Could the US EVER pay off its debt? A mathematical perspective


Could the US EVER pay off its debt? A mathematical perspective

By Debtor’s Prison

Greetings Fellow Inmates,

Today we will take a break from the URC series for a speculative, fun post of Numbers!  We will use one of our three trusty abaci to finally explore a statement we made initially in Count The Money v2.0: “The [US] debt WILL NEVER BE PAID OFF”.    The following is a greatly simplified model, and as such we will properly outline its variables, parameters, equations, simplifications, assumptions, uncertainties, weaknesses and inflection points, as we promised we’d do in the About Us section.   We will then of course weave this “technical” picture into a coherent story.  Please stick with the first half where we lay down the premises of the experiment, we want to make sure you understand the foundations of our thought experiment.   The real cool, mind-bending stuff and results are in the second half.  We promise that even for those NON-technical amongst you, we will provide enough visual support to clearly and vividly illustrate our points.   We will leave the actual equation definitions of our first-ever appendix, in order to not distract the less-math-prone Inmates.

We are setting out to construct a model to attempt to answer the following question.   Given the United States of America’s current TOTAL PUBLIC DEBT SECURITIES and the total size of the US economy, as measured by NOMINAL GDP, what is the likelihood the that United States debt will ever be paid off?  Remember, as we always say, that the TOTAL DEBT SECURITIES (ie, US Treasuries mostly) is not the total amount of debt since the government has many other liabilities that are equally enormous, such as Medicare, Medicaid, GSEs, etc.   So, in any real thorough analysis of the likely evolution of the economy and the debt, these additional liabilities would have to be taken into account.   Clearly, they would make the situation, the current system, even more unsustainable than it already is.    This falls outside the purview of the following model, where we will attempt to demonstrate through simple math that even when just looking at the securities, which are just part of the total debt, the system is already guaranteed to fail.  

OK, on to the basics of the model.    We have split up the exercise into two parts.   In the first experiment, only the INTEREST on the debt securities is paid down.    In the second, the INTEREST is paid down, as well as some PRINCIPAL, with the intent of eventually paying down the debt, as a percentage of total GDP.   In both cases, we assume that NO MORE DEBT IS ISSUED IN EXCESS OF THAT INTENDED TO PAY DOWN INTEREST, or at least until the end of our simulations, in 2333.   This is a very important point, as any deductions, conclusions or recommendations we derive from this model will be predicated upon this assumption.     It is clear a priori that the only chance for the debt to be paid off is if the US starts paying down some of that principal.    This, we will see, can only come from real economic output.

For those of you that are math, reason, logic and rigour junkies such as Ourselves, we strongly urge you at the moment to stroll down to the appendix and read the description of the model before returning to read right here.    It’s a very simple model.   For starters, we assume that there is a fixed interest rate and economic growth.   Of course, this is a far cry from reality, and we will not repeat nor apologize for the simplicity of this model.  It is intended to be simple, it is in fact conservative, since what we are trying to demonstrate is the inherent instability of The System.   And the great thing about the little Excel abacus is that we can make it dynamic, and allow you to play around with it, to really wrap your mind around the absolute ridiculousness of it all.   When you play around with some of the parameters you realize the sheer absurdity of our current system and where it is likely to lead us in the future.   The over-simplifications in the model are of course not trivial and thus impede precise predictive power, but you can say the same about most anything.   The over-simplifications are meant for the simple reason that they illustrate certain key points without the cloudiness of confusion, and because OUR POINT is not to predict the future, but rather clearly demonstrate the nonsensical foundations of our monetary system.   In this purpose, the oversimplifications of the model become marginal, in our humble opinion.

You might also notice that of course the model must be iterative, as a simplified model such as this must clearly be; meaning that the total NOMINAL US GDP and TOTAL US DEBT SECURITIES OUSTANDING (the two main variables in which we are interested) in any given year depend on the values in the preceding year.   This exactly parallels reality, so this model assumption is safe.

