Numerical Problems: The U.S. National Debt

[sfgradv]

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.

 

[teclo]

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?

 

[sgodwin]

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?

 

[harie]

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.

 

[asteriatic]

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.