Numerical Problems: The U.S. National Debt

In summary, the government accrues compound interest on its loans, with the number of years it takes for the amount of money owed to increase by a factor of x being given by Y=1/r ln(x), where ln is the natural logarithm. With an average interest rate of 5%, it would take approximately 14.4 years for the total debt to double. However, to completely pay off the $14 trillion debt, it would require a daily payment of $1.97 billion for 2010 years. A debt management service can provide guidance on managing expenses and finding ways to save money.
  • #1
sfgradv
13
0
Like any loan, the government accrues interest that compounds over time on the amount it owes. If the annual interest rate is r, then the number of years it takes for the amount of money owed to increase by a factor of x is

Y=1/r ln(x)

where ln is the natural logarithm.

The average interest rate on the U.S. national debt is about 5%. If the government neither borrows any more money, nor pays back any of the money it owes, how many years will it take for the total debt to double?

Give your answer using the built-in function ln.
 
Physics news on Phys.org
  • #2
sfgradv said:
Like any loan, the government accrues interest that compounds over time on the amount it owes. If the annual interest rate is r, then the number of years it takes for the amount of money owed to increase by a factor of x is

Y=1/r ln(x)

where ln is the natural logarithm.

The average interest rate on the U.S. national debt is about 5%. If the government neither borrows any more money, nor pays back any of the money it owes, how many years will it take for the total debt to double?

Give your answer using the built-in function ln.

have you even tried this? you have the r, you have x, all you have to do is evaluate.

what's the confusion?

edit: misread - it's even easier than i thought?
 
  • #3
the rule of 72 : (divide interest rate by 72)
a compoundeed value doubles every 14.4 years at 5%

there, that was simple. But the real question is, what payment and for how long would be needed to actually reduce the $14 trillion debt to 0? Since my HP 12c 25th anniversary platinum calculator only goes to 999 billion I had to use an excel spreadsheet to figure that out as I did not have one of the newly issued governemnt calculators that does trillions.

It would take $1.97 BILLION A DAY FOR 2010 years to repay that amount.

Since we started counting time.

The $112 trillion unfunded liability assuming the same interest rate? $15.3 BILLION A DAY for 2010 years.

that's a grand total of $17. 27 BILLION A DAY for 2010 years to be debt free or "pay as you go" as they like to say in Congress.

Got any gold?
 
  • #4
Debt management service is pretty straight forward and you will be on your way for hassle free life..There are number of things which one has to take care of -Insurance,mortgage and cut the cost of your expenses ...A person has to be vigilant about the hidden cost and charges... There are professionals from http://www.bestdebthelpprogram.com/ who actually give a sound advice to their clients so that they can have hard earned money saved for their families.
 
Last edited by a moderator:
  • #5


Based on the equation Y=1/r ln(x), we can calculate the number of years it takes for the total debt to double by setting x=2 (since we want the debt to increase by a factor of 2). So, the equation becomes Y=1/0.05 ln(2). Using a calculator or a computer program, we can find that ln(2) is approximately 0.693. Plugging this value into the equation, we get Y=1/0.05 * 0.693 = 13.86 years. Therefore, if the government neither borrows nor pays back any money, it will take approximately 13.86 years for the U.S. national debt to double. This is assuming that the interest rate remains at 5% throughout this time period.
 

What is the current U.S. national debt?

As of September 2021, the current U.S. national debt is approximately $28.7 trillion.

How is the national debt calculated?

The national debt is calculated by adding up all of the outstanding debt that the U.S. government owes to creditors, including individuals, businesses, and foreign governments.

What are the consequences of a high national debt?

A high national debt can lead to several consequences, such as higher interest rates, inflation, and a decrease in economic growth. It can also limit the government's ability to fund important programs and services.

Who owns the U.S. national debt?

The majority of the national debt is owned by American institutions and individuals, such as banks, pension funds, and individual investors. A significant portion is also owned by foreign governments and investors.

Can the national debt be paid off?

It is possible for the national debt to be paid off, but it would require significant budget cuts and/or tax increases to generate a surplus and pay down the debt. Another option is for the economy to grow at a faster rate, which would increase tax revenue and decrease the debt-to-GDP ratio.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
2K
  • STEM Academic Advising
Replies
6
Views
1K
  • Precalculus Mathematics Homework Help
Replies
1
Views
900
  • General Discussion
2
Replies
44
Views
8K
Replies
1
Views
3K
  • Precalculus Mathematics Homework Help
Replies
8
Views
3K
Replies
73
Views
10K
  • General Math
Replies
5
Views
3K
  • Introductory Physics Homework Help
Replies
1
Views
2K
Back
Top