Answer:
11 years
Explanation:
Formula for annual compound interest:
. In context of this problem, P and A are not relevant as they aren't mentioned. So, the equation we want to end up solving is
, where t is the unknown variable we're solving for, and r = .065. We desire to double the amount, A, so the left side of the equation is set to 2.
- Set up the equation:

- To solve this, you should know the format of a basic logarithm:
.
2. Set up the logarithm and solve:
t = 11 years
As a side note that may be irrelevant if this is a math course, economists often use the "rule of 72" for compound interest doubling time. Meaning
returns the doubling time in years. 72/6.5 gives us ≈ 11.079, or 11 years as well.