an amount invested in an account that offers 5% interest which is compounded annually. how long will it take for this amount to double?

There is an old rule of thumb that states that the time required for an investment to double is equal to 72 divided by the interest rate in percent. Example, for $10,000 to double to $20,000 at 6% interest, compounded annualy, it would have to remain on deposit for 72/6 = 12 years.

Lets see exactly how close this is to the real growth. In compound interest, the interest due at the end of the interest period is added to the starting principal to form a new principal, and this new principal becomes the amount on which the interest for the next interest period is based. The original principal is said to be compounded, and the difference between the the final total, the compound amount, accumulated at the end of the specified interest periods, and the original amount, is called the compound interest. If S is the final compounded amount accumulated then S = P(1+i)^n where P is the initial principal, i is the periodic interest rate in decimal form = %Int./(m(100)), n is the number of interest bearing periods, and m is the number of interest paying periods per year. For example, the compound amount and the compound interest on $5000.00 resulting from the accumulation of interest at 6% annual interest compounded monthly for 10 years is as follows: Since m = 12, i = .06/12 = .005. Since we are dealing with a total of 10 years with 12 interest periods per year, n = 10 x 12 = 120. From this we get S = $5000(1+.005)^120 = $5000(1.8194) = $9097. Consequently, the compound interest realized is $9097 - $5000 = $4097. Of course the compound interest can be calculated directly from I = P[(1+i)^n - 1].
Taking our initial example from above, with P = 10,000 and i = .06, we get S = 10000(1.06)^12 = 20,122. Pretty close to double. If our $10,000 deposit were compounded monthly, then we would have S = 10000(1.005)^144 = $20,507.
As you can readily see, the initial deposit P is not the variable in determining the growth factor. The interest rate is the primary factor with the compounding period a secondary factor.