Currency as Debt: A New Theory of Money
New Equations for a Better World Economy
 

Other than engineers and scientists, few people ever attempt to analyze from a mathematical perspective how the world functions. Yet, many physical relationships in the world can be described mathematically.

Long ago people starting loaning property, specifically currency, to other people. The general practice was to charge a fee (interest) on the unpaid balance of the original principal. This general practice still drives today’s world economy. In concept the origin of this practice is ancient, hundreds, maybe thousands of years old. This practice was eventually described mathematically:

B_(n) = L(1 + i)ⁿ – (R / i)[(1 + i)ⁿ - 1]
 

Where:

B_(n) = Loan Balance after n payments have been made

L = Loan amount

R = Equal Repayment amount

n = number of equal periods, usually months

i = interest rate per period expressed as a decimal

The right side of this equation can be separated into two parts by the minus sign (-) in the middle.

To the left of that middle minus sign, the term L(1 + i)ⁿ represents the increasing quantity of a sum of currency with respect to time. A lender doesn’t just lend a static sum of currency, but expects the quantity of that currency to increase with time expressed as n periods. In other words, a lender expects repayment of the original loan plus a fee for the use of that currency. That fee, commonly called interest, i, is expressed as a relative magnitude per unit of time; for example: 6% per year. Notice that the total amount repaid grows larger with increases in the size of the original loan, L, or increases in the size of the interest fee, i, or increases in the number of periods of time, n, before the loan is due to be repaid.

To the right of that middle minus sign, the term (R / i)[(1 + i)ⁿ - 1] represents periodic repayments on the loan. Again the terms i and n are found, here used to weight the relative value of the currency repayments, R, early repayments being worth more than later repayments.

One noteworthy aspect of this basic equation: The periods of time, n, are exponents, giving rise to compound interest. Interest, i, is said to be compounded when, at stated intervals, n, the interest due but unpaid is added to the principal and begins to earn interest.

With any positive value for i and time proceeding positively forward in successive periods toward infinity, the resultant quickly exceeds measurable values in the physical world; that is, debt compounded into every increasing debt.

Consider the following age-old brain-teaser. Suppose you made a New Year’s resolution to save twice as much each day as you did the day before, starting with a penny a day. On January 1 you would save one penny; on January 2, you would save 2 pennies; on January 3 you would save 4 pennies; on January 4 you would save 8 pennies, and so on. On January 31, how many pennies would you have saved?

The answer is 1,073,741,824 pennies, or $10,737,418.24. Mathematically, the puzzle’s solution can be expressed as $0.01×2^(n-1), where n is the number of days. Notice the extraordinary increase of the amount. More interestingly, any person observing the numbers grow day-by-day would notice that at day 20 a person saves “only” $5,242.88. Most of the exponent magic takes effect only during the last few days of the puzzle.

Equations of this type are inherently unstable. An avalanche can start as a small snowball on the top of a mountain. As the snowball rolls downhill, it becomes bigger and bigger and moves faster and faster until it crashes in the valley below. Consider that first, the volume of the snowball is mathematically related to the cube of the radius; and the snowball accumulates more snow while rolling downhill. The velocity of the snowball is subject to the acceleration due to gravity, which is related to the square of the elapsed period of motion. In other words, the problem compounds itself exponentially, growing rapidly out of control until physically stopped by the valley below. That sudden physical stop releases a tremendous amount of energy, often causing damage. Hardly surprising, unstable economic systems may behave similarly.

Exponents are commonly used to mathematically express natural physical relationships in the world, including economic systems. Apart from questions of mathematical instability due to the common use of such equations, moral questions plague economic systems.

Lawful interest is compensation paid to a lender for the temporary loss of use of their own currency. This makes perfectly good sense for loans from Uncle Henry or Aunt Sue, but what if a person borrows at a commercial bank? Is the charged fee interest or usury?

