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?

Homework Helper
The idea is that you show what you already know,
or how you're thinking, so we know where you're stuck.
Since you already have the formula AND a hint,
maybe you don't know that "double" means "2".

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?

okay, look - it's as easy as filling in the variables with the data that's given.

Y -- that's what your trying to find
r -- that's the interest rate
x -- that's the factor by which it will change

so

r -- what is the interest rate given?
x -- what is the factor given?

it's pretty straight forward

timeformation
Start amount X e or 2.71 yada yada to the exponent of rate X periods