Handout 2: More on the National Debt – Ratios, Percentages, and Percentage Change
STAT 100 – Spring 2016
In Handout 1, we worked towards gaining a better understanding of large numbers (such as the
size of our national debt). I believe that it is important for us to grasp the enormity of such
figures so that we can be more engaged citizens in our society. To understand various
arguments people make concerning the national debt, however, we need more than just a sense
for how large it really is. Many arguments concerning the national debt involve calculating
ratios, percentages, and tracking numbers over time. In both this handout and the next, we will
examine some of these calculations in more detail so that when you encounter such arguments,
you will do so as a more informed citizen.
Definition: A ratio is one number expressed in relation to another number by division; i.e.,
a ratio is calculated by dividing one number by the other.
Examples you might encounter when discussing the national debt:
•
Debt/GDP (Debt-to-GDP ratio)
•
Debt/Citizen
Questions:
1. As of 9/30/15, the end of the federal government’s fiscal year, our national debt was
$18,150,604,277,750.63. According to the U.S. Census Bureau, the resident population of
the United States on that date was estimated to be 322,128,984. Calculate the
Debt/Citizen ratio for 2015.
Debt/Citizen = $18,150,604,277,750.63 / 322,128,984 citizens = $56,345.77 per citizen
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Handout 2: More on the National Debt – Ratios, Percentages, and Percentage Change
STAT 100 – Spring 2016
2. Write a sentence that explains what the value calculated in the previous question means
in everyday language.
For every American citizen, the United States has $56,345.77 in national debt.
3. In 2015, the Gross Domestic Product (GDP) for the U.S. was approximately
$17,418,930,000,000. Calculate the Debt/GDP ratio for 2015.
Debt/GDP = $18,150,604,277,750.63 / $17,418,930,000,000 = 1.04
4. Write a sentence that explains what the value calculated in the previous question means
in everyday language.
For every $1.04 of the nation’s debt, the nation has $1 in GDP.
Or, for every $1 of the nation’s GDP, there is $1.04 in national debt.
5. Complete the following table by calculating the appropriate ratios.
Year
National Debt
U.S.
Population
U.S. GDP
Debt/Citizen
Debt/GDP
2015
$18,150,604,277,750.63
322,128,984
$17,418,930,000,000
$56,345.77
1.042
2005
$7,932,709,661,723.5
296,297,982
$13,093,726,000,000
$26,772.74
0.606
1995
$4,973,982,900,709.39
267,173,186
$7,664,060,000,000
$18,617.07
.649
Why might it be a good idea to also consider the Debt/Citizen and Debt/GDP ratios
when considering the national debt and making comparisons across time? Explain.
These ratios allow us to take into account changes in the population and economy as
we track the national debt over time.
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Handout 2: More on the National Debt – Ratios, Percentages, and Percentage Change
STAT 100 – Spring 2016
Definition: A proportion is a special case of a ratio. When calculating a proportion, the
denominator is some total and the numerator is a subpart of this total. To calculate a
percentage, simply multiply the proportion by 100.
Examples of percentages you might encounter when discussing how to reduce the budget
deficit:
•
•
The percentage of the national budget allocated to foreign aid
The percentage of the national budget allocated to “wasteful spending”
Questions:
1. To address our current budget deficit (which results from the United States government
spending more than they bring in, subsequently adding to our existing national debt),
many politicians and citizens suggest that we cut off all foreign aid. In 2016, the federal
government has budgeted to spend about $3.8 trillion. Approximately $37.9 billion is
allocated to foreign aid (if you include assistance to foreign militaries). What percentage
of the federal budget is allocated to foreign aid?
$37.9 × 10 9
$3.8 × 10 12
= .01 = 1%
2. Do you feel that cutting off foreign aid is a feasible solution towards cutting the budget
deficit? Why or why not?
Answers will vary. One should recognize, however, since a very small percentage of
the federal budget is set aside for foreign aid, making this change alone likely won’t
fix the problem.
3. An article titled “Price of fixing, upgrading Obamacare website rises to $121 million”
written in the Washington Times cites that a contractor estimated the government would
need to spend $121 million to fix the website after the original contractor was fired.
