using logarithms, what formula would be used to solve this word problem?

Question

At what point does the compound interest on the national debt double the amount from
the current year? The current national debt is $17,000,000,000. Solve algebraically and
show all of your work. Find the exact value. Assume the interest rate is 8%.

Answer 1

Let x equal the time in years for the debt to double.

 

You don't need to know what the actual debt is.  If you want to double it, then you would just use the equation:

 

1.08^x = 2

 

Take the logarithm of both sides:

 

x log 1.08 = log 2

 

x = log 2 / log 1.08

 

Find these values on a calculator and do the division to get x.