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.