Many citizens were upset, as they considered this wasteful spending. What percentage
of the federal budget is $121 million?
$121 × 10 6
$3.8 × 10 12
= .0000318 = .00318% (which is just over 3/1000 of 1 percentage point)
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Handout 2: More on the National Debt – Ratios, Percentages, and Percentage Change
STAT 100 – Spring 2016
4. If you had $1,000 and lost .003% of it, how much did you lose? Does this put the $121
million of “wasteful spending” mentioned above into a different perspective? Explain.
.003% of $1000 = .00003 × $1000 = $.03 (which is 3 cents)
Definition: One way to describe the change in a quantity over time is to calculate absolute
change. To find this number, subtract the original quantity from the new quantity.
Absolute Change = New value – Original value
To calculate the percentage change, first find the absolute change and then divide that
number by the original amount. To convert your answer into a percentage, multiply by 100.
Percentage Change =
New value - Original value
× 100%
Original value
There’s no doubt about it… the national debt tends to be increasing each year. It is not very
realistic to expect that we would ever have no national debt; however, most citizens agree that it
would be nice to at least slow the rate at which the debt increases each year. Our final focus in
this handout is on measuring the change in the national debt over time.
Date
1/11/2016
1/31/2012
1/20/2009
1/20/2001
National Debt (in dollars)
18,852,358,798,097.00
15,356,140,493,616.06
10,626,877,048,913.08
5,727,776,738,304.64
Source: http://www.treasurydirect.gov/NP/debt/current
Questions:
1. Calculate the absolute change in the national debt from 1/20/2009 (Obama’s first day in
office) to 1/11/2016 (approximately present day).
$18,852,358,798,097.00 - $10,626,877,048,913.08 = $8.2 trillion
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Handout 2: More on the National Debt – Ratios, Percentages, and Percentage Change
STAT 100 – Spring 2016
2. Calculate the absolute change in the national debt from 1/20/2001 to 1/20/2009 (Bush’s
term in office).
$10,626,877,048,913.08 - $5,727,776,738,304.64 = $4.9 trillion
3. Calculate the percentage change in the national debt from 1/20/2009 (Obama’s first day
in office) to present day.
$18,852,358,798,097.00 - $10,626,877,048,913.08
= .77 = 77% increase
$10,626,877,048,913.08
4. Calculate the percentage change in the national debt from 1/20/2001 to 1/20/2009 (Bush’s
term in office).
$10,626,877,048,913.08 - $5,727,776,738,304.64
= .86 = 86% increase
$5,727,776,738,304.64
5. A CBS News article from March of 2012 was titled ”National Debt has Increased More
Under Obama than Bush.” Here is a quote from this article: “The National Debt has now
increased more during President Obama's three years and two months in office than it did during
8 years of the George W. Bush presidency. The Debt rose $4.899 trillion during the two terms of
the Bush presidency. It has now gone up $4.939 trillion since President Obama took office” (note
that this was written in March of 2012 – it has now risen even more under Obama).
Is the author referring to absolute change or percentage change? Is this article fair, in
your opinion? Explain.
The article is referring to absolute change. Answers regarding opinions will vary.
6. I believe that both the absolute change and the percentage change are important and
should be reported together in a reputable news story. Read the following post on
FactCheck.org ”Dueling Debt Deceptions”), which does discuss both. An excerpt from
this article is shown below.
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Handout 2: More on the National Debt – Ratios, Percentages, and Percentage Change
STAT 100 – Spring 2016
Verify the calculations behind the two values that are highlighted in this excerpt (use the
data in the table from page 4, which was obtained from the “debt to the penny” website
the article refers to.
•
Show how the $4.7 trillion was calculated:
$15,356,140,493,616.06 - $10,626,877,048,913.08 = $4.7 trillion
•
Show how the 44.5 percent was calculated:
$15,356,140,493,616.06 - $10,626,877,048,913.08
= .445 = 44.5%
10,626,877,048,913.08
Final Thought: When you’re presented with charts/figures/calculations from people
trying to persuade you to believe something, keep in mind how important it is for you to
be able to verify what they are saying!
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