You invest $4000 in a bank account with 5% interest compounded annually. you are wondering how long it would take for your money to double.

A = P(1 + r)^n; where A is the amount after time, n; P is the principal (the invested amount); r is the interest rate and n is the number of periods (i.e. no of years since the amount is compounded annually).

8000 = 4000(1 + 5/100)^n
8000/4000 = (1 + 0.05)^n
(1.05)^n = 2
n log 1.05 = log 2
n = log 2 / log 1.05 = 14.2067

Therefore, the amount will double in approximately 14 years.