. C. Riegel), then the money loaned is what the thing would have cost had you had all the money on the day of the sale. Using the example, that piece of real estate you “bought,” but are still paying for, is actually costing you more than half of the principal what it would have cost by the time you finish paying for it; by that date by the normal formula, you would have paid nearly two and a half times what that property cost when you “bought” it. (And of course in addition, in many localities, you are obliged to pay taxes on the entire assessed value of the property, not just the percentage of that property that you have actually purchased through the finance contract, often called a mortgage. But that's another matter.)

Using the standard formula, if your interest rate is 6% instead of 3%, it looks like this:

A = 100,000 ( 1 + .06/12 ) ^{12 x 30}
A = 100,000 ( 1.005 ) ³⁶⁰A = 100,000 ( 6.02257521226 )
A = 602,257.52

Your monthly payment by this method is $1,672.94. By the time this loan is retired, in 30 years, you will have paid over six times the principal on the day you “bought” whatever that money went for. We said that compound interest was like “usury on steroids” and I trust now, since figures DO lie, you can see that the higher the rate of interest, the worse the taking is. Again, do the math on your own situation and see what you discover.

Using the standard formula, the exponential growth rate of compound interest can be seen with reference to a standard loan of $100,000 for 30 years, where P = the principle, from 1% through 10% interest compounded monthly as follow:

at 1% A = 134,969 or 135% of P & I = 35% of P
at 2% A = 182,121 or 182% of P & I = 82% of P
at 3% A = 245,684 or 246% of P & I = 146% of P
at 4% A = 331,350 or 331% of P & I = 231% of P
at 5% A = 446,774 or 447% of P & I = 347% of P
at 6% A = 602,258 or 602% of P & I = 502% of P
at 7% A = 811,650 or 812% of P & I = 712% of P
at 8% A = 1,093,573 or 1,094% of P & I = 994% of P
at 9% A = 1,473,058 or 1,473% of P & I = 1,373% of P
at 10% A = 1,983,740 or 1,983% of P & I = 1,883% of P

Therefore at 1% over 30 years, you pay $34,969 on $100,000 borrowed, or 35% in interest. That money was not created by the loan and over 30 years amounts to $1,165.63 each year of money that was not created anywhere else, but that must be grubbed back from someone to repay the interest on the loan, thus shrinking the money supply that much per year. The higher the interest, as is seen graphically, the worse the money drain from the economy becomes. I want the enormity of that to sink in for a moment.

Genuine usury always involves the lending of money and nothing else and demands back more of it than was originally lent, in the process deliberately causing -as a mathematical certainty- the perpetual scarcity of money. No matter how much of this loaned money the government or corporations spend into the economy in order to keep it afloat, factors involving payment of interest, money that was never created, demand a “growth or die economy,” that will ultimately crash.

The principle of $100,000 divides over 30 years as $3,333.33 each year and does not change regardless of the interest rate. Therefore, where the term of the loan is always 30 years, and where P = the principal paid per year and I = the interest paid per year, the interest rates for such loans are as follows:

at 1% P = $3,333.33, I = $1,165.63 or 34.97% of P per year
at 2% P = $3,333.33, I = $2,737.37 or 82.12% of P per year
at 3% P = $3,333.33, I = $4,856.13 or 145.68% of P per year
at 4% P = $3,333.33, I = $7,711.67 or 231.35% of P per year
at 5% P = $3,333.33, I = $11,559.13 or 346.77% of P per year
at 6% P = $3,333.33, I = $16,741.93 or 502.26% of P per year
at 7% P = $3,333.33, I = $23,721.67 or 711.65% of P per year
at 8% P = $3,333.33, I = $33,119.10 or 993.57% of P per year
at 9% P = $3,333.33, I = $45,768.60 or 1,373.06% of P per year
at 10% P = $3,333.33, I = $62,791.33 or 1,883.74% of P per year