Usury usually means an undeserved gain or profit to the lender. The doctrine of intention is controlling. Perhaps a better modern definition of usury would be an excessive charge to someone for the monetization of their own debt through a commercial bank license. The question then becomes, “What is a reasonable fee for the banking service provided?”

Banks operating on fractional reserves by virtue of a government issued license make loans by monetizing the borrower’s debt. By contract with the bank, a borrower’s promise to repay a loan is converted into currency as a simple bank bookkeeping entry that the borrower can then spend. The actual wealth backing the newly created currency originates with the community, not with the bank, or even with the bank’s depositors as is commonly assumed.

The difference between the bank’s loan of currency and a loan from Aunt Sue is that Aunt Sue loans existing property; that is, currency already in existence. Banks create new currency out of their customer’s debt, and by special license at that. The moral implications are profound.

Laws governing commercial bank operations are arbitrary man-made rules, not the immutable laws of nature. Therefore, the equations that financial institutions use in daily commercial activity are merely the long-standing customs of merchants, subject to change by legislative statute.

The following chart shows bank gross profit—customer cost, for a bank loan of $100,000 at 5, 7, and 9 percent interest, calculated in 5 year increments from 5 to 30 years. The bank earns $93,255.78 for a 30 year loan at just 5% interest, increasing to $189,664.14 at 9% interest earned for exactly the same service.

Considering that the public, by natural right, owns a nation’s monetary system, and that banks participate in operating that system by license as public utilities, it would seem that people should be entitled to a better share of the benefits.

One legislative proposal to remedy this imbalance is the National Economic Stabilization and Recovery Act, NESARA, offered by the NESARA Institute. The proposal states in Part I, Section 7(F):

(F) All tenders in repayment which have been previously made or which are made on any secured loans outstanding on and after the date of passage of this Act with any financial institution making such loans on a fractional reserve basis will be credited to repayment of the loan principal prior to any credits being applied to any monetization-fee on that loan. Compound monetization-fees or charges on monetization-fees earned are prohibited. A service charge may be imposed by the lender for each tender in payment recorded, retroactively and on future tenders in payment, provided it does not exceed a total of 25 dollars monthly for any one loan. All new secured loans made on a fractional reserve basis may —

(1) be subject to a maximum origination fee of 50 dollars or 1 percent of the principal loan amount, whichever is greater; and,

(2) be issued with a prepayment of discount points up to a maximum of 5 percent of the principal amount of the loan, the allowed maximum being proportionally decreased at the rate of 1 percent for each 1 percent increase in the loan interest rate above 7 percent.

While this proposed statute seems simple, its social impact is immense because it not only changes fundamental practices of an enormous commercial banking system, it mandates retroactive changes to all existing contracts for secured loans obtained from financial institutions making loans on a fractional reserve basis; that is, billions of dollars of loan contracts must be recalculated. And, under NESARA, those recalculations prohibit banks from charging compounded interest.

Under the NESARA plan, with repayments made each month, consider making an installment loan L for 1 year at 12% annual interest. Total Cost, C, of such a loan would be:

Where:

L = Loan amount

n = number of equal periods, usually months

i = interest rate per period expressed as a decimal

The part of the equation after the + sign represents the interest fee. In other words, the total repayment equals the amount of the loan L plus a simple interest fee.

Because the loan is repaid in equal monthly installments, the average effective loan balance for the year is only ½ the total borrowed. Because the fee is a simple interest fee and not compounded, the easy way to calculate the fee is to calculate the fee due for an entire year and then divide that total by 2.

For example, a $1,000 loan for 1 year at 12% simple interest repaid in equal monthly payments returns a $60 profit for a total repayment of $1,060, not a $120 profit for a total repayment of $1,120.

By making 12 equal payments the base monthly repayment amount, M_b = C / 12 or, fundamentally equals [L + (Lni / 2)] / n.

