"The Magic Of Compounding" - The Impact Of 1% Change In Rates On Total 2022 US Debt

Tyler Durden's picture

They say "be careful what you wish for", and they are right. Because, in the neverending story of the American "recovery" which, sadly, never comes (although in its place we keep getting now semiannual iterations of Quantitative Easing), the one recurring theme we hear over and over and over is to wait for the great rotation out of bonds and into stocks. Well, fine. Let it come. The question is what then and what happens to the US economy when rates do, finally and so overdue (for all those sellside analysts and media who have been a broken record on the topic for the past 3 years), go up. To answer just that question, which in a country that is currently at 103% debt/GDP and which will be at 109% by the end of 2013, we have decided to ignore the CBO's farcical models and come up with our own. Our model is painfully simple, and just to give our readers a hands on feel, we have opened up the excel file for everyone to tinker with (however, unlike the CBO, we do realize that when calculating average interest, one needs to have circular references enabled so please do that before you open the model).

Our assumptions are also painfully simple:

i) grow 2012 year end GDP of ~$16 trillion at what is now widely accepted as the 'New Normal' 1.5% growth rate (this can be easily adjusted in the model);

ii) assume the primary deficit is a conservative and generous 6% of GDP because America will never, repeat never, address the true cause of soaring deficits: i.e., spending, which will only grow in direct proportion with demographics but as we said, we are being generous (also adjustable), and

iii) sensitize for 3 interest rate scenarios: 2% blended cash interest; 3% blended cash interest and 5% blended cash interest.

And it is here that we get a reminder of a very key lesson, one that even the CBO admitted on Friday they had forgotten about, in what compounding truly looks like in a country that is far beyond the Reinhart-Rogoff critical threshold of 80% sovereign debt/GDP.

The bottom line: going from just 2% to 3% interest, will result in total 2022 debt rising from $31.4 trillion to $34.1 trillion; while "jumping" from 2% to just the long term historical average of 5%, would push total 2022 debt to increase by a whopping $9 trillion over the 2% interest rate base case to over $40 trillion in total debt!

Sadly, this is no "magic" - this is the reality that awaits the US.

And for those more curious about that other critical economic indicator, debt/GDP, the three scenarios result in the following 2022 debt/GDP ratios:

  • 2% interest - 169%;
  • 3% interest - 183.5%; and 
  • 5% interest - 217%, or just shy of where Japan is now.

Which reminds us: in the next few days we will recreate the same exercise for Japan's ¥1 quadrillion in total sovereign debt, which will show why any more "exuberance" arising from Abe's latest economic lunacy, will promptly send the country spiraling into that twilight zone where every dollar in tax revenue is used only to fund interest expense.

Once again, it is not our intention to predict what US GDP or debt/GDP will be in 2022: only the IMF can do that with decimal level precision, apparently, and not just with anyone, but Greece. The whole point is to show that when dealing with a debt trap lasting a decade, even the tiniest change in input conditions has profound implications on the final outcome. We invite readers to come up with their own wacky and wonderful projections of what the futures of the US may look like.

And that one should, indeed, be careful what one wishes for.

The results summarized for the three scenarios:

Total debt: 2013-2022.

Debt/GDP: 2013-2022:

The Zero Hedge open source model, for everyone to play around with, can be found here. Remember: don't be a CBO, enable circs!

P.S. don't even think of modelling a recession: everything Refs up then.

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yogibear's picture

It's bluffing and BS. The market reacts. Wait until it doesn't.

q99x2's picture

I'm not even going to look because it will probably say that I'll owe more than the buck sevent-five that I have in my pocket and they ain't getting that because its for the AA Sunday night hat pass. F'U Bernanke.

RagnarDanneskjold's picture

I did a static model here, and I incorporate the ZeroHedge forecast with mine here. My model is more optimistic than ZeroHedges, and it compares interest costs to revenue to predict a funcing crisis. It is more optimistic in its assumptions and the result is even more pessimistic.

zen0's picture

So the dollar has lost 98% over the last 100 years. The chart looks to flatline just above zero. It could be another 100 years of approaching zero. Maybe it approaches zero to infinity.


Sure seems like it.

AccreditedEYE's picture

Once again, it is not our intention to predict what US GDP or debt/GDP will be in 2022: only the IMF can do that with decimal level precision, apparently, and not just with anyone, but Greece.