Now, just to be fair, we'll take the same series as expressed in monthly payments A, for a standard mortgage:

at 1% A = $321.64 x 360 = 115,790.40, I = 15,790.40 or 15.7904% of P
at 2% A = $369.62 x 360 = 133,063.20, I = 33,063.20 or 33.0632% of P
at 3% A = $421.60 x 360 = 151,776.00, I = 51,776.00 or 51.776% of P
at 4% A = $477.42 x 360 = 171,871.20, I = 71,871.20 or 71.8712% of P
at 5% A = $536.82 x 360 = 193,255.20, I = 93,255.20 or 93.2552% of P
at 6% A = $599.55 x 360 = 215,838.00, I = 115,838.00 or 115.838% of P
at 7% A = $665.30 x 360 = 239,508.00, I = 139,508.00 or 139.508% of P
at 8% A = $733.76 x 360 = 264,153.60, I = 164,153.60 or 164.1536% of P
at 9% A = $804.62 x 360 = 289,663.20, I = 189,663.20 or 189.6632% of P
at 10% A = $877.57 x 360 = 315,925.20, I = 215,925.20 or 215.9252% of P

All values given above are for the total duration of the loan. Notice that between 5% and 6% the total interest begins to crest over 100% and that above 9% interest begins to crest over 200%.

In addition to all this, someone owning a home as their prime asset that they live in, isn't necessarily wealthy, unless that home is itself a source of income, either as a place where anything having to do with earning a living is done, or wherein actual business is transacted on a regular basis. On the other hand, those who own real estate and rent it to others are wealthy by our definition, because their property use falls under the definition of wealth that will be used uniformly throughout this blog; wealth is that capable of providing income, usually measured by the month.

You should easily be able to see the daunting task of acquiring real estate under the usual methods and these days trying to turn a profit on any of it. It doesn't help that most of it, all of it, is probably overvalued as a result of the financial bubble that was allowed to grow during the recent past. It should also be quite apparent why they were so interested in loaning all that money, much of it on far less generous terms than the illustrations used here. And this also explains why the whole business represents such a colossal drain on the money supply of every country, because most mortgages the world over are settled on comparable terms.

Now, we have an alternative model under consideration and we're constantly seeking to answer people like Professor Greco's young man in Tacoma who wondered when any complementary money would ever be able to pay for things people needed like housing, food, clothing, etc. The Value Exchange Network (VEN) is the market made up of nodes each representing a geographical area, each node called an Independent Exchange (IE), but none of them will ever be a source of money to lend for real estate or anything else; they will never be in that business. The IE is only responsible for passing judgement on the loan per the rules, which are clear and make a lot of things simpler. All applications for loans to be accepted by the IE are called Credit Contracts.

The rules for credit contracts are pretty simple:

1. No more money is created than is required to make a trade
2. Compounding of interest is forbidden
3. All loans must be of money that already exists
4. All lenders are responsible for their own risk
5. We would think that loans out to 49 years (7 x 7) would make most property purchases more than sufficient, for we intend on posting a Jubilee Year for all debts 50 years out from either the inauguration of the VEN (whenever that is) or from the inception of the Value Unit (proposed as already begun on 2 November, 2011).

Credit Contracts should be simple enough that their terms can be summarized on one side of a piece of paper with the conditions that would void the contract, the “voids,” on the opposite side. One copy each goes to the buyer, the seller and the local IE that would administer the schedule of transactions.

Now of course, wherever you live, you'll perhaps have to “pay unto Caesar that which is Caesar's” in the local currency, and that probably includes insurance too. The insurance business is based on trading debt, so they don't like having to pay out unless they have to, because dealing in debt instruments, one is basing one's return on time; knowing the redemption dates of the various bonds one holds, while being subject to sudden payouts in cases of settling some policy holder's loss.

You can see how the whole financial pyramid is based on promises to pay, way too many and the basis (reserves) of loanable money consisting in mere fractions of what a banker is allowed to lend and despite interest drawing money out that was never created, what the government spends and the inevitable inflation it causes, is even worse.

In the debt instrument world there are words in common use that more people should get to know; bills, notes and bonds. In the parlance of standard debt trading, a “note” (a Value Unit exchange note included) is offered in trade by a buyer for an item or service, presenting a pledge to the seller that a comparable monetary value of whatever it is the seller might want, exists in the market, which in VEN terms could be instantly worldwide.