For easier and quicker future calculations, divide the base monthly repayment, M_b, by the loan amount, L, to determine a repayment rate, R_r; or R_r = M_b/ / L. That rate can be expressed as a decimal when the number of periods, n, and the period interest rate, i, expressed as a decimal, are known. R_r can then be expressed in units of $s repaid per $ borrowed for the period.

Setting the borrowed principal, L, equal to $1, further reduces the original equation to R_r = 1 / n + i / 2. When n is expressed in months, R_r can be expressed as $s repaid per $s borrowed for the month.

By knowing the repayment rate, R_r, the monthly payment amount can be calculated by multiplying R_r times the principal, L.

With compounded interest, a borrower would owe $1,066.19. For a one-year example, simple interest provides a somewhat better deal than traditional methods. Of course, the repayment amount increases rapidly with increases in the principal, the term of the loan, or the interest rate.

But the question remains, is simple interest fair in this case? After all, banks are still creating currency out of thin air—all by a simple bookkeeping entry. Additionally, the bank might charge “points” on the loan, the equivalent of a bribe to the bank encouraging the banker to approve the loan.

Under NESARA, because principal must be repaid before any monetization fee can be collected, that first month’s payment made to the bank will free a proportional amount of reserves which the bank may use to make an additional loan. And, to ensure timely payment, payments are often made a few days early. The bank may use those early payments as an overnight loan to other banks short on reserves, and without so much as a “with your permission,” pockets the profits, never says thank you, and never shares the profits made. Then there is that $25 monthly service fee which more than likely will easily cover the nominal bookkeeping services provided; and in today’s world of computerized banking, is assuredly overly generous for the amount of work performed.

Under the old system, which was merely the long-standing custom of merchants, the banks certainly took every benefit they could, including the increasing value of currency they were due made on loans of currency which they never really had and calculated with compound interest.

Perhaps it would be fair under the new plan if borrowers were to receive compensation for the value of their early payments, early payments being worth more than later payments, that benefit now going to borrowers and not to the bank.

B_(n) = (R / i)[(1 + i)ⁿ - 1]

This equation is used to calculate the balance due on a series of equal monthly payments at rate R for n months at i interest rate. The bank could hold these payments in an interest bearing account until they were sufficient to pay off the loan. In effect, the bank would not be allowed to charge compound interest because it created the currency for the loan out of thin air, whereas the currency used to repay the loan was earned and should be collecting compound interest for the life of the loan.

It would seem that while simple interest is better for the borrower than compound interest, it is not much better. And giving the borrower compounded compensation for any initial payment plus those regular monthly payments but refusing the same to the bank puts the bank at a huge disadvantage compared to the current system. Thus, such a deal would be intensely resisted by bankers. Obviously, the need is for a new equation, something between the two extremes; something that benefits both parties. The new equations should be politically doable, that is, fair to all, and work within the range of numbers customarily encountered in making long-term secured bank loans.

The basic repayment rate equation of R_r = 1 / n + i / 2, can be mathematically rearranged using “2n” as the lowest common denominator:

Next, we rewrite the “2” in the numerator into its mathematical equivalent, 1+1.

Notice at this point the equation is mathematically equivalent to the original equation. That is, using either version provides the same answer.

The next objective is to modify this equation by adding a mathematical function that will greatly reduce large numbers yet have little effect on small numbers, exactly the opposite response from the equations now used. A square root function is ideal for this — the square root of 4 is 2, of 16 is 4 and of 64 is 8 — providing a smooth, continuous relationship between large positive numbers and smaller numbers.

Getting better. Notice that high values of n and i will now result in a much lower repayment rate, R_r, a better deal for the bank’s customers. With an interest rate of i = 0, the equation reduces to R_r = 1 / n, repaying the loan without payment of any interest, the same kind of deal one might get from a family member.