Below are the results of our experiment, for a sample CASE STUDY.    You can download the full Excel file here.   We highly recommend you download it, since you can simply play with the parameters, in the RED BOXES, to see the wild outcomes that come out, in other words, you can make ANY SAMPLE CASE you want.   You are encouraged to explore all the embedded functions, check them for consistency, modify them, use them, distribute them, no copyright.    For our purposes we chose as parameters the following: an interest rate of 5% (equivalent to weighted average yield of outstanding US debt securities), and economic growth of 4%.   Of course, we are being somewhat generous given what we expect of the economy, but since our simulation is over 322 years at the max, 40 years at the least, we figure this would be a good “average” value to use over that horizon.    As for the interest rate, we are also being generous, ie “pro”-system-biased, by assuming that the IR will be only 5%, given that we are likely to see SuperInflation and much higher yields in the mid-term future.     So, all in all, we would call these estimates for GDP and DEBT safe, pheasible and conservative ballparks.  Remember, this is the base case we are going to work with where annual GDP growth = 4% and the yield on US bonds is 5%

The following chart shows the result of a case study with the preceding parameters.   Notice that the chart is divided in two parts, the left when ONLY INTEREST IS PAID, and the right, where INTEREST AND PRINCIPAL are paid.   In the second case, in which we assume that principal is paid down, we show that parameter in another RED BOX, as % of GDP.      Notice that for both parts, we calculate the ratio of DEBT/GDP and of GDP/DEBT.   In our CASE STUDY, we assume that the US designates 2% of its annual real economic output to pay down principal on the debt.   


We can notice several things.   Let’s start in the case where the US only pays down its INTEREST.   Then we see that by 2020, the total DEBT/GDP ratio will be 0.90.   By 2050, 1.20 (ie, the total DEBT outstanding is 20% larger than the size of the total US economy).   By 2333, the total DEBT will be 78 times larger than the economy!     In the case where the US uses 2% of its annual GDP to pay down PRINCIPAL, in addition to the interest, then we see that it is actually WORSE.   Up until 2050, things look pretty similar, but they begin to diverge about 2100.   In this case, by 2200, the total DEBT will be 297 times larger than the economy.    Then, in 2207, the GDP goes negative!  Clearly this is a sheer absurdity and the model has “broken down”, partly indicating a “systemic failure”, since remember that THEY do want us to believe that the system works in such simple fashion and there aren’t any nefarious Invisible Hands lurking around. 

Now, why exactly does the GDP go negative? Well, that happens because the debt NEVER stops growing (at least in this base case we are working with now), so at some point the interest payments on the debt become so large that even if we only pay 1% of the interest with real economic output, the cost is so large relative to the economy that it eats it all up.   Everyone dead.   Everything approaches zero; somehow our “system” managed to complete eradicate ALL VALUE FROM ALL THINGS.    Let’s look at what happens to our base case (GDP growth = 4%, Yield = 5%) when we only pay INTEREST and where we use different distributions of DEBT and OUTPUT to pay down the principal.   In other words, at some point we will pay some of the interest with mostly new debt, run the spectrum, until we pay for the interest with mostly real output.   Here are the graphic results.

Yikes!  Notice that given our base case, paying for 99% of the interest by issuing new debt, is the only level shown that prevents GDP from turning negative by 2333.   Anything less than that, even 95/5 is bound to result in sharply negative GDP eventually, with increasingly parabolic results.   In all cases, the debt grows parabolically, but such is the nature of compounding interest and we shouldn’t be surprised.    Perhaps you think we are being facetious by extrapolating all the way to 2333, I mean, really, who cares about what happens to their GreatGreatGreatGrandchildren?   So, let’s take a smaller-window view into the exact same thing, and selfishly look only until 2050.

Very interesting.   For starters we notice that of course, the discrepancy is not as huge.   When we change from paying for the interest with almost all NEW DEBT all the way to paying for the interest with almost ALL REAL OUTPUT, the outcomes are largely the same.    Between 2030 and 2042, the TOTAL US PUBLIC DEBT will surpass the size of the economy.    Big surprise.  