A Bill is a loan of money for a year or less, a Note is an intermediate term loan, usually out to 5 years, and a Bond is a loan of money for a longer period of time, 10 years or more. All debt instruments are usually sold at some discount to their face value and are redeemable when they mature at their face value on a specific date. Traders play the spreads between what they buy a debt instrument for and what it is worth when redeemed.

As we've said, no IE will ever be involved in any of this business, but those who desire to raise money for a project by use of debt instruments may do so, operating as a B member, subject to all the rules listed above. Nevertheless, IE's will be involved in the transactions involving any live debt instrument, so we can make some reasonable statements concerning debt trading and its excesses that the VEN seeks to eliminate.

All Value Unit based credit contracts in order to be valid, will have to be accepted by the administering IE and all IE's will be under the same rules. Debt instruments are among the most widely used financial vehicles in the world for deceiving people and cheating them out of their property so we want to make sure all avenues for known deceptions are eliminated. Let's take a look at a valid credit contract.

A credit contract could be a Bill payable in instalments over several months during a year or less. These would probably include the majority of capital goods or other appliance purchases. Perhaps most vendors operating under this form of extended credit wont need a credit contract to enforce payment, but they should use them because they have certain added good will features; completed credit contracts build a reputation for all concerned, both the vendor extending credit and the buyer receiving the credit as any member of the VEN is allowed a look at the number of completed credit contracts, the amount of extended credit and the rating given by sellers on the buyer's payment performance.

If credit needs to be extended out to SEVEN years (7), we'll call it a Note. These include every Value Unit Exchange Note circulating in the system. So should VEN operation commence in 2013 and notes begin appearing soon thereafter, all IE's would begin replacement in 2020 with a new set of notes. [2/23/17: Of course since this was written, the idea of a circulating community check, the V-Check, was developed because it is easier to implement right now.  V-Checks would expire in six months but would still be capable of either exchange for a new one or deposit.]  Of course if someone held old VU notes past their redemption year, their IE would replace them when turned in, with newer ones. Managing exchange note distribution and redemption is one of the responsibilities of the International Value Exchange Society (IVES) to be explained further in another post. Other valid Notes could include any purchase where payments need to extend out to seven years.

Bonds are credit contracts where instalment payments extend out to FORTY-NINE (49) years from the year of the VEN's official launch, as we expect to exempt the fiftieth year as a Jubilee Year, where all outstanding debts are settled. We will no longer be willingly subject to any system of perpetual debt.

Now here is a decent question, who owns these credit contacts? They are objects in and of themselves, but what are they? They are promises to pay a valid debt for a real good or service provided in the exchange; the buyer got the use of whatever it was he bought, the seller gets the contract as his property, until paid off in exchange notes, which the seller trades for other goods or services of value to him. Credit contracts are literally extending the terms of a sale out long enough for the measuring of value, accomplished by money, to work measuring whatever it is, so that the buyer can have his “time preference” ahead of actually being able to afford whatever it is he is buying.

But again, to who do debt instruments belong? They belong to the seller in exchange for the good or service sold to the buyer. Hence the seller could sell his contract to someone else, after all it is his property. He can do this regardless of the buyer's continuing payment obligations. These debt instruments are the property of those who possess them.

Let's examine one class of debt instruments, mortgages, more closely. We have a loan of a specific amount of money with a schedule of payments for paying it back and upon completion, the mortgage is paid off and the official title to the property passes to the buyer. However, let's say that the original seller, who owns the mortgage, for whatever reasons wants to unload the responsibilities for taking in the monthly payments, etc. and would be willing to take less than the potential value of the mortgage from anyone willing to take over the receipt of mortgage payments, delivery of title upon completion, etc. Potentially a debt instrument is worth more when it is young than when it is close to maturity; a mortgage for $100K at a rate of 6% for 30 years would net someone in excess of 115.838% as we've just seen. You can see immediately I hope, just how the bankers got the idea of making more money up front by trading in these debt instruments. The real estate buyer however sees, or maybe he doesn't, that his monthly payments no longer go to ABC Bank but instead to XYZ Bank.