Plotting a graph of R_r in terms of the usual values associated with commercial bank loans for home mortgages, that is, interest rates of 5 to 10 percent and periods of 5 to 30 years, reveals a curve with the desired shape but somewhat below a reasonable split of profit/cost between the commercial banks and their customers. (See NESARA Curve #1 in the following example.) To provide a better balance, an arbitrary constant, 2, is added to the equation which has the effect of shifting the repayment rate somewhat higher while maintaining the basic shape of the curve.

Example: The following graph shows bank profit, that is, customer cost, for a bank loan of $100,000 at 7.5% with a service charge of $25/month calculated in 5 year increments from 5 to 30 years. Each curve represents a different equation. With a conventional 30 year loan, the bank profit is $150,000. Curves 1, 2, and 3 show the bank profit under NESARA equations, the arbitrary multiplier being set to the same number as the curve.

NESARA Curve #2 shows an almost even split of the exorbitant bank profit (borrower cost) on a conventional loan between the bank and its customer. Notice too, the shape of the curves: the curve of the conventional loan bending upward indicating bank profits increasing at ever faster rates for longer term loans while the curves for the NESARA equations bend toward the horizontal indicating relatively declining costs for longer term loans.

Magenta Curve: Arbitrary multiplier = 1 
Yellow Curve: Arbitrary multiplier = 2 
 Cyan Curve: Arbitrary multiplier = 3 
Dark Blue Curve: Conventional loan

The following set of equations, proposed by the NESARA Institute, provide an engineered solution to the problem, a solution which offers a better distribution of the benefits of participating in the nation’s monetary system for both the commercial banks and their customers:

Where:

R_r = repayment rate, $ per $ per month

n = number of equal payments, months

f_m = bank monetizing-fee per month, expressed as a decimal

C_f = cost factor for the loan

L = amount of the loan

M_b = base monthly payment

C_b = base cost for the loan

The term f_m for the bank monetizing fee replaces the conventional interest term, i, as better characterizing the process of obtaining a loan from a bank operating on fractional reserves. And the term n, representing the number of equal periods for repayment, no longer appears as an exponent in any of the equations.

Notice that the new system operates based on the new equation for repayment rate, R_r, with the other equations being derived from that equation.

The practical effect of applying these new equations is that a periodic repayment at any positive constant rate always eventually retires a loan. Under the current system, miss a few payments and the compounded interest will grow faster than the GDP, which is the primary concern with the National Debt. Under NESARA, miss a few payments and the overall total cost will rise, but as soon as the borrower resumes making payments they resume retiring the loan; something not always possible in the world of exponents.

This practical effect changes the basic characteristic of commercial debt.

In addition to the mathematical stability of the new equations, NESARA also requires bankers to recognize customer demand deposits as property, and cannot loan those deposits without customer notification and agreement to participate in the risk, as is possible under the current system. Fundamentally then, NESARA compels banks to use the concept of virtual wealth in creating new currency for all secured loans made on a fractional reserve basis. Therefore, in the absence of fraud or misconduct, bank failures become virtually impossible. Furthermore, borrowers not only convert their debt into wealth at a much faster rate; they do so at much lower costs.

Bankers too will like the new equations:

1. As existing loans are converted, for typical loans bankers watch borrowers build equity much faster and by building equity faster borrowers remain highly motivated to pay the loan in full.
2. Loan terms are shortened and the overall debt burden reduced, therefore bankers need not always foreclose but will be more willing to work with borrowers during difficult times.
3. Because equity builds faster, should borrowers unfortunately default on a loan bankers will see a much better return on foreclosures because of the higher equity.
4. As borrowers build equity faster with loans, those customers provide bankers much better collateral when applying for future loans.
5. By repaying principal up front, bankers free reserves much faster which will allow them to make more loans in the same period.
6. By repaying principal up front and restricting banks to only creating new currency, insurance is no longer needed as practiced under the facade of FDIC.

Just as importantly, the moral question of, “Who owns the nation’s monetary system and derives the benefits of that ownership?” is finally answered.