LMAO!! Indeed. Fantastic. And... BTFD

Sizzurp's picture

There is really no easy way out of the debt problem. They will tax, and tax some more. Recession will ensue, GDP will sink, government revenues will decline. The debt will grow.  It will end with severe austerity, loss of entitlements, civil unrest, and probably an authoritarian regime.  It would certainly be better to come clean with US creditors now and make a settlement, but I don't see that happening. The banks and bondholders will first suck every last bit of blood they can before that happens.  Then finally, when we are at the very end of our rope, the debt will be erased with overnight monetary reform, and perhaps some sort of asset transfer for the creditors.  It looks like it is going to be a rough decade or two.  My advice, drink heavily.

NeedleDickTheBugFucker's picture

I assume it's just a matter of time before the Treasury includes a PIK toggle option in all future issuance.

AgAu_man's picture

Ah, grade 7 math and "The Rule of 71".  Fantastic!

On a more important topic -- and sorry for re-posting from your article ("Is this what the new Swiss Passport looks like?") earlier today, but I... just "gots to":

FYI...  I just learned that my absolutely favorite YouTube News program on the Financial News -- RT CAPITAL ACCOUNT with (smart & irresistible) LAUREN LYSTER has just aired its last program on Jan. 4, 2013.  Out of the blue.  No reason or explanation for why it is ending, but clearly 'someone' in RT pulled the plug -- or was 'persuaded' to.  Bass-turds!

What am I to do for real analysis of financial, economic and market events?   I just can't go back to Bloo'berg or CNBC after Capital Account!  What a disaster!

Did one of the Tylers (smart, good looking guy in Miami who Lauren liked to flirt with) propose to her, as one of the ZH comments some days ago foreshadowed?  If so, you lucky ba$tard, you "owe" us for stealing Lauren!

To RT Mgmt:  Can we 'talk', brainstorm, negotiate?  Or has the Fed and TPTB had 'enough' of this inconvenient program?  Else I'm boycotting your "little waters" (vodka).

Now, where's that special Bordeaux/Claret, I've been saving?  Ah, here it is... gulp, gulp.

Hey Tyler (spoken with slurred speech), how about YOU starting a YouTube channel -- with a Lauren-clone?

fonzannoon's picture

I thought she said she was going to daily ticker/yahoo finance

holdbuysell's picture

Very. Well. Done.
Thanks, ZH.

Coldfire's picture

Fair share = zero.

Ghostdog's picture

Paul Krugmen for Fed Secretary! He is good for 250 to 500 trillion of printing and if that doesnt work then it wont be his fault, it was just too damn little....................................................

holdbuysell's picture

Over the years, I look forward to reviewing this analysis (and I'm hoping ZH will update accordingly, just as ZH has done for Greece) to see where we are relative to the bogies.

Issues with the petrodollar, for example, tell me the hockeystick may be more pronounced than this baseline.

gooey center's picture

Tylers: The slopes of your projections look very gradual, calm, somnambulent even. Natural. Sort of building to a boil, so to speak. Nothing to worry about, everythings under control; see, looky here, see this mild upswing, that means it's ok. It's that darn gold chart we gotta watch, what with its exponential rise and radical slope.That stuff is trouble.




Let The Wurlitzer Play's picture

These long term debt projections are a good basis to start the conversation.  Now lets incorprate the the effect of bond price declines on a leveraged portfolio at the same time as the interest rate increase on the debter.


devo's picture

Sasquach recovery.

Hear about it but never see it.

yogibear's picture

More and more people join the government gravy train and collect money.

No worry, Benny Bernake and the Federal Reserve Banksters will come to the rescue with their printing.

Keep handing money created from thin air to the Chinese, Koreans and Arabs for stuff. As long as they keep taking US dollars Bernanke and Obama know they have suckers.


q99x2's picture

From CNBC:

"The economies of the United States, China and much of the developing world have decoupled from Europe, leaving it to wallow in various stages of recession and fiscal disarray."

All this shows is that it is easier for the banksters to control a political system and financial system over larger nations of people than over many smaller nations. It does not mean anything is decoupled. It does not mean that the larger systems are in any better shape. It only means that fraud is easier to carry out over large systems rather than smaller systems. 

CNBC suck. Romney suck too.

resurger's picture

Nice growth projections! I love this kind of growth its very haelthy.