Alright, so it has now been unequivocally shown that in this simple base case, the US can NEVER be paid off if they limit themselves to paying only the interest.   We believe that this statement of course applies to all debt, anywhere, at any time, but we would welcome some debate on the matter.    Now, let’s see if there is any chance of paying off the debt if the US actually intends to pay principal.

In the CASE STUDY presented in the first chart, we saw that using 2% of GDP to pay down the principal actually resulted in a WORSE economic condition and faster deterioration towards ZERO GDP, or the ELIMINATION OF ALL VALUE.   However, by playing around with the parameters we realize that this is NOT always true.   We found that if the US were to designate 6% of all REAL ECONOMIC OUTPUT to paying down the INTEREST, then the DEBT would be in effect paid off, before GDP hit zero.     Voilá! Using 6% of GDP to pay down interest would result in the DEBT being paid off in 2074, and please look at the Excel file and notice how GLORIOUS it is that after the debt is paid down, the GDP begins to grow parabolically.   Of course!!! This is what SHOULD happen, in a RATIONAL DEBT-FREE world.    Below is a graphical sample of simulations all the way to 2100, using different values for the percentage of GDP assigned to pay down PRINCIPAL.

Wow, many interesting things once again.   Notice that when the US designates ONLY 5% of its GDP to pay down the debt the debt begins to decrease (as does GDP of course), but there is a point in which the debt begins to rise again, and once again runs away.       Why does this happen? Well, as GDP decreases, so does the amount of principal the US is able to pay, at some point, the principal payment becomes LESS than the mounting interest, so debt begins to rise again, never to fall for the rest of time.   At 6% however, this “barrier” is overcome and the debt can in fact be paid down.   So, between 5-6% we have another inflection point.      If 6% is designated, then the debt would be paid off in 1974; if 10% is designated, then it would be paid in 2033, and if 15% is designated the US would be debt free by 2023.  

So what are the chances of this happening?   Slim to none.   All we did was show under what circumstances it would even be possible to pay down the US debt.     So, if reality actually mirrored this greatly simplified model (it doesn’t), if Americans learned to live frugally for an entire generation (they can’t), if the macroeconomic conditions actually maintained the levels of our base case (they won’t), and the US government instituted serious fiscal reforms to bring this about (hahaha), then the US DEBT COULD BE PAID OFF.

Ultimately however, it is important to remember that THEY don’t want the debt to be paid off.   Of course not, that is how they keep us slaves.   But enough about blaming THEM.   It is time to blame OURSELVES.   Here it is, in vivid TechniColor, the sheer absurdity of this House of Cards, this Tower of Basel.   So why do you still participate in this system Inmates? 

“Because I must”  Why? 

“Because I have no other choice”  Why? 

“Because I don’t have enough firepower” Why do you need firepower? 

“Because the system gives me benefits and comforts which I’m happy to pay for?”  Even at the risk of death?

“Because I don’t care enough”  You should.

May your capital be safe and your investments prosperous,





gOD(Y) = gross Outstanding US Debt securities on year (Y),

IR = representative interest rate of total US debt securities, ie, the yield on the weighted average maturity of outstanding US debt ,

INTEREST(Y) = the interest rate cost on year Y, equal to gOD(Y)*IR

GDP(Y) = nominal US GDP on year Y,

GDPchg  = the annual percentage change in nominal US GDP, in decimal units,

DebtPer = percentage of the annual interest cost that will be paid through new debt issuance,

OutputPer = percentage of the annual interest cost that will be paid through real economic output

PrinPer = percentage of nominal US GDP to be used to pay down principal,

PRINCIPAL(Y) = the total principal payment on year Y, equal to PrinPer*GDP(Y)

Then, the model stipulates that:

GDP(Y) = [ GDP(Y-1) – OutputPer*INTEREST(Y-1) – PRINCIPAL(Y-1) ]*[1 + GDPchg];

gOD(Y) = gOD(Y-1) + DebtPer*INTEREST(Y-1) – PRINCIPAL(Y-1) ;


GDP(Yi), and gOD(Yi) are the initial conditions, in our case

gOD(2010) = $11.9tr

GDP(2010) = $14.5tr