# Numerical Problems: The U.S. National Debt

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1. Sep 9, 2005

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?

2. Sep 10, 2005

### teclo

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. Feb 1, 2011

### 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?

4. Apr 17, 2012

### harie

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Last edited by a moderator: May 5, 2017