The US Government spending / Revenue will be 2,000% by 2022 and Japan 4,0000000000%


hooligan2009's picture

beware circular references they are way too close to being political!

in my (painful) experience always hide errors in logic...perhaps use Solver!

happy to produce a spreadsheet without the circular references, 

Julian's picture

What a fantastic example of open source modelling....beats the CBO "behind closed doors and politcally spun for political purposes" process anyday.

smacker's picture

I have long seen the US debt problem (and to be fair, other countries too) as unsustainable and therefore unrepayable. This article confirms that in spades.

Its continuance without resolution is creating massive knock-on consequences which we see all around us every day: economic stagflation, unemployment, impoverishment of savers/investors etc etc.

That being so, there seems only one solution: The Big Reset.

Obama's continued wreckless spending without taking any serious action to reign it in adds weight to my view.

What will trigger this and how it will unfold is a mystery. But I am increasingly convinced by ongoing events that it is unavoidable.

hooligan2009's picture

we can perhaps "borrow" some of the principles of mean reversion here.

the debt has been run up by deficits over particular time periods. 

obamas attempts to rescue the economy post the GFC of 2007/8/9 are no longer necessary; most of the bailed out institutions are either out of bankruptcy or have returned to share prce levels prevailing back then.

the structural deficit put in by obama needs to be reversed, which means unravelling the increases in spending and cuts in taxes he and the congress sanctioned in 2009/2010. this needs to be done now. the increase in debt above and beyond nominal gdp growth for the three years to 31 december 2012 needs to be repaid. this is c.  5 trillion dollars. spreadsheets at the CBO or OMB or GS or BofA or JPM can work this out and spin it to wring the last drop of liquidity out of this sodden wet blanket.

after that, debt needs to be rolled back at the same rate as it was increased that is at c. 2-3% of GDP or c. 150-300 billion of surpluses until debt gdp is returned to sane levels of c. 40% (i.e. repay debt of ten trillion in total, by running surpluses of 1 trillion a year for the next 5 years and 5 trillion over the next 15-20 years.

these are the numbers. 

i suggest that this is the size of the money that needs to be reclaimed from bankers and insurnace company staff bonuses (via sequestration of assets as with a drug dealer or a racketeer) and politicians who have served at any time during the periods where annual deficits were incurred. there wil be issues with that crook clinton and his off balance sheet account rigging of federal liabilities, but i am sure that there are people who know how to work this out.

smacker's picture

Indeed. That all looks like an excellent solution to the debt problem. I especially like the suggestion of sequestration of assets from the wrong-doers.

I'm not sure how many lifetimes you'll need to carry out that plan but I wish you much luck with it :-)

Monedas's picture

Monedaism:     Compound Fractional Reserve Banking

andyupnorth's picture

Stein's law – If something cannot go on forever, it will stop. If a trend cannot go on forever, there is no need for action or a program to make it stop, much less to make it stop immediately; it will stop of its own accord.

Much like ZH's motto.

Avocado's picture

There are two rates. Short rates (ZIRP) and long rates. The FED can control short rates almost indefinitely, they have certainly succeeded in keepthing them at zero or close to zero for a long time. And as long as the market is willing to buy treasury bills with zero interest they can maintain this.

What they have less control over is the long rates. Even with FED buying we are seeing a spike upwards in the 10 and 30 year rates, both breaking out of a consolidation pattern, (or even a bottom formation). So there is the very real possibility that long rates may go up quite a bit over the next few months.

So what? Only if they stay that way for a very long time does this matter.

The rates only affect NEW debt issued by the government, not current debt. Current debt is at a fixed rate, or at a rate the FED has considerable control over. And if the economy tanks again (quite likely) then long rates will fall again. You only get rising rates in a strong economy. Anyone happen to notice a strong economy aywhere?

I'm expecting the 10 year note to climb to perhaps 2.8% and the 30 year to 4% before the next downcycle begins. If by some miracle Washington does something serious about spending then rates will likely start to fall sooner. But if you notice, the latest spike got started when the tax package was approved.


fuu's picture

If you set the blended interest rate on debt to -100% we are out of debt entirely by 2025!

I did it by Occident's picture

 "in the next few days we will recreate the same exercise for Japan's ¥1 quadrillion in total sovereign debt, which will show why any more "exuberance" arising from Abe's latest economic lunacy, will promptly send the country spiraling into that twilight zone where every dollar in tax revenue is used only to fund interest expense."

reminds me of my old physics classes about the topic of black holes as one crosses the event horizon.  Strange stuff (not good usually) starts to happen.