Clearly we need some reform here, but we aren't going to get it from the powers that be, because they already play games with “intellectual property” that suit themselves at the expense of everyone else; they insist that all who use “their” money are then subject to being told what, how, and with whom they may do business, while they insist they have the right to sell one package of securitized debt to many people at the same time! These are clearly folks who have lost their reason for any trust.

I hope that everyone so far also sees the connection between the lure of returns, “yield” based on compounding of interest, and selling debt instruments, especially those made into securities to be traded on the paper market. There wont be anything like that allowed within the VEN and I might say that anyone caught will be thrown out of the VEN and probably kept out for at least 5 years, as we will not suffer the same frauds perpetuated on us in the present system to continue on in the VEN. So we make the following stipulations as normative:

1. Debt instruments may be sold ONLY to other accredited members of the VEN.

Some have suggested to us that certain kinds of debt instruments, mortgages, not be allowed sold to any member outside a local IE and that will suit many just fine, except that by enacting such a rule they might be cutting themselves off from other needful sources of credit.

2. No debt instrument may be sold while retaining it's repayment stream. If you sell it, all future payments go to the new owner.

In the bond world, you have bonds with coupons attached that were normally plucked off the main bond and turned in for various kinds of payments, dividends, etc. that were specified as terms of the bond. Well obviously you have the bond itself, which has a face value payable on a certain date, and then you have the coupons that pay off on their own schedule. It was and still is common to clip off all the coupons and sell the bond, retaining the coupon payments while relinquishing the final payout at bond maturity..

A mortgage is like a bond in reverse that “dies” upon completion. It's ONLY source of value is in its repayment stream. Therefore it cannot be disassociated from its payment stream as otherwise it has no value. Of course if the mortgage falls delinquent, the lender has recourse to foreclosure and what gives him this right is the title to the property. This brings us to our third point,

3. No mortgage within the VEN may be sold to another without surrendering the title to the property as well.

Conveyance of ownership over credit contracts shall be accompanied by a transfer of ownership attached to the original contract and filed at the IE for further contract fulfilment responsibilities. The seller's account changes and all new payments on the contract now go to the new account. The buyer is informed of the change including the name, address and contact information for the new owner of the credit contract. A statement is also made and verified by the new owner of the contract, copy to all parties concerned, to the effect that the title to the property under the contract has changed hands.

Now comes the hard part, determining what the market for finance capital will bear, meeting the challenge of the normal trade in property, capital goods, etc. without recourse to compounding of interest which as we have demonstrated causes interest to grow exponentially rather than as a linear function. And again, in order for all transactions to be honest, all must know exactly what they are paying based on how long it takes to pay off their purchases and besides no money can be added or subtracted from that purchase by the terms of the contract.

Briefly stated, a property today selling for $100,000 is worth that sum to one who has all the money to buy it on or near the date the property is offered for sale. But how much is that property worth in seven years or in forty-nine years? There is no way of telling. It may still be worth $100,000 so that isn't the real question. Is the question rather what is the cost of borrowing the money to buy the $100,000 property if one hasn't the money? But that's not exactly the right question either, because right away one assumes that available money is a commodity with a current market value, which it is, but one that is made of value measurement rather than substance so therefore, and please pay attention, comparing amounts of available money and any other commodity is comparing apples to oranges, like comparing a ruler to what it measures.

We get closer when we recall the story about the man buying a refrigerator for $700 when had he had all the money at the date of the sale he would have had it for $400. In any case the value of the same exact refrigerator holds whatever value the buyer paid for it. He may have a $700 refrigerator only because he lacked the $400 on the day of the sale and had to resort to credit to complete the sale. Who owned the refrigerator until it was paid off? The seller did, who could if he chose get the refrigerator back from the buyer for failing to repay his debt to the seller in full. Notice that filing a valid credit contract, a Bill in the case of the refrigerator, with one's local IE, removes a large part of the uncertainty in such deals because the IE automatically takes care of the transfers for both buyer and seller based on the schedule agreed to by the parties to the contract.

Now what if you liked a house for sale for $100,000 and really wanted it but you don't have the cash to buy it today, what could you do? You could get someone else to buy it for you who would sell it back to you at a higher price with terms allowing you to pay it off over a longer period of time. Now we aren't considering what the money costs to borrow at all, we are placing all the value in the trade where it belongs, in the property itself. The question is thus how much is the same property worth to the man who can't afford it, but could if he had seven years, ten years, out to forty-nine years under the proposed VEN rules, to pay for it?

