If you deposit money today into an account that pays 6.5 percent interest, how long will it take for you to double your money?

There's a quick way to estimate this, called "The Rule of 72." Divide 72 by the interest rate percent, and you get the number of years it takes to double. Here 72/6.5 = 11.07years.

If you want a more precise answer, the answer depends on how frequently the bank pays interest. Assuming interest is paid annually you need to solve the following for N: (1+i)^N = 2. If you know how to use logarithms, you can change this to N= log(2)/log(1+i). This gives a value of N = 11.01 years.

However, if interest is compounded more frequently than annually, the equation to use is:
(1+i/p)^Np = 2, where p is the number of periods per year. For example, if they pay interest monthly, then p = 12. Solve for N in the above equation and you get N= 10.69years. This shows why it's better for you if the bank compounds monthly (which is common practice).

Finally, if you happen to be lucky enough to have an investment that compounds continuously, the equation you need to solve is e^iN = 2. This gives a value for N of 10.66 years.

Rule 72... very simple