Here's a little hint. It is customary to regard certain periods of time as appropriate for repayment of certain kinds of debts. Under VEN rules of parlance, a note pays off in seven years or less, a bill in less than a year. Meanwhile what is the replacement cost to a seller of what he sells? What will he have to pay to buy something to sell to someone else and what will his reasonable mark-up have to be to make it worth his while, the time before getting his money back, etc.?

Most do not know the first thing about these matters and they should. For instance the larger the operation is, the less profit it has to make in order to survive. The smaller any operation is, the more profit is required in order for it to survive. There are theoretical points on either side where a business is unlikely to survive, so there is a survival range for a business, just like a temperature range for life, where the percentage of sales that must be realized as profit determines the chances of a business's survival.  At the lower end are those who require a huge profit in order to make the financing worthwhile at all, while at the upper end there are those who might consider financing a property sale and can afford to take less profit on each sale because they have many times the value of this particular property as assets already so they can afford to take less profit on each.

This works up to the point called diminished profits to scale where the more business that is taken on, reduces the profit of the entire enterprise so that no further business is desired. We anticipate that the numbers of businesses engaged in financing property will probably increase under the VEN rules, but in order to survive may require a higher profit margin than those currently engaged in financing these sales.

What could we expect? If it's customary to see a return of one's money on a loan within seven years, then a return of 200% in seven years represents replacement cost; 100% of the principal, plus a doubling of one's money over the seven years. This would mean that someone might be willing to buy the property for $100,000 and sell it back to a buyer for $200,000 if the buyer can pay for it in 7 years; 84 months. But one's monthly payment would then have to be $2,380.95 and one would sort of get the point that the real estate was perhaps too expensive to buy unless of course one had other sources of income whereby a monthly payment this high would be within the realm of possibility for the buyer.

Throughout this post we have used dollars. A Value Unit can never go below $2.16 in fair trade value, so $100,000 is 46,296.30 Value Units and that monthly payment is 1,102.29 Value Units. These figures would be less due to the death throes of the present system; their ruinous and futile attacks on the prices of precious metals and their continued deficit spending as well as spending money on their beloved paper markets which give their “bodies” these figments called corporations whatever life they may presume to possess. Either way, they are doomed.

We further say that since only simple interest is acceptable for drawing comparisons, because we do not accept as either logically valid or moral that idle money deserves a reward, or that value measurement can be made on the premise that value measurement in and of itself represents value, we conclude that the safest way to proceed is that in all transactions of whatever size value must be traded for value, not the measurement of value itself used to acquire more measurement of value. It is one thing to accept the notion that a Note represents a string of Bills or a Bond a string of Notes, and it is quite another that money acquired above a dealer's cost itself may acquire additional money with each successive debt instrument payoff. We say that such money does not in fact deserve this favour, as it is already figured into the value of what is being bought, and that compounding will hence not be permitted under any circumstances within the VEN. This means in fact that the only basis for making a sizable trade of this kind is where the seller actually owns the property outright (has and retains title) and sells it to the buyer on mutually acceptable terms such that the buyer knows ahead of time the entire cost of what he is buying and how and when he can expect to receive the title.

But how about the circumstance where one lives in a property and wants to refinance it into the VEN? It's really simply a matter of clearing off the old mortgage, paying it off completely and securing the title (and in all cases we shall insist on Allodial title to all property in any of these contracts so if you don't know what that means look it up). Then the new owner within the VEN sells it to the buyer under terms described in an accepted credit contract.

We've touched on a wide range of subjects here, but will probably refine them in future posts as we get more feedback. Assuredly, getting rid of notions like the time value of money, which is an erroneous idea since no one can possibly know what one is relinquishing by making a financial decision in the present, or that interest paid deserves to earn more interest with every successive turn of a payment schedule, when that money earned is more of just the same, money that was never created that must be paid back so someone can have a rich life by providing nothing but money as a means of making more of it, would provide better for more people worldwide.

David Burton
dpbmss